Rayleigh-Be´nard Convection in a Small Aspect Ratio Enclosure: Part II—Bifurcation to Chaos

1993 ◽  
Vol 115 (2) ◽  
pp. 367-376 ◽  
Author(s):  
D. Mukutmoni ◽  
K. T. Yang
Keyword(s):  
Numerical Study ◽  
Period Doubling ◽  
Small Aspect Ratio ◽  
Mean Flow ◽  
Average Temperature ◽  
Aspect Ratios ◽  
Transition To Chaos ◽  
The Mean ◽  
Route To Chaos ◽  
Boussinesq Fluid

The present numerical study documents bifurcation sequences for Rayleigh-Be´nard convection in a rectangular enclosure with insulated sidewalls. The aspect ratios are 3.5 and 2.1 and the Boussinesq fluid is water (average temperature of 70°C) with a Prandtl number of 2.5. The transition to chaos observed in the simulations and experiments is similar to the period-doubling (Feigenbaum) route to chaos. However, special symmetry conditions must be imposed numerically, otherwise the route to chaos is different (Ruelle-Takens-Newhouse). In particular, the Feigenbaum route to chaos can be realized only if the oscillating velocity and temperature field preserves the fourfold symmetry that is observed in the mean flow in the horizontal plane.

Rayleigh-Be´nard Convection in a Small Aspect Ratio Enclosure: Part I—Bifurcation to Oscillatory Convection

1993 ◽  
Vol 115 (2) ◽  
pp. 360-366 ◽  
Author(s):  
D. Mukutmoni ◽  
K. T. Yang
Keyword(s):  
Temperature Field ◽  
Oscillatory Flow ◽  
Numerical Study ◽  
Oscillatory Convection ◽  
Small Aspect Ratio ◽  
Subharmonic Bifurcation ◽  
Average Temperature ◽  
Aspect Ratios ◽  
Boussinesq Fluid ◽  
Steady Convection

The present numerical study documents bifurcation sequences for Rayleigh-Be´nard convection in a rectangular enclosure with insulated sidewalls. The aspect ratios are 3.5 and 2.1 and the Boussinesq fluid is water (average temperature of 70°C) with a Prandtl number of 2.5. Two transitions are documented numerically. The first transition is from steady-state to oscillatory flow and the second is a subharmonic bifurcation as the Rayleigh number is increased further. The dynamics of the flow and temperature field is analyzed in detail for the subcritical steady convection and the supercritical oscillatory convection. The numerical results compared well with experiments, both qualitatively and quantitatively.

scholarly journals Generation of Reverse Meniscus Flow by Applying An Electromagnetic Brake

2021 ◽  
Author(s):  
Alexander Vakhrushev ◽  
Abdellah Kharicha ◽  
Ebrahim Karimi-Sibaki ◽  
Menghuai Wu ◽  
Andreas Ludwig ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Lorentz Force ◽  
Applied Magnetic Field ◽  
Numerical Study ◽  
Flow Direction ◽  
Experimental Studies ◽  
Submerged Entry Nozzle ◽  
Mean Flow ◽  
Slab Caster ◽  
The Mean

AbstractA numerical study is presented that deals with the flow in the mold of a continuous slab caster under the influence of a DC magnetic field (electromagnetic brakes (EMBrs)). The arrangement and geometry investigated here is based on a series of previous experimental studies carried out at the mini-LIMMCAST facility at the Helmholtz-Zentrum Dresden-Rossendorf (HZDR). The magnetic field models a ruler-type EMBr and is installed in the region of the ports of the submerged entry nozzle (SEN). The current article considers magnet field strengths up to 441 mT, corresponding to a Hartmann number of about 600, and takes the electrical conductivity of the solidified shell into account. The numerical model of the turbulent flow under the applied magnetic field is implemented using the open-source CFD package OpenFOAM®. Our numerical results reveal that a growing magnitude of the applied magnetic field may cause a reversal of the flow direction at the meniscus surface, which is related the formation of a “multiroll” flow pattern in the mold. This phenomenon can be explained as a classical magnetohydrodynamics (MHD) effect: (1) the closure of the induced electric current results not primarily in a braking Lorentz force inside the jet but in an acceleration in regions of previously weak velocities, which initiates the formation of an opposite vortex (OV) close to the mean jet; (2) this vortex develops in size at the expense of the main vortex until it reaches the meniscus surface, where it becomes clearly visible. We also show that an acceleration of the meniscus flow must be expected when the applied magnetic field is smaller than a critical value. This acceleration is due to the transfer of kinetic energy from smaller turbulent structures into the mean flow. A further increase in the EMBr intensity leads to the expected damping of the mean flow and, consequently, to a reduction in the size of the upper roll. These investigations show that the Lorentz force cannot be reduced to a simple damping effect; depending on the field strength, its action is found to be topologically complex.

