scholarly journals Two- and three-dimensional numerical simulations of the transition to oscillatory convection in low-Prandtl-number fluids

1998 ◽  
Vol 374 ◽  
pp. 145-171 ◽  
Author(s):  
DANIEL HENRY ◽  
MARC BUFFAT
Keyword(s):  
Prandtl Number ◽  
Relative Concentration ◽  
Three Dimensional ◽  
Power Spectra ◽  
Hadley Circulation ◽  
Time Dependent ◽  
Two Dimensional ◽  
General Behaviour ◽  
Shallow Cavities ◽  
Dependent Flow

The convective flows which arise in shallow cavities filled with low-Prandtl-number fluids when subjected to a horizontal temperature gradient are studied numerically with a finite element method. Attention is focused on a rigid cavity with dimensions 4×2×1, for which experimental data are available. The three-dimensional results indicate that, after a relative concentration of the initial Hadley circulation, a transition to time-dependent flows occurs in the form of a roll oscillation with a purely dynamical origin. This transition corresponds to a Hopf bifurcation with a breaking of symmetry that gives some specific properties to the time evolution of the flow: these properties are shown to be the result of the general behaviour of the dynamical systems. Calculations performed in the case of mercury compare well with the experiments with similar power spectra of the temperature, and this validates the analysis of the nature of the global flow performed in the limiting case Pr=0. All these results are discussed with respect to the linear and nonlinear analyses and to other computational experiments. Numerical results obtained in the corresponding two-dimensional situation give a different transition to the time-dependent flow: it is shown that in the three-dimensional cavity this type of two-dimensional transition is less probable than the observed transition with breaking of symmetry.

The transition from two-dimensional to three-dimensional planforms in infinite-Prandtl-number thermal convection

1990 ◽  
Vol 216 ◽  
pp. 71-91 ◽  
Author(s):  
Bryan Travis ◽  
Peter Olson ◽  
Gerald Schubert
Keyword(s):  
Aspect Ratio ◽  
Prandtl Number ◽  
Time Dependence ◽  
Thermal Convection ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Time Dependent ◽  
Two Dimensional ◽  
Random Initial Conditions ◽  
The Stability

The stability of two-dimensional thermal convection in an infinite-Prandtl-number fluid layer with zero-stress boundaries is investigated using numerical calculations in three-dimensional rectangles. At low Rayleigh numbers (Ra < 20000) calculations of the stability of two-dimensional rolls to cross-roll disturbances are in agreement with the predictions of Bolton & Busse for a fluid with a large but finite Prandtl number. Within the range 2 × 104 < Ra [les ] 5 × 105, steady rolls with basic wavenumber α > 2.22 (aspect ratio < 1.41) are stable solutions. Two-dimensional rolls with basic wavenumber α < 1.96 (aspect ratio > 1.6) are time dependent for Ra > 4 × 104. For every case in which the initial condition was a time-dependent large-aspect-ratio roll, two-dimensional convection was found to be unstable to three-dimensional convection. Time-dependent rolls are replaced by either bimodal or knot convection in cases where the horizontal dimensions of the rectangular box are less than twice the depth. The bimodal planforms are steady states for Ra [les ] 105, but one case at Ra = 5 × 105 exhibits time dependence in the form of pulsating knots. Calculations at Ra = 105 in larger domains resulted in fully three-dimensional cellular planforms. A steady-state square planform was obtained in a 2.4 × 2.4 × 1 rectangular box. started from random initial conditions. Calculations in a 3 × 3 × 1 box produced steady hexagonal cells when started from random initial conditions, and a rectangular planform when started from a two-dimensional roll. An hexagonal planform started in a 3.5 × 3.5 × 1 box at Ra = 105 exhibited oscillatory time dependence, including boundary-layer instabilities and pulsating plumes. Thus, the stable planform in three-dimensional convection is sensitive to the size of the rectangular domain and the initial conditions. The sensitivity of heat transfer to planform variations is less than 10%.

