scholarly journals Numerical simulation of reynolds number effect of a free incompressible isothermal turbulent coaxial jet

2022 ◽  
pp. 3-11
Author(s):  
Olanrewaju Miracle Oyewola ◽  
Olawale Saheed Ismail ◽  
Lateef Anjola Sanni
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Finite Volume ◽  
Radial Profile ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Self Similarity ◽  
Potential Core

This paper studies the effect of Reynolds number on a two-dimensional free incompressible isothermal coaxial turbulent jet over a range of high Reynolds numbers. This is necessary because of its application in noise control and mixing. The Reynolds numbers at the nozzle exit were 9824, 19648, 29472, 39296 and 49120. The models were designed in ANSYS Design Modeler and the numerical simulation was done using a finite volume based Computational Fluid Dynamics (CFD) in ANSYS FLUENT using the two-dimensional Realizable turbulence model. The Governing equations were discretized using the finite volume method with the solution based on the PISO algorithm. The decay of centerline velocity, turbulent kinetic energy profile, the radial profile of axial velocity and similarity profile were investigated along the flow direction. Contour plot indicates that the velocity is high at the jet exit and decreases downstream due to the rapid mixing of the inner and outer jet and the surrounding fluid. It is found generally that Reynolds number plays significant role especially before self-similarity region. The result shows that increasing the Reynolds number give rise to more turbulence which in turn decreases the potential core length, turbulent kinetic energy and enhances the mixing of the fluid. However, at the jet exit, the flow with the lowest Reynolds number has the highest turbulent kinetic energy because it suffers the greater shear. The spreading of the jet was more or less independent of the Reynolds number beyond the self-similarity region. It is also found that the velocity profile is brought to congruence at about z/D=25 for the Reynolds numbers considered

Large-scale modes of turbulent channel flow: transport and structure

2001 ◽  
Vol 448 ◽  
pp. 53-80 ◽  
Author(s):  
Z. LIU ◽  
R. J. ADRIAN ◽  
T. J. HANRATTY
Keyword(s):  
Shear Stress ◽  
Kinetic Energy ◽  
Shear Layer ◽  
Turbulent Kinetic Energy ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Reynolds Numbers ◽  
Upstream Region ◽  
Two Dimensional ◽  
Normal Plane

Turbulent flow in a rectangular channel is investigated to determine the scale and pattern of the eddies that contribute most to the total turbulent kinetic energy and the Reynolds shear stress. Instantaneous, two-dimensional particle image velocimeter measurements in the streamwise-wall-normal plane at Reynolds numbers Reh = 5378 and 29 935 are used to form two-point spatial correlation functions, from which the proper orthogonal modes are determined. Large-scale motions – having length scales of the order of the channel width and represented by a small set of low-order eigenmodes – contain a large fraction of the kinetic energy of the streamwise velocity component and a small fraction of the kinetic energy of the wall-normal velocities. Surprisingly, the set of large-scale modes that contains half of the total turbulent kinetic energy in the channel, also contains two-thirds to three-quarters of the total Reynolds shear stress in the outer region. Thus, it is the large-scale motions, rather than the main turbulent motions, that dominate turbulent transport in all parts of the channel except the buffer layer. Samples of the large-scale structures associated with the dominant eigenfunctions are found by projecting individual realizations onto the dominant modes. In the streamwise wall-normal plane their patterns often consist of an inclined region of second quadrant vectors separated from an upstream region of fourth quadrant vectors by a stagnation point/shear layer. The inclined Q4/shear layer/Q2 region of the largest motions extends beyond the centreline of the channel and lies under a region of fluid that rotates about the spanwise direction. This pattern is very similar to the signature of a hairpin vortex. Reynolds number similarity of the large structures is demonstrated, approximately, by comparing the two-dimensional correlation coefficients and the eigenvalues of the different modes at the two Reynolds numbers.

Inverse cascade of kinetic energy in two-dimensional β-Plane magnetohydrodynamic turbulence

2020 ◽  
Author(s):  
Timofey Zinyakov ◽  
Arakel Petrosyan
Keyword(s):  
Numerical Simulation ◽  
Kinetic Energy ◽  
Cascade Process ◽  
Two Dimensional ◽  
Mhd Turbulence ◽  
Self Similarity ◽  
Magnetohydrodynamic Turbulence ◽  
Zonal Flows ◽  
Inverse Cascade ◽  
Kolmogorov Spectrum

