scholarly journals ENTROPIC LATTICE BOLTZMANN SIMULATION OF THE FLOW PAST SQUARE CYLINDER

2004 ◽  
Vol 15 (03) ◽  
pp. 435-445 ◽  
Author(s):  
SANTOSH ANSUMALI ◽  
SHYAM SUNDER CHIKATAMARLA ◽  
CHRISTOS EMMANOUIL FROUZAKIS ◽  
KONSTANTINOS BOULOUCHOS
Keyword(s):  
Reynolds Number ◽  
Lattice Boltzmann ◽  
Large Scale ◽  
Stokes Equations ◽  
Coarse Grained ◽  
Navier Stokes ◽  
Square Cylinder ◽  
Flow Past ◽  
Lattice Boltzmann Simulation ◽  
Decaying Turbulence

Minimal Boltzmann kinetic models, such as lattice Boltzmann, are often used as an alternative to the discretization of the Navier–Stokes equations for hydrodynamic simulations. Recently, it was argued that modeling sub-grid scale phenomena at the kinetic level might provide an efficient tool for large scale simulations. Indeed, a particular variant of this approach, known as the entropic lattice Boltzmann method (ELBM), has shown that an efficient coarse-grained simulation of decaying turbulence is possible using these approaches. The present work investigates the efficiency of the entropic lattice Boltzmann in describing flows of engineering interest. In order to do so, we have chosen the flow past a square cylinder, which is a simple model of such flows. We will show that ELBM can quantitatively capture the variation of vortex shedding frequency as a function of Reynolds number in the low as well as the high Reynolds number regime, without any need for explicit sub-grid scale modeling. This extends the previous studies for this set-up, where experimental behavior ranging from Re ~O(10) to Re ≤1000 was predicted by a single simulation algorithm.1–5

Fine Structure of Vortex Sheet Rollup by Viscous and Inviscid Simulation

1991 ◽  
Vol 113 (1) ◽  
pp. 31-36 ◽  
Author(s):  
G. Tryggvason ◽  
W. J. A. Dahm ◽  
K. Sbeih
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Large Scale ◽  
Stokes Equations ◽  
Flow Region ◽  
Vortex Sheet ◽  
Navier Stokes ◽  
Vortex Sheets ◽  
Limiting Behavior ◽  
High Reynolds

Numerical simulations of the large amplitude stage of the Kelvin-Helmholtz instability of a relatively thin vorticity layer are discussed. At high Reynolds number, the effect of viscosity is commonly neglected and the thin layer is modeled as a vortex sheet separating one potential flow region from another. Since such vortex sheets are susceptible to a short wavelength instability, as well as singularity formation, it is necessary to provide an artificial “regularization” for long time calculations. We examine the effect of this regularization by comparing vortex sheet calculations with fully viscous finite difference calculations of the Navier-Stokes equations. In particular, we compare the limiting behavior of the viscous simulations for high Reynolds numbers and small initial layer thickness with the limiting solution for the roll-up of an inviscid vortex sheet. Results show that the inviscid regularization effectively reproduces many of the features associated with the thickness of viscous vorticity layers with increasing Reynolds number, though the simplified dynamics of the inviscid model allows it to accurately simulate only the large scale features of the vorticity field. Our results also show that the limiting solution of zero regularization for the inviscid model and high Reynolds number and zero initial thickness for the viscous simulations appear to be the same.

Unsteady flow past a rotating circular cylinder at Reynolds numbers 103 and 104

1990 ◽  
Vol 220 ◽  
pp. 459-484 ◽  
Author(s):  
H. M. Badr ◽  
M. Coutanceau ◽  
S. C. R. Dennis ◽  
C. Ménard
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Unsteady Flow ◽  
Rotation Rate ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Number Range ◽  
Flow Past

The unsteady flow past a circular cylinder which starts translating and rotating impulsively from rest in a viscous fluid is investigated both theoretically and experimentally in the Reynolds number range 103 [les ] R [les ] 104 and for rotational to translational surface speed ratios between 0.5 and 3. The theoretical study is based on numerical solutions of the two-dimensional unsteady Navier–Stokes equations while the experimental investigation is based on visualization of the flow using very fine suspended particles. The object of the study is to examine the effect of increase of rotation on the flow structure. There is excellent agreement between the numerical and experimental results for all speed ratios considered, except in the case of the highest rotation rate. Here three-dimensional effects become more pronounced in the experiments and the laminar flow breaks down, while the calculated flow starts to approach a steady state. For lower rotation rates a periodic structure of vortex evolution and shedding develops in the calculations which is repeated exactly as time advances. Another feature of the calculations is the discrepancy in the lift and drag forces at high Reynolds numbers resulting from solving the boundary-layer limit of the equations of motion rather than the full Navier–Stokes equations. Typical results are given for selected values of the Reynolds number and rotation rate.