Flow Mixing Enhancement from Balloon Pulsations in an Intravenous Oxygenator

2004 ◽  
Vol 127 (3) ◽  
pp. 400-415 ◽  
Author(s):  
Amador M. Guzmán ◽  
Rodrigo A. Escobar ◽  
Cristina H. Amon
Keyword(s):  
Numerical Simulations ◽  
Oxygen Transfer ◽  
Fiber Bundle ◽  
Transfer Rate ◽  
Oxygen Transfer Rate ◽  
Three Dimensional ◽  
Time Dependent ◽  
Fiber Placement ◽  
Flow Mixing ◽  
Dependent Flow

Computational investigations of flow mixing and oxygen transfer characteristics in an intravenous membrane oxygenator (IMO) are performed by direct numerical simulations of the conservation of mass, momentum, and species equations. Three-dimensional computational models are developed to investigate flow-mixing and oxygen-transfer characteristics for stationary and pulsating balloons, using the spectral element method. For a stationary balloon, the effect of the fiber placement within the fiber bundle and the number of fiber rings is investigated. In a pulsating balloon, the flow mixing characteristics are determined and the oxygen transfer rate is evaluated. For a stationary balloon, numerical simulations show two well-defined flow patterns that depend on the region of the IMO device. Successive increases of the Reynolds number raise the longitudinal velocity without creating secondary flow. This characteristic is not affected by staggered or non-staggered fiber placement within the fiber bundle. For a pulsating balloon, the flow mixing is enhanced by generating a three-dimensional time-dependent flow characterized by oscillatory radial, pulsatile longitudinal, and both oscillatory and random tangential velocities. This three-dimensional flow increases the flow mixing due to an active time-dependent secondary flow, particularly around the fibers. Analytical models show the fiber bundle placement effect on the pressure gradient and flow pattern. The oxygen transport from the fiber surface to the mean flow is due to a dominant radial diffusion mechanism, for the stationary balloon. The oxygen transfer rate reaches an asymptotic behavior at relatively low Reynolds numbers. For a pulsating balloon, the time-dependent oxygen-concentration field resembles the oscillatory and wavy nature of the time-dependent flow. Sherwood number evaluations demonstrate that balloon pulsations enhance the oxygen transfer rate, even for smaller flow rates.

Upstream motions in stratified flow

1988 ◽  
Vol 187 ◽  
pp. 487-506 ◽  
Author(s):  
I. P. Castro ◽  
W. H. Snyder
Keyword(s):  
Body Height ◽  
Three Dimensional ◽  
Time Dependent ◽  
Experimental Measurements ◽  
Two Dimensional ◽  
Towing Tank ◽  
First Order ◽  
Density Perturbations ◽  
Small Obstacle ◽  
Obstacle Height

In this paper experimental measurements of the time-dependent velocity and density perturbations upstream of obstacles towed through linearly stratified fluid are presented. Attention is concentrated on two-dimensional obstacles which generate turbulent separated wakes at Froude numbers, based on velocity and body height, of less than 0.5. The form of the upstream columnar modes is shown to be largely that of first-order unattenuating disturbances, which have little resemblance to the perturbations described by small-obstacle-height theories. For two-dimensional obstacles the disturbances are similar to those found by Wei, Kao & Pao (1975) and it is shown that provided a suitable obstacle drag coefficient is specified, the lowest-order modes (at least) are quantitatively consistent with the results of the Oseen inviscid model.Discussion of some results of similar measurements upstream of three-dimensional obstacles, the importance of towing tank endwalls and the relevance of the Foster & Saffman (1970) theory for the limit of zero Froude number is also included.

Numerical Calculation of Pressure Fluctuations in the Volute of a Centrifugal Fan

2005 ◽  
Vol 128 (2) ◽  
pp. 359-369 ◽  
Author(s):  
Rafael Ballesteros-Tajadura ◽  
Sandra Velarde-Suárez ◽  
Juan Pablo Hurtado-Cruz ◽  
Carlos Santolaria-Morros
Keyword(s):  
Fluid Dynamics ◽  
Pressure Fluctuations ◽  
Three Dimensional ◽  
Power Spectra ◽  
Operating Conditions ◽  
Experimental Results ◽  
Time Dependent ◽  
Centrifugal Fan ◽  
Wall Pressure Fluctuations ◽  
Good Agreement

In this work, a numerical model has been applied in order to obtain the wall pressure fluctuations at the volute of an industrial centrifugal fan. The numerical results have been compared to experimental results obtained in the same machine. A three-dimensional numerical simulation of the complete unsteady flow on the whole impeller-volute configuration has been carried out using the computational fluid dynamics code FLUENT®. This code has been employed to calculate the time-dependent pressure both in the impeller and in the volute. In this way, the pressure fluctuations in some locations over the volute wall have been obtained. The power spectra of these fluctuations have been obtained, showing an important peak at the blade passing frequency. The amplitude of this peak presents the highest values near the volute tongue, but the spatial pattern over the volute extension is different depending on the operating conditions. A good agreement has been found between the numerical and the experimental results.

scholarly journals Experimental and Computational Study of the Unsteady Flow in a 1.5 Stage Axial Turbine With Emphasis on the Secondary Flow in the Second Stator