<p>Numerical studies of two-dimensional β-plane homogeneous magnetohydrodynamic turbulence are presented. The study of the fundamental properties of such turbulence allows understanding the evolution of various astrophysical objects from the Sun and stars to planetary systems, galaxies, and galaxy clusters. Energy spectra and cascade process in two-dimensional β-plane MHD are studied.</p><p>In this work the equations of two-dimensional magnetohydrodynamics with the Coriolis force in the β-plane approximation are used for the qualitative analysis and numerical simulation of processes in plasma astrophysics. The equations are solved on a square box of edge size 2π with periodic boundary conditions applying a the pseudospectral method using the 2/3 rule for dealiasing. The results of numerical simulation of two-dimensional β-plane MHD turbulence with a spatial resolution of 1024 × 1024 and 4096 × 4096 with different Rossby parameters β and different Reynolds numbers are presented.</p><p>It is found that only unsteady zonal flows with complex temporal dynamics are formed in two-dimensional β-plane magnetohydrodynamic turbulence. It is shown that flow nonstationarity is due to the appearance of isotropic magnetic islands caused by the Lorentz force in the system. The formation of Iroshnikov–Kraichnan spectrum is shown in the early stages of evolution of two-dimensional β-plane magnetohydrodynamic turbulence. The self-similarity of the decay of Iroshnikov–Kraichnan spectrum is studied. On long time scale violation of self-similarity of the decay and formation of Kolmogorov spectrum is discovered. The inverse cascade of kinetic energy, which is characteristic of the detected Kolmogorov spectrum, provides the formation of zonal flows.</p><p>This work was supported by the Russian Foundation for Basic Research (project no. 19-02-00016).</p>

Fluid Flow Analysis in a Pebble Bed Modular Reactor Using RANS Turbulence Models

2008 ◽  
Author(s):  
Margaret Mkhosi ◽  
Richard Denning ◽  
Audeen Fentiman
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulence Intensity ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Pebble Bed ◽  
Rans Turbulence Models ◽  
Flow Domain

The computational fluid dynamics code FLUENT has been used to analyze turbulent fluid flow over pebbles in a pebble bed modular reactor. The objective of the analysis is to evaluate the capability of the various RANS turbulence models to predict mean velocities, turbulent kinetic energy, and turbulence intensity inside the bed. The code was run using three RANS turbulence models: standard k-ε, standard k-ω and the Reynolds stress turbulence models at turbulent Reynolds numbers, corresponding to normal operation of the reactor. For the k-ε turbulence model, the analyses were performed at a range of Reynolds numbers between 1300 and 22 000 based on the approach velocity and the sphere diameter of 6 cm. Predictions of the mean velocities, turbulent kinetic energy, and turbulence intensity for the three models are compared at the Reynolds number of 5500 for all the RANS models analyzed. A unit-cell approach is used and the fluid flow domain consists of three unit cells. The packing of the pebbles is an orthorhombic arrangement consisting of seven layers of pebbles with the mean flow parallel to the z-axis. For each Reynolds number analyzed, the velocity is observed to accelerate to twice the inlet velocity within the pebble bed. From the velocity contours, it can be seen that the flow appears to have reached an asymptotic behavior by the end of the first unit cell. The velocity vectors for the standard k-ε and the Reynolds stress model show similar patterns for the Reynolds number analyzed. For the standard k-ω, the vectors are different from the other two. Secondary flow structures are observed for the standard k-ω after the flow passes through the gap between spheres. This feature is not observable in the case of both the standard k-ε and the RSM. Analysis of the turbulent kinetic energy contours shows that there is higher turbulence kinetic energy near the inlet than inside the bed. As the Reynolds number increases, kinetic energy inside the bed increases. The turbulent kinetic energy values obtained for the standard k-ε and the RSM are similar, showing maximum turbulence kinetic energy of 7.5 m2·s−2, whereas the standard k-ω shows a maximum of about 20 m2·s−2. Another observation is that the turbulence intensity is spread throughout the flow domain for the k-ε and RSM whereas for the k-ω, the intensity is concentrated at the front of the second sphere. Preliminary analysis performed for the pressure drop using the standard k-ε model for various velocities show that the dependence of pressure on velocity varies as V1.76.

