Low Prandtl Number Fluids Research Articles

Mixed convection along a rotating vertical slender cylinder in an axial flow

A general analysis has been developed to study fluid flow and heat transfer characteristics for mixed convection along a rotating vertical slender cylinder. Transformed set of coupled non-linear partial differential equations is solved by an implicit finite difference scheme in combination with the quasilinearisation technique. The effects of rotational, buoyancy and suction/injection parameters have been investigated in the present study. The effects of various parameters on the velocity profiles in x- and θ-directions and the temperature profile are reported in the present study. The buoyancy force causes considerable velocity overshoot for low Prandtl number ( Pr) fluids. The Prandtl number ( Pr) strongly affects the surface heat transfer rate. Numerical results are presented for the skin friction coefficients in x- and θ-directions and for the Nusselt number.

Ultrasonic visualization of thermal convective motion in a liquid gallium layer

For low Prandtl number fluids including liquid metals, optical methods cannot be utilized to visualize convective motion, and in this paper the velocity profile in a liquid gallium layer was measured using ultrasonic velocity profiling, UVP. The applicability of the measurement system was confirmed with the rotating flow of liquid gallium and in the natural convection appearing in a glycerol solution layer. The vessel for the liquid gallium layer was optimized for the acoustic properties of liquid gallium. The measured velocity profile shows a cell like convective motion. The spatio-temporal behavior of large-scale convective motion in turbulent convection was observed as a temporal variation of the velocity profile with two kinds of periodic fluctuations of the convection cell.

A numerical study of the target system of an ADSS with different flow guides

The mechanical design of the target module of an accelerator driven subcritical nuclear reactor system (ADSS) calls for an analysis of the related thermal-hydraulic issues because of large amount of heat deposition in the spallation region during the course of nuclear interactions with the molten lead bismuth eutectic (LBE) target. The LBE also should carry the entire heat generated as a consequence of the spallation reaction. The problem of heat removal by the LBE is a challenging thermal-hydraulic issue. For this, one has to examine the flows of low Prandtl number fluids (LBE) in a complex ADSS geometry. In this study, the equations governing the laminar flow and thermal energy are solved numerically using the streamline upwind Petrov-Galerkin (SUPG) finite element (FE) method. The target systems with a straight and a nozzle guide have been considered. The principal purpose of the analysis is to trace the flow and temperature distribution and thereby to check the suitability of the flow guide in avoiding the recirculation or stagnation zones in the flow space that may lead to hot spots.

Flow and heat transfer in a pipe with a fin attached to inner wall

Enhancement of heat transfer to the fluid can be done by turbulence promoters such as attached fins to the pipe walls. In this study, the flow field and the heat transfer rates were numerically investigated in a pipe with an internally attached fin. Numerical simulations were conducted for four different types of fluids and for different fin heights and locations, and as the Reynolds number was varied, the effects of the fin on Nusselt number and friction factors were investigated. For all the Reynolds numbers considered in this study, the effect of fin location on the heat transfer rate and friction factor was negligible. As the fin height was increased, the mean Nusselt number and the friction factor also increased in the turbulent flow regimes. For low Prandtl number fluids (Pr = 0.011), the main heat transfer mode is conduction, and hence the mean Nusselt number slightly affected the flow rates.

Thermal hydraulics of the spallation target module of an accelerator driven sub-critical system: A numerical study

The mechanical design of the target module of an accelerator driven sub-critical nuclear reactor system (ADSS) calls for an analysis of the related thermal–hydraulic issues because of the sheer large amount of heat generation in its spallation target system during the course of nuclear interactions with the molten lead bismuth eutectic (LBE) target. The window of the target module is subject to high heat fluxes due to the direct impingement of high energy proton beam on its surface. A large amount of heat is deposited on the window and in the bulk of the LBE in the spallation region. Therefore, the problem of heat removal by the LBE is a challenging thermal–hydraulic issue. For this, one will need to examine the laminar/turbulent flows of low Prandtl number fluids (LBE) in a complex target module of an ADSS. In this study, the equations governing the flow and thermal energy are solved numerically using the streamline upwind Petrov–Galerkin (SUPG) finite element (FE) method. Special consideration has been given to the window under various thermal conditions, such as, isothermal, uniform and variable heat flux. The analysis has been extended to the case of heat generation in the liquid LBE. The principal purpose of the analysis is to trace the temperature distribution on the beam window and in the LBE. This also helps to check the suitability of the geometry in avoiding the recirculation or stagnation zones in the flow space that may lead to hot spots.