1998 ◽  
Author(s):  
Ralf E. Walraevens ◽  
Heinz E. Gallus ◽  
Alexander R. Jung ◽  
Jürgen F. Mayer ◽  
Heinz Stetter
Keyword(s):  
Unsteady Flow ◽  
Secondary Flow ◽  
Computational Study ◽  
Three Dimensional ◽  
Cross Flow ◽  
Axial Flow ◽  
Time Dependent ◽  
Flow Structures ◽  
Mean Flow ◽  
Dependent Flow

A study of the unsteady flow in an axial flow turbine stage with a second stator blade row is presented. The low aspect ratio blades give way to a highly three-dimensional flow which is dominated by secondary flow structures. Detailed steady and unsteady measurements throughout the machine and unsteady flow simulations which include all blade rows have been carried out. The presented results focus on the second stator flow. Secondary flow structures and their origins are identified and tracked on their way through the passage. The results of the time-dependent secondary velocity vectors as well as flow angles and Mach number distributions as perturbation from the time-mean flow field are shown in cross-flow sections and azimuthal cuts throughout the domain of the second stator. At each location the experimental and numerical results are compared and discussed. A good overall agreement in the time-dependent flow behaviour as well as in the secondary flow structures is stated.

Time-based two dimensional modelling of NATM tunnelling

2002 ◽  
Vol 39 (3) ◽  
pp. 710-724 ◽  
Author(s):  
J H Shin ◽  
D M Potts
Keyword(s):  
Three Dimensional ◽  
Two Dimensions ◽  
Time Dependent ◽  
Soil Conditions ◽  
Measuring Instruments ◽  
Two Dimensional ◽  
Time Dependent Behaviour ◽  
Decomposed Granite ◽  
Granite Soil ◽  
Dependent Behaviour

A two dimensional model is commonly employed in practice for the analysis of tunnelling. Such analyses are computationally cheap and are useful for assessing the sensitivity of the problem to the construction method, studying the influence of varying soil conditions, and (or) finding appropriate locations for placing measuring instruments. However, simulating the three dimensional nature of tunnelling in two dimensions requires certain simplifications, including the use of empirical parameters to represent the construction sequence. In many cases the choice of parameter values are arbitrary and often not fully explained. In addition, the modelling methods are often only applicable for undrained or fully drained soil conditions where no time-dependent behaviour is involved during tunnel construction. In this paper an alternative two dimensional approach termed the "time-based modelling method" is proposed that can simulate both the three dimensional effects at the tunnel heading and the time-dependent behaviour during construction. It is proposed that the new approach is appropriate for the analysis of tunnelling in a relatively permeable soil and, as an example, the method is applied to the analysis of a new Austrian tunnelling method (NATM) tunnelling problem in decomposed granite soil. The results are compared with field data and excellent agreement is obtained.Key words: numerical modelling, time-dependent behaviour, NATM tunnelling, decomposed granite soil.

On the similarity of particle and photon tunneling and multiple internal reflections in one-dimensional, two-dimensional and three-dimensional photon tunneling

2014 ◽  
Vol 23 (06) ◽  
pp. 1460006 ◽  
Author(s):  
V. S. Olkhovsky
Keyword(s):  
Quantum Electrodynamics ◽  
Electromagnetic Waves ◽  
Relativistic Quantum ◽  
Three Dimensional ◽  
Time Dependent ◽  
Two Dimensional ◽  
Relativistic Quantum Field Theory ◽  
One Dimensional ◽  
Quantum Equation ◽  
Photon Tunneling

The formal mathematical analogy between time-dependent quantum equation for the nonrelativistic particles and time-dependent equation for the propagation of electromagnetic waves had been studied in [A. I. Akhiezer and V. B. Berestezki, Quantum Electrodynamics (FM, Moscow, 1959) [in Russian] and S. Schweber, An Introduction to Relativistic Quantum Field Theory, Chap. 5.3 (Row, Peterson & Co, Ill, 1961)]. Here, we deal with the time-dependent Schrödinger equation for nonrelativistic particles and with time-dependent Helmholtz equation for electromagnetic waves. Then, using this similarity, the tunneling and multiple internal reflections in one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) particle and photon tunneling are studied. Finally, some conclusions and future perspectives for further investigations are presented.

scholarly journals Modelling time dependent flow fields over three dimensional dunes

2014 ◽  
pp. 1045-1052
Author(s):  
R Hardy ◽  
T Marjoribanks ◽  
D Parsons ◽  
A Reesink ◽  
B Murphy ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Flow Fields ◽  
Time Dependent ◽  
Dependent Flow
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