Direct Numerical Simulation of Homogeneous Turbulent Shear Flow Containing Bubbles

2006 ◽  
Author(s):  
T. Kawamura ◽  
T. Nakatani
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Production Rate ◽  
Turbulent Flows ◽  
Reynolds Numbers ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Hypothetical Model ◽  
Turbulent Reynolds Number

Direct numerical simulations of homogeneous shear turbulent flows containing deformable bubbles were carried out for clarifying the mechanism of drag reduction by microbubbles. The results show that presence of bubbles can suppress or enhance the development of turbulence depending on condition. The dissipation rate of turbulent kinetic energy is always increased by bubbles, while the production rate can be either increased or decreased depending on the turbulent and shear Reynolds numbers. As a result, the growth rate of turbulent kinetic energy can be either increased or decreased by bubbles depending on conditions. It was shown that the production rate tends to decrease at smaller shear Reynolds number, at larger turbulent Reynolds number, and at larger Weber number. Based on the results, a hypothetical model to explain the dependency on the Reynolds numbers has been proposed.

scholarly journals Two-dimensional energy spectra in high-Reynolds-number turbulent boundary layers

2017 ◽  
Vol 826 ◽  
Author(s):  
Dileep Chandran ◽  
Rio Baidya ◽  
Jason P. Monty ◽  
Ivan Marusic
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Spatial Spectrum ◽  
Two Dimensional ◽  
Hot Wire ◽  
Self Similarity ◽  
Low Reynolds Numbers ◽  
High Reynolds

Here, we report the measurements of two-dimensional (2-D) spectra of the streamwise velocity ($u$) in a high-Reynolds-number turbulent boundary layer. A novel experiment employing multiple hot-wire probes was carried out at friction Reynolds numbers ranging from 2400 to 26 000. Taylor’s frozen turbulence hypothesis is used to convert temporal-spanwise information into a 2-D spatial spectrum which shows the contribution of streamwise ($\unicode[STIX]{x1D706}_{x}$) and spanwise ($\unicode[STIX]{x1D706}_{y}$) length scales to the streamwise variance at a given wall height ($z$). At low Reynolds numbers, the shape of the 2-D spectra at a constant energy level shows$\unicode[STIX]{x1D706}_{y}/z\sim (\unicode[STIX]{x1D706}_{x}/z)^{1/2}$behaviour at larger scales, which is in agreement with the existing literature at a matched Reynolds number obtained from direct numerical simulations. However, at high Reynolds numbers, it is observed that the square-root relationship tends towards a linear relationship ($\unicode[STIX]{x1D706}_{y}\sim \unicode[STIX]{x1D706}_{x}$), as required for self-similarity and predicted by the attached eddy hypothesis.

Bifurcation Characteristics of Flows in Rectangular Sudden Expansion Channels

2005 ◽  
Author(s):  
Francine Battaglia ◽  
George Papadopoulos
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Expansion Ratio ◽  
Sudden Expansion ◽  
Two Dimensional ◽  
Effective Expansion ◽  
Three Dimensional Simulations

The effect of three-dimensionality on low Reynolds number flows past a symmetric sudden expansion in a channel was investigated. The geometric expansion ratio of in the current study was 2:1 and the aspect ratio was 6:1. Both experimental velocity measurements and two- and three-dimensional simulations for the flow along the centerplane of the rectangular duct are presented for Reynolds numbers in the range of 150 to 600. Comparison of the two-dimensional simulations with the experiments revealed that the simulations fail to capture completely the total expansion effect on the flow, which couples both geometric and hydrodynamic effects. To properly do so requires the definition of an effective expansion ratio, which is the ratio of the downstream and upstream hydraulic diameters and is therefore a function of both the expansion and aspect ratios. When the two-dimensional geometry was consistent with the effective expansion ratio, the new results agreed well with the three-dimensional simulations and the experiments. Furthermore, in the range of Reynolds numbers investigated, the laminar flow through the expansion underwent a symmetry-breaking bifurcation. The critical Reynolds number evaluated from the experiments and the simulations was compared to other values reported in the literature. Overall, side-wall proximity was found to enhance flow stability, helping to sustain laminar flow symmetry to higher Reynolds numbers in comparison to nominally two-dimensional double-expansion geometries. Lastly, and most importantly, when the logarithm of the critical Reynolds number from all these studies was plotted against the reciprocal of the effective expansion ratio, a linear trend emerged that uniquely captured the bifurcation dynamics of all symmetric double-sided planar expansions.

Numerical Simulation of Flows in a Pipe with an Aneurismal Sac (Effects of Aneurismal Models and Stents)

2008 ◽  
Vol 33-37 ◽  
pp. 1025-1030
Author(s):  
Gulbahar Wahap ◽  
Tatsuya Kobori ◽  
Yoko Takakura ◽  
Norio Arai ◽  
Yoshifumi Konishi ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Human Blood ◽  
Steady States ◽  
Computational Results ◽  
Two Dimensional ◽  
Blood Flows ◽  
Inflow Condition ◽  
Inflow Conditions ◽  
Two Dimensional Flows

Recently, the intravascular therapy using microcoils and stents to treat aneurysms has attracted researcher’s interest. In this study, in order to evaluate the effects of the stents, a numerical simulation of two-dimensional flows has been carried out for a pipe with a model of an aneurismal sac. Using aneurismal models with different inclined angles to the pipe, inflow conditions with steady states or pulsations have been applied in the range of Reynolds number in human blood flows. First, the computational results are compared with experiments under the steady inflow condition, which has shown the reliability of the numerical simulation. Furthermore, the mechanism of flows with an aneurismal model is discussed in the case with or without a stent, and consequently the effect of the stent is clarified.