scholarly journals DEVELOPING CHAOS ON BASE OF TRAVELING WAVES IN A CHAIN OF COUPLED OSCILLATORS WITH PERIOD-DOUBLING: SYNCHRONIZATION AND HIERARCHY OF MULTISTABILITY FORMATION

2002 ◽  
Vol 12 (08) ◽  
pp. 1895-1907 ◽  
Author(s):  
A. SHABUNIN ◽  
V. ASTAKHOV ◽  
V. ANISHCHENKO
Keyword(s):  
Traveling Waves ◽  
Coherence Function ◽  
Period Doubling ◽  
Spatial Structures ◽  
Transition To Chaos ◽  
Spatial Periodicity ◽  
Route To Chaos ◽  
Analysis Of Dynamics ◽  
A Chain ◽  
Loss Of Coherence

The work is devoted to the analysis of dynamics of traveling waves in a chain of self-oscillators with period-doubling route to chaos. As a model we use a ring of Chua's circuits symmetrically coupled via a resistor. We consider how complicated are temporal regimes with parameters changing influences on spatial structures in the chain. We demonstrate that spatial periodicity exists until transition to chaos through period-doubling and tori birth bifurcations of regular regimes. Temporal quasi-periodicity does not induce spatial quasi-periodicity in the ring. After transition to chaos exact spatial periodicity is changed by the spatial periodicity in the average. The periodic spatial structures in the chain are connected with synchronization of oscillations. For quantity researching of the synchronization we propose a measure of chaotic synchronization based on the coherence function and investigate the dependence of the level of synchronization on the strength of coupling and on the chaos developing in the system. We demonstrate that the spatial periodic structure is completely destroyed as a consequence of loss of coherence of oscillations on base frequencies.

scholarly journals A numerical study on the impact of nonlinear interactions on the amplitude of the migrating semidiurnal tide

2006 ◽  
Vol 24 (12) ◽  
pp. 3241-3256 ◽  
Author(s):  
C. M. Huang ◽  
S. D. Zhang ◽  
F. Yi
Keyword(s):  
Numerical Study ◽  
Steady Solution ◽  
Nonlinear Interactions ◽  
Semidiurnal Tide ◽  
Mean Flow ◽  
Structure Variation ◽  
Amplitude Difference ◽  
The Mean ◽  
The Impact ◽  
Mlt Region

Abstract. To quantitatively study the effects of nonlinear interactions on tide structure, a nonlinear numerical tidal model is developed, and the reliability and convergence of the adopted algorithm and coding are checked by numerical experiments. Under the same conditions as those employed by the GSWM-00 (Global Scale Wave Model 2000), our model provides the nonlinear quasi-steady solution of the migrating semidiurnal tide, which differs from the GSWM-00 result (the linear steady solution) in the MLT region, especially above 100 km. Additionally, their amplitude difference displays a remarkable month-to-month variation, and its significant magnitudes occur during the month with strong semidiurnal tide. A quantitative analysis suggests that the main cause for the amplitude difference is that the initial migrating 12-h tide will interact with the mean flow as well as the nonlinearity-excited 6-h tide, and subsequently yield a new 12-h tidal part. Furthermore, our simulations also show that the mean flow/tidal interaction will significantly alter the background wind and temperature fields. The large magnitudes of the tidal amplitude difference and the background alteration indicate that the nonlinear processes involved in tidal propagations should be comprehensively considered in the description of global atmospheric dynamics in the MLT region. The comparisons among our simulations, the GSWMs and some observations of tides suggest that the nonlinearity-induced tidal structure variation could be a possible mechanism to account for some discrepancies between the GSWMs and the observations.