Symmetry breaking of melt flow typically encountered in a Bridgman configuration heated from below

A computational model is developed to investigate three-dimensional fluid flow instability and transition to unsteadiness. The simulated domain corresponds to a parallelepiped configuration which is a restriction to the fluid phase of commonly used configurations in crystal growth (viz. Bridgman configuration). In the present work, this problem is studied using three-dimensional simulations and focuses on symmetry breaking and transition to unsteadiness occurring for a low Prandtl number fluid ( Pr = 0.01). Three-dimensional simulations presented thus overcome the limitation of the two-dimensional approach. It has been found that the initially steady symmetric flow in the three-dimensional case becomes asymmetric for lower Ra number than for the two-dimensional case. The breaking in symmetry occurs firstly in the transverse plane. For the relatively low Ra number we still have no intensification in the global heat transfer but it appears that the heat transfer increases locally on the bottom and decreases on the vertical active walls. The classical spiral flows typical characterizing the three-dimensional effect (in the third direction) are also identified.

Thermocapillary Instabilities of Low Prandtl Number Fluid in a Laterally Heated Vertical Cylinder

Stabilities of surface-tension-driven convection in an open cylinder are investigated numerically. The cylinder is heated laterally through its sidewall and is cooled at free surface by radiation. A seeding crystal at constant temperature is in contact with the free surface. Axisymmetric base flow is solved using the high-order finite difference method. Three-dimensional perturbation is applied to the obtained base flow to determine the critical Marangoni numbers at which the axisymmetry is broken. The eigenvalue matrix equation is solved using linear fractional transformation with banded matrix structure taken into account. Critical Marangoni-Reynolds numbers are obtained at various boundary conditions.

Measurement of Liquid Metal Flow using Ultrasonic Velocity Profiler (2nd Report, Visualization of Thermal Convective Motion in Liquid Gallium Layer)

Thermal convection in liquid gallium layer was investigated as a fundamental study for Rayleigh-Bénard convection in low Prandtl number fluid using ultrasonic velocity profiler, UVP. Temperature dependence of sound speed in liquid gallium was measured for a velocity profile measurement by UVP. Measured velocity profiles visualized a convective motion in the liquid gallium layer, and it is a roll shape motion. Spatio-temporal velocity profile showed that there are two types of spatial fluctuation of the convection roll, and there are 3 modes on the number of convection rolls in the fluid layer, 2, 3 or 4 rolls. Two axes-simultaneous velocity profile measurement clarified that expand and contraction of convection roll has a phase delay on the direction of the rotating axis of the roll.

Three-dimensional CFD Simulation of Rayleigh–Benard Convection for Low Prandtl Number Fluids

Transient three-dimensional numerical simulations were successfully carried out for the Rayleigh-Benard convection for the low Pr fluid (Pr = 0.025) in a rectangular enclosure. Transient simulations revealed the transitions from contra-rotative cells to the parallel roll formation. The oscillatory behaviour is attributed to recirculation of ascending and descending flows towards central region of the enclosure producing organized rolled motions. The oscillatory characteristics of the fluid for two aspect ratios have been analysed and flow structures have been obtained. The onset of thermal instability has been analysed and observed at the critical Ra from the CFD simulations, and is found to be in agreement with the available experimental data.