Fully developed MHD turbulence near critical magnetic Reynolds number

1981 ◽  
Vol 104 ◽  
pp. 419-443 ◽  
Author(s):  
J. Léorat ◽  
A. Pouquet ◽  
U. Frisch
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Mhd Equations ◽  
Liquid Sodium ◽  
Turbulent Heat ◽  
Mhd Turbulence

Liquid-sodium-cooled breeder reactors may soon be operating at magnetic Reynolds numbers RM where magnetic fields can be self-excited by a dynamo mechanism (as first suggested by Bevir 1973). Such flows have kinetic Reynolds numbers RV of the order of 107 and are therefore highly turbulent.This leads us to investigate the behaviour of MHD turbulence with high RV and low magnetic Prandtl numbers. We use the eddy-damped quasi-normal Markovian closure applied to the MHD equations. For simplicity we restrict ourselves to homogeneous and isotropic turbulence, but we do include helicity.We obtain a critical magnetic Reynolds number RMc of the order of a few tens (non-helical case) above which magnetic energy is present. RMc is practically independent of RV (in the range 40 to 106). RMc can be considerably decreased by the presence of helicity: when the overall size of the flow L is much larger than the integral scale l0, RMc can drop below unity as suggested by an α-effect argument. When L ≈ l0 the drop can still be substantial (factor of 6) when helicity is a maximum. We examine how the turbulence is modified when RM crosses RMc: presence of magnetic energy, decreased kinetic energy, steepening of kinetic-energy spectrum, etc.We make no attempt to obtain quantitative estimates for a breeder reactor, but discuss some of the possible consequences of exceeding RMc, such as decreased turbulent heat transport. More precise information may be obtained from numerical simulations and experiments (including some in the subcritical regime).

Turbulent kinetic energy production and flow structures in flows past smooth and rough walls

2019 ◽  
Vol 866 ◽  
pp. 897-928 ◽  
Author(s):  
P. Orlandi
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Energy Production ◽  
Compressive Strain ◽  
Turnover Time ◽  
Flow Structures ◽  
Wall Region ◽  
Rate Of Dissipation

Data available in the literature from direct numerical simulations of two-dimensional turbulent channels by Lee & Moser (J. Fluid Mech., vol. 774, 2015, pp. 395–415), Bernardini et al. (J. Fluid Mech., 742, 2014, pp. 171–191), Yamamoto & Tsuji (Phys. Rev. Fluids, vol. 3, 2018, 012062) and Orlandi et al. (J. Fluid Mech., 770, 2015, pp. 424–441) in a large range of Reynolds number have been used to find that $S^{\ast }$ the ratio between the eddy turnover time ($q^{2}/\unicode[STIX]{x1D716}$, with $q^{2}$ being twice the turbulent kinetic energy and $\unicode[STIX]{x1D716}$ the isotropic rate of dissipation) and the time scale of the mean deformation ($1/S$), scales very well with the Reynolds number in the wall region. The good scaling is due to the eddy turnover time, although the turbulent kinetic energy and the rate of isotropic dissipation show a Reynolds dependence near the wall; $S^{\ast }$, as well as $-\langle Q\rangle =\langle s_{ij}s_{ji}\rangle -\langle \unicode[STIX]{x1D714}_{i}\unicode[STIX]{x1D714}_{i}/2\rangle$ are linked to the flow structures, and also the latter quantity presents a good scaling near the wall. It has been found that the maximum of turbulent kinetic energy production $P_{k}$ occurs in the layer with $-\langle Q\rangle \approx 0$, that is, where the unstable sheet-like structures roll-up to become rods. The decomposition of $P_{k}$ in the contribution of elongational and compressive strain demonstrates that the two contributions present a good scaling. However, the good scaling holds when the wall and the outer structures are separated. The same statistics have been evaluated by direct simulations of turbulent flows in the presence of different types of corrugations on both walls. The flow physics in the layer near the plane of the crests is strongly linked to the shape of the surface and it has been demonstrated that the $u_{2}$ (normal to the wall) fluctuations are responsible for the modification of the flow structures, for the increase of the resistance and of the turbulent kinetic energy production.

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