Fluid Pr Research Articles

Numerical research on heat transfer enhancement for high Prandtl-number fluid

The molten salt, Flibe, has been recommended as a candidate coolant material in the blanket system of the FFHR fusion reactor though it is high Prnadtl-number ( Pr) fluid that leads to low heat transfer performance. This paper, describes the results of numerical simulations performed in order to estimate the effects of cylinders as obstructions for heat-transfer enhancement in high- Pr fluid duct flow. Two-dimensional thermofluid simulations were performed for cases with 44, 24 and 48 cylinders, respectively, inserted perpendicularly to the fluid flow, and acting as heat transfer enhancers between parallel plates. From these analyses, the flow contraction created by the cylinders causes a high-vorticity around the heated wall. This high-vorticity plays an important role in the heat-transfer enhancement. In the high-vorticity region, the momentum perpendicular to a wall has a large gradient along the stream direction. In fact, the fluid flows down while rotating and “washing” the heated wall. This effect is also governed by the arrangement of cylinders. A staggered arrangement is adopted in the case with 44 cylinders, while square arrangement is employed in the cases with 24 and 48 cylinders. The enhancement of perpendicular flow is very effective when using a staggered arrangement, procuring a higher heat transfer downstream of the cylinders. The estimated pressure drop for high- Pr fluid flow was larger for the with 44 cylinders than for the cases with 24 and 48 cylinders. This result indicates that the heat transfer of high- Pr fluid flow strongly depends on the effect of flow stirring caused by obstructions.

Pattern formation in Rayleigh-Bénard convection: numerical simulation with a coupled-map-lattice model

The various patterns formed in Rayleigh-Benard convection under different conditions are numerically simulated with a coupled-map-lattice model. In the case of a lower aspect ratio (L/d=5), the simulations vividly depicted the main features of the transition process from a laminar state to a soft turbulence and then to a hard turbulence. In this case, the cellular structure in a horizontal section is also reproduced. In the case of a larger aspect ratio (L/d=30), the simulations successfully reproduced the spiral-defect chaos and target chaos in the initial stage of the pattern evolution which were recently found in experiments. In this case, for a fluid ofPr=1, it is verified in simulations that both the ideal straight rolls and spiral-defect chaos are stable attractors in the same parameter regime, and that the initial condition is a decisive factor for which one of the two is formed. In the same case, for a fluid ofPr=4, the target patterns are dominant instead of the spirals, the sizes and distributions of the target are also notably dependent on the initial condition.

Instability of convection of an ethanolwater solution in a vertical tank

An experimental and numerical investigation has been carried out into the instability characteristics of natural convection of an ethanol–water solution in a vertical tank with aspect ratio (height/width) of 15. The solution contains 39 wt% ethanol with Prandtl number . These convection cells are unsteady even at low supercritical states, similar to earlier observations for higher Pr fluids. The cause of such unsteadiness of the flow has been determined by studying the streak images constructed by superposing individual frames of a digital movie sequence. New cells are generated in the upper and lower portions of the tank and then migrate toward the centre, causing the convection cells in the mid-section to merge. At higher Gr, even the tertiary cells, which rotate in the opposite direction of the secondary cells, participate in the merging process. Numerical simulations of the two-dimensional natural convection of a Boussinesq fluid with constant thermophysical properties, carried out at low supercritical Gr equivalent to the experimental value, show the same process of cell generation and merging as that observed in the experiments. By analysing the substantial time rate of change of the kinetic energy of the fluid using the mechanical energy equation, it is determined that the energy needed for the cell generation process is supplied by the work of the dynamic pressure. The subsequent migration of the cells toward the middle is caused by the pressure gradient in the tank. The total kinetic energy of the fluid attains a relative maximum right after a merging process due to the reduction of dissipation associated with the region of strong shear between the cells.

Numerical simulation of magnetic control of heat transfer in thermal convection

We report on numerical study of effects of orientation and distribution of an external magnetic field on the reorganization of convective structures and heat transfer in thermal convection in electrically conductive fluids. The simulations were performed using a transient RANS (T-RANS) approach in which the large-scale deterministic structures are numerically resolved in time and space and the unresolved contribution is modelled using an algebraic stress–flux three-equation subscale model. For low Prandtl ( Pr) fluids the subscale model was extended to include Pr-dependent molecular dissipation of heat flux. The method was first validated in natural convection in a side-heated cubical enclosure subjected to magnetic fields of different orientation, strength and penetration depth, showing good agreement with the previous benchmark studies. Subsequently, a series of simulations was performed of turbulent Rayleigh–Bénard convection subjected to different magnetic fields over a range of Rayleigh ( Ra) and Hartmann ( Ha) numbers. The computed Nusselt number showed good agreement with the available experimental results. Numerical visualization of instantaneous flow patterns showed dramatic differences in the convective structures and local heat transfer for different orientation of the magnetic field with respect to the gravitation vector. A gradual, step-like increase in the magnetic strength revealed an interesting outcome of the “competition” between the buoyancy and the Lorentz forces, leading first to chaotic transition and eventually to laminarization. For specific ranges of Ha, it was found that a local magnetic field confined to the wall boundary layer along the thermally active walls provides almost equal effects as the homogeneous field over the whole flow, indicating an interesting possibility for controlling thermal convection and associated heat transfer.

On the Prandtl or Schmidt number dependence of the turbulent heat or mass transfer coefficient

Numerical experiments using a direct numerical simulation (DNS) of turbulent flow between two parallel plates in conjunction with Lagrangian scalar tracking (LST) of trajectories of thermal markers in the flow field are conducted for Prandtl or Schmidt numbers between 0.01 and 50,000. The LST methodology is used