scholarly journals Direct numerical simulation of the oscillatory flow around a sphere resting on a rough bottom

2017 ◽  
Vol 822 ◽  
pp. 235-266 ◽  
Author(s):  
Marco Mazzuoli ◽  
Paolo Blondeaux ◽  
Julian Simeonov ◽  
Joseph Calantoni
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Oscillatory Flow ◽  
Stokes Equations ◽  
Coarse Sand ◽  
Spherical Particles ◽  
Navier Stokes ◽  
Sea Waves ◽  
Spherical Object ◽  
Navier Stokes Equations

The oscillatory flow around a spherical object lying on a rough bottom is investigated by means of direct numerical simulations of the continuity and Navier–Stokes equations. The rough bottom is simulated by a layer/multiple layers of spherical particles, the size of which is much smaller that the size of the object. The period and amplitude of the velocity oscillations of the free stream are chosen to mimic the flow at the bottom of sea waves and the size of the small spherical particles falls in the range of coarse sand/very fine gravel. Even though the computational costs allow only the simulation of moderate values of the Reynolds number characterizing the bottom boundary layer, the results show that the coherent vortex structures, shed by the spherical object, can break up and generate turbulence, if the Reynolds number of the object is sufficiently large. The knowledge of the velocity field allows the dynamics of the large-scale coherent vortices shed by the object to be determined and turbulence characteristics to be evaluated. Moreover, the forces and torques acting on both the large spherical object and the small particles, simulating sediment grains, can be determined and analysed, thus laying the groundwork for the investigation of sediment dynamics and scour developments.

LATTICE BOLTZMANN SIMULATION OF TWO-DIMENSIONAL WALL BOUNDED TURBULENT FLOW

2010 ◽  
Vol 21 (05) ◽  
pp. 669-680 ◽  
Author(s):  
GÁBOR HÁZI ◽  
GÁBOR TÓTH
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Lattice Boltzmann ◽  
Numerical Study ◽  
Power Laws ◽  
Energy Spectra ◽  
Small Scale ◽  
Two Dimensional ◽  
Lattice Boltzmann Simulation ◽  
Decaying Turbulence

This paper reports on a numerical study of two-dimensional decaying turbulence in a square domain with no-slip walls. The generation of strong small-scale vortices near the no-slip walls have been observed in the lattice Boltzmann simulations just like in earlier pseudospectral calculations. Due to these vortices the enstrophy is not a monotone decaying function of time. Considering a number of simulations and taking their ensemble average, we have found that the decay of enstrophy and that of the kinetic energy can be described well by power-laws. The exponents of these laws depend on the Reynolds number in a similar manner than was observed before in pseudospectral simulations. Considering the ensemble averaged 1D Fourier energy spectra calculated along the walls, we could not find a simple power-law, which fits well to the simulation data. These spectra change in time and reveal an exponent close to -3 in the intermediate and an exponent -5/3 at low wavenumbers. On the other hand, the two-dimensional energy spectra, which remain almost steady in the intermediate decay stage, show clear power-law behavior with exponent larger than -3 depending on the initial Reynolds number.

scholarly journals Simulation of flow past two tandem cylinders using deterministic vortex method

2012 ◽  
Vol 16 (5) ◽  
pp. 1460-1464 ◽  
Author(s):  
Guo Huang ◽  
Haiming Huan ◽  
Xiaoliang Xu ◽  
Yu Liu
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Sudden Change ◽  
Vortex Method ◽  
Simulation Method ◽  
Critical Distance ◽  
Navier Stokes ◽  
Tandem Cylinders ◽  
Flow Past

The vortex method is a direct numerical simulation method for solving the Navier-Stokes equations. In order to reveal the influence of Reynolds number and distances between the cylinders, the incompressible flow past a pair of tandem cylinders is solved on the base of the vortex method. The results show that for the flow past two tandem cylinders, there is a critical distance of the tandem cylinders. Over the critical distance, the flow field will have a sudden change, and the drag coefficient, lift coefficient and Strouhal number will also change dramatically. The critical distance will diminish as the Reynolds number rises.