Numerical simulations of periodic flow oscillations in low Prandtl number fluids

The transition from steady to oscillatory flow for a very low Prandtl number fluid ( Pr = 0.008) is computed for rectangular enclosures with aspect ratios (length/height) of 0.25, 0.4, 1.0, and 2.0 and are found to occur at Rayleigh numbers of 250,000, 130,000, 83,500, and 30,000 respectively. The structures of the oscillations are graphically depicted and are manifested in corner cells which dissipate into centered cells and then into opposite corner cells. A secondary flow transition is detected for a geometry with an aspect ratio of 1.0 at Ra = 1.2 Ra c2.

Unsteadiness and control by using thermal boundary modulation in restricted fluid domain of vertical Bridgman apparatus

The behaviour of heat and mass transfer in a square vertical Bridgman cavity containing a low Prandtl number fluid and subjected to oscillatory heating is investigated with respect to the flow instability and transition from steady to unsteady regimes for fluid isothermally heated from below. Effects of thermal modulation on the all regimes occurring in the cavity when increasing the convection intensity are analysed. To focus on the control by using the modulation, two cases are distinguished according to the initial state of the melt flow, steady or time dependent. The steady regime exhibits the existence of a characteristic modulation frequency allowing the reduction of the average intensity of the flow. For the range of the unsteady flows considered in this study, the existence of a critical modulation frequency allowing the control of the amplitude of the oscillating heat and flow, has been identified.

3424 溶融スズによる低Pr流体の液柱マランゴニ対流(S89-2 微小重力・宇宙環境利用(2),S89 微小重力・宇宙環境利用)

The experimental study on thermocapillary convection of low Prandtl number fluid was carried out to estimate the mode structure after the onset of oscillatory flow. The half-zone liquid bridge of molten tin was used as a experimental configuration. In order to detect very slight temperature changes, the temperature measurement system was improved. Temperature oscillations at the interface between liquid and cold rod were obtained by several thermocouples. The mode structure appeared in a low frequency oscillation region after the onset was presumed from the phase differences among them. The mode structure was supposed to be 2 and rotation with a frequency of 0.008Hz.

低 Pr 数流体液柱の振動マランゴニ対流遷移過程の実験研究

低 Pr 数流体液柱の振動マランゴニ対流遷移過程の実験研究

Numerical simulation of Marangoni flow in partially confined half-zone liquid bridge of low-Prandtl-number fluids

Direct numerical simulation using a finite difference method was done to reveal the fundamental characteristics of the flow in a half-zone liquid bridge of low Prandtl number fluids with the free surface partially confined by oxide films (non-slip adiabatic rigid walls). The critical Marangoni number Ma c1 was calculated for several geometries, which are determined by the free surface ratio ( ξ= L w/ L, L w: length of the free surface, L: height of the whole liquid bridge) and the axial position of the free surface. When the oxide film exists between the free surface and the cold disc, the flow separates from the oxide film, and a weak cell with a counter flow arises near the cold disc. An axisymmetric flow exhibits a direct transition to an oscillatory flow, when the free surface ratio ξ is sufficiently small and free surface was located away from the cold disc.

B213 低プラントル数流体のマランゴニ対流流れ場可視化技術の開発(2)

In the observation of thermocapillary flow using a molten metal which is an opaque low Prandtl number fluid, the internal flow pattern has to be estimated from the fluctuation pattern of the surface temperature. In order to obtain the internal flow pattern directly, the visualization technique using an ultrasonic wave has been developed. The position of a tracer can be detected by small array transducer, and the internal flow pattern can be visualized from dynamic position change of the tracers. The tracer and signal processing equipment which is used for an actual flow examination were manufactured, and these were checked satisfying a required function by the test. Moreover, the numerical simulation was performed to verify the capability of this system.

Étude numérique des instabilités de la phase fluide et de l'interface de solidification en croissance dirigée horizontale

Convective instabilities of low Prandtl number fluids are subject to various studies. The purpose here is an extension to hydrodynamic transitions in the fluid phase with a free or rigid surface under phase change and to construct the corresponding bifurcation diagram. Investigations interesting the process control by using the latent heat and the solid/liquid thermal conductivity difference are considered. The solution methodology is based on a front localisation approach showing a very good ability to describe convection regimes coupled to the phase change transition in the case of vertical solidification with confinement. To cite this article: E.A. Semma et al., C. R. Mecanique 331 (2003).