Passive pitching of splitters in the trailing edge of elliptic cylinders

2017 ◽  
Vol 826 ◽  
pp. 363-375 ◽  
Author(s):  
Y. Jin ◽  
L. P. Chamorro
Keyword(s):  
Vortex Shedding ◽  
Semimajor Axis ◽  
Wake Flow ◽  
Recirculation Region ◽  
Mean Flow ◽  
Trailing Edge ◽  
Flow Measurements ◽  
High Background ◽  
Aspect Ratios ◽  
The Mean

The distinctive pitching of hinged splitters in the trailing edge of elliptic cylinders was experimentally studied at various angles of attack ($AoA$) of the cylinder, Reynolds numbers, splitter lengths, aspect ratios ($AR$) of the cylinder and freestream turbulence levels. High-resolution telemetry and hotwire anemometry were used to characterize and gain insight on the dynamics of splitters and wake flow. Results show that the motions of the splitters contain various dominating modes, e.g. $f_{p}$ and $f_{v}$, which are induced by the mean flow and wake dynamics. High background turbulence dampens the coherence of the regular vortex shedding leading to negligible $f_{v}$. For a sufficiently long splitter, namely twice the semimajor axis of the cylinder, dual vortex shedding mode exists close to the leading and trailing edges of the splitter. In general, the splitters oscillate around an equilibrium position nearly parallel to the mean direction of the flow; however, a skewed equilibrium is also possible with a strong recirculation region. This is the case with cylinders of low $AR$ and high $AoA$, where higher lift and drag occurs. Flow measurements at various transverse locations within the wake of the cylinder–splitter system indicate that the signature of the low-frequency splitter pitching is shifted in the wake in the cases with non-zero $AoA$ of the cylinder. Although the splitter pitching exhibits two dominant vortex shedding modes in various configurations, only the higher frequency is transmitted to the wake.

scholarly journals CURRENT CHARACTERISTICS IN THE PRESENCE OF NEAR-ORTHOGONAL WAVES

2012 ◽  
Vol 1 (33) ◽  
pp. 41
Author(s):  
Kian Yew Lim ◽  
Ole Secher Madsen ◽  
Hin Fatt Cheong
Keyword(s):  
Profile Analysis ◽  
Numerical Study ◽  
Flow Profile ◽  
Wave Direction ◽  
Mean Flow ◽  
Wave Basin ◽  
Current Interaction ◽  
The Mean ◽  
Current Flows ◽  
Wave Induced

An experimental study involving near-orthogonal wave-current interaction in a wave basin is reported in this paper. Due to previous shortcomings associated with 2D bottom configurations, i.e. occurrence of ripple-induced turning of flows close to the bed, the present experiments were conducted with the bottom covered by closely packed ceramic marbles (mean diameter of 1.25cm). Three types of flows were generated over this bottom: current-alone, wave-alone and combined wave-current flow. For current-alone and wave-current cases, the log-profile analysis was used to resolve the equivalent Nikuradse sand grain roughness, kn, while the energy dissipation method was used to estimate kn for wave-alone case. The results show that kn obtained for current- and wave-alone tests is roughly 2.2 times the diameter of the marbles. For orthogonal wave-current flows, the kn value, when used in combination with the Grant-Madsen (GM) model to reproduce the experimental apparent roughness, is found to be smaller than the measured current-alone and wave-alone kn. Similar under-prediction of bottom roughness is also observed when the GM model is compared with a numerical study, thus supporting the conjecture that when the current is weak compared to the waves, simple theoretical models like GM are not sufficiently sensitive to the angle of wave-current interaction. Experiments with currents at angles of 60° and 120° to the wave direction yield apparent roughness smaller than the 90° case, which is counter-intuitive since one would expect the mean flow to experience a stronger wave-induced turbulence when it is more aligned with the wave direction. This result indicates a possible contamination from wave-induced mass transport to the mean flow profile for non-orthogonal combined flow cases, and therefore highlights the need for other alternatives to the log-profile analysis when attempting to resolve kn from current velocity profiles from combined wave-current flows.

A Numerical Study of Vortex Breakdown in Turbulent Swirling Flows

1999 ◽  
Vol 122 (1) ◽  
pp. 179-183 ◽  
Author(s):  
Robert E. Spall ◽  
Blake M. Ashby
Keyword(s):  
Reynolds Stress ◽  
Stokes Equations ◽  
Vortex Breakdown ◽  
Numerical Study ◽  
Reynolds Stress Model ◽  
Navier Stokes ◽  
Stress Model ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
The Mean

Solutions to the incompressible Reynolds-averaged Navier–Stokes equations have been obtained for turbulent vortex breakdown within a slightly diverging tube. Inlet boundary conditions were derived from available experimental data for the mean flow and turbulence kinetic energy. The performance of both two-equation and full differential Reynolds stress models was evaluated. Axisymmetric results revealed that the initiation of vortex breakdown was reasonably well predicted by the differential Reynolds stress model. However, the standard K-ε model failed to predict the occurrence of breakdown. The differential Reynolds stress model also predicted satisfactorily the mean azimuthal and axial velocity profiles downstream of the breakdown, whereas results using the K-ε model were unsatisfactory. [S0098-2202(00)01601-1]