Vortex Shedding From a Square Cylinder With Ground Effect

2003 ◽  
Author(s):  
S. Bhattacharyya ◽  
D. K. Maiti
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Stokes Equations ◽  
Numerical Study ◽  
Ground Effect ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Square Cylinder ◽  
Navier Stokes Equations ◽  
Cylinder Length

Numerical study on the wake behind a square cylinder placed parallel to a wall has been made. Flow has been investigated in the laminar Reynolds number (based on the cylinder length) range. We have studied the flow field for different values of the non-dimensional gap length between cylinder and the wall. The case when the cylinder is placed on the wall has also been considered. The governing unsteady Navier-Stokes equations are discretised through the finite volume method on staggered grid system. A SIMPLER type of algorithm has been used to compute the discretised equations iteratively. Vortex shedding has been found to be influenced by the wall. Vortex shedding suppression occurs beyond a critical value of the gap length. Due to the shear, the drag experienced by the cylinder is found to increase with the reduction of gap length. The flow is found to be steady when the cylinder is placed on the wall at a range of Reynolds number.

scholarly journals The Sensitivity Analysis for the Flow Past Obstacles Problem with Respect to the Reynolds Number

2012 ◽  
Vol 4 (1) ◽  
pp. 21-35 ◽  
Author(s):  
Kazufumi Ito ◽  
Zhilin Li ◽  
Zhonghua Qiao
Keyword(s):  
Sensitivity Analysis ◽  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Irregular Domains ◽  
Time Step ◽  
Immersed Interface Method ◽  
Navier Stokes Equations ◽  
Flow Past

AbstractIn this paper, numerical sensitivity analysis with respect to the Reynolds number for the flow past obstacle problem is presented. To carry out such analysis, at each time step, we need to solve the incompressible Navier-Stokes equations on irregular domains twice, one for the primary variables; the other is for the sensitivity variables with homogeneous boundary conditions. The Navier-Stokes solver is the augmented immersed interface method for Navier-Stokes equations on irregular domains. One of the most important contribution of this paper is that our analysis can predict the critical Reynolds number at which the vortex shading begins to develop in the wake of the obstacle. Some interesting experiments are shown to illustrate how the critical Reynolds number varies with different geometric settings.

Lattice-Boltzmann Simulations of Complex Fluids

1997 ◽  
Vol 08 (04) ◽  
pp. 783-792 ◽  
Author(s):  
G. Gonnella ◽  
E. Orlandini ◽  
J. M. Yeomans
Keyword(s):  
Free Energy ◽  
Fluid Flow ◽  
Phase Separation ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Positive Curvature ◽  
Navier Stokes ◽  
Two Phase ◽  
Lattice Boltzmann Simulation ◽  
Lattice Boltzmann Simulations

We show that by including thermodynamic functions derived from a chosen free energy in a lattice-Boltzmann simulation of fluid flow it is possible to ensure that the fluid relaxes to a well-defined equlilibrium corresponding to the minimum of the input free energy. Two examples are given of phase separation in a binary fluid: bulk two-phase coexistence and a lamellar phase stabilised by a competition between negative surface tension and positive curvature energy. The lattice-Boltzmann framework simulates the Navier–Stokes equations of fluid flow and hence allows investigation of the effects of hydrodynamics on the kinetics of phase separation and on the rheology of the ordered structures.

A note on the solution of the Navier-Stokes equations for a spherically symmetric expansion into a very low pressure

1973 ◽  
Vol 59 (2) ◽  
pp. 391-396 ◽  
Author(s):  
N. C. Freeman ◽  
S. Kumar
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Low Pressure ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Type Flow

It is shown that, for a spherically symmetric expansion of a gas into a low pressure, the shock wave with area change region discussed earlier (Freeman & Kumar 1972) can be further divided into two parts. For the Navier–Stokes equation, these are a region in which the asymptotic zero-pressure behaviour predicted by Ladyzhenskii is achieved followed further downstream by a transition to subsonic-type flow. The distance of this final region downstream is of order (pressure)−2/3 × (Reynolds number)−1/3.

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