Low-order dynamical model for low-Prandtl number fluid flow in a laterally heated cavity

By applying proper orthogonal decomposition (method of snapshots) to low Prandtl number fluid flow in a laterally heated cavity of dimensions 4×2×1 in length×width×height, characteristic basic modes have been extracted. Using Galerkin projection of the governing equations on these basic modes, a low-dimensional dynamical model (set of ordinary differential equations) was constructed. Some results obtained from the low-order model are presented and compared with those calculated by direct numerical simulation (DNS). The factors influencing the reliability of the low-order model such as the length of the reference signal, the snapshot density, the number of modes chosen for Galerkin projection, the characteristic velocity, and the chosen expansions for velocity and temperature are discussed. It is found that the low-order model can exactly reproduce the results obtained by DNS at the design conditions (i.e., for the Grashof and Prandtl numbers at which the basic modes have been obtained). The model can also fairly well approach the DNS results in a domain around these conditions. Nevertheless, it seems that such models have to be used with care and that, in any case, they can qualitatively predict the DNS results only in a not very large range around the design conditions.

Magnetoconvective ow of a liquid metal in partially open cavities

The influence of thermocapillary force on the buoyancy driven convection flow of a low Prandtl number fluid in partially open cavities is investigated in the presence of a uniform magnetic field. Numerical solutions of the governing equations are obtained using an unconditionally stable numerical scheme consisting of Alternating Direction Implicit and Successive Over Relaxation methods. Streamline and isotherm plots are drawn for a wide range of parameter values and different geometrical configurations. The isotherms and average heat transfer rate calculated reveal that the effect of magnetic field is to suppress the convective heat transport inside the cavity.

3D numerical simulation of on ground Marangoni flow instabilities in liquid bridges of low Prandtl number fluid

The influence of gravity on the Marangoni flow instability in half zone liquid bridges in the case of liquid metals is investigated by direct 3D and time‐dependent simulation of the problem. The computations are carried out for different heating conditions and environments (zero g conditions and on ground liquid zone heated from above or from below). The case of cylindrical shape (simplified model) and of melt/air interface deformed by the effect of gravity (real conditions) are considered. The comparison among these situations gives insight into the separate (gravity) effects of buoyancy forces and of the free surface deviation with respect to straight configuration. Body‐fitted curvilinear co‐ordinates are adopted to handle the non‐cylindrical problem. The liquid bridge exhibits different behaviours according to the allowed bridge shape. If the shape is forced to be cylindrical, the flow field is stabilized in the case of heating from above and destabilized if gravity is reversed. If the deformation is taken into account, gravity always stabilizes the Marangoni flow regardless of its direction (parallel or antiparallel to the axis) and the 3D flow structure is different according to the heating condition (from above or from below). In the latter case, the critical Marangoni number is larger and the critical wave number is smaller, compared with the opposite condition. In addition, for Pr=0.02 (Gallium), a surprising heretofore unseen behaviour arises. No steady bifurcation occurs and the flow becomes unstable directly to oscillatory disturbances. This phenomenon has never been reported before in the case of low Prandtl number liquids.

From stationary to complex time-dependent flows at moderate Rayleigh numbers in two-dimensional annular thermal convection

Two-dimensional nonlinear thermal convection in a cylindrical annulus is numerically analyzed for a Boussinesq fluid of low Prandtl number σ=0.025. For a fixed value of the radius ratio, η=0.3, different types of steady columnar patterns are found. The stability of these convection patterns and the spatial interaction between them, which result in the formation of mixed modes, are investigated by considering the full nonlinear set of Navier–Stokes equations. Special attention is paid to the strong spatial interaction of the initially unstable modes with wavenumbers n=2 and n=4, which leads, through global bifurcations, to multiple stable quasi-periodic states of the system. A detailed picture of the nonlinear dynamics until temporal chaotic patterns set in is presented and understood in terms of local and global symmetry-breaking bifurcations of the O(2)-symmetric system.