Numerical study on mean flow field of turbulent dual offset jet

2021 ◽  
pp. 095440622110007
Author(s):  
Tanmoy Mondal ◽  
Shantanu Pramanik
Keyword(s):  
Flow Field ◽  
Numerical Study ◽  
Jet Flow ◽  
Separation Distance ◽  
Bottom Wall ◽  
Mean Flow ◽  
Reattachment Point ◽  
The Mean ◽  
Two Jets ◽  
Offset Jet

A numerical investigation on the mean flow and turbulence characteristics of dual offset jet for various separation distances between the two jets with a fixed offset height of the lower jet from the bottom wall is reported in this study. The numerical simulations have been performed by solving the Reynolds-averaged Navier-Stokes equations (RANS) with two-equation standard [Formula: see text] turbulence model. The Reynolds number based on the jet width and the inlet turbulence intensity are considered as 15,000 and 5%, respectively. The computational results for the mean flow reveal that after issuing from the nozzles, the adjacent shear layers of the offset jets meet together at the merging point and then the merged jets reattaches on the bottom wall at the reattachment point before they combine together at the combined point forming a single jet flow. In the far downstream, the flow field behaves like a classical single wall jet flow. The self-similarity of mean flow field is achieved at far down stream of combined point. An increase in separation distance between the two jets [Formula: see text] results in a decrease in magnitude of the streamwise maximum velocity of the combined jet but with same rate of decay. The converging region of the jets has depicted considerable growth of turbulence as the jet centrelines bend towards the merging point. According to the mean flow results, the distances of the reattachment point and the combined point from the nozzle exit gradually increase with the progressive increase in separation distance between the two jets within the range d/ w = 3–8.

Numerical study of turbulent magnetohydrodynamic channel flow

2007 ◽  
Vol 572 ◽  
pp. 179-188 ◽  
Author(s):  
THOMAS BOECK ◽  
DMITRY KRASNOV ◽  
EGBERT ZIENICKE
Keyword(s):  
Channel Flow ◽  
Numerical Study ◽  
Layer Structure ◽  
Momentum Balance ◽  
Mean Flow ◽  
Mean Velocity ◽  
Static Approximation ◽  
The Mean ◽  
Magnetohydrodynamic Channel ◽  
Normal Magnetic Field

Mean flow properties of turbulent magnetohydrodynamic channel flow with electrically insulating channel walls are studied using high-resolution direct numerical simulations. The Lorentz force due to the homogeneous wall-normal magnetic field is computed in the quasi-static approximation. For strong magnetic fields, the mean velocity profile shows a clear three-layer structure consisting of a viscous region near each wall and a plateau in the middle connected by logarithmic layers. This structure reflects the significance of viscous, turbulent, and electromagnetic stresses in the streamwise momentum balance dominating the viscous, logarithmic, and plateau regions, respectively. The width of the logarithmic layers changes with the ratio of Reynolds- and Hartmann numbers. Turbulent stresses typically decay more rapidly away from the walls than predicted by mixing-length models.

LOW-DIMENSIONAL CHAOS IN A PERTURBED KORTEWEG–DE VRIES EQUATION

1995 ◽  
Vol 05 (04) ◽  
pp. 1221-1233 ◽  
Author(s):  
X. TIAN ◽  
R. H. J. GRIMSHAW
Keyword(s):  
Steady State ◽  
Vries Equation ◽  
Numerical Study ◽  
Kdv Equation ◽  
Period Doubling ◽  
Subharmonic Bifurcation ◽  
De Vries ◽  
Route To Chaos ◽  
Low Dimensional ◽  
Perturbed Kdv Equation

Spatial chaos has been observed in the steady state from a numerical study of a perturbed Korteweg–de Vries equation. The onset of chaos is due to a subharmonic bifurcation sequence. A second route to chaos is also observed via a period-doubling sequence generated from each fundamental subharmonic state. In this paper, the question of determining low-dimensional chaos in this perturbed KdV equation is addressed. The dimension of this system in the steady state is estimated from the corresponding ordinary differential equation via the Lyapunov spectrum, and also from a numerical investigation via a reconstructed attractor using a spatial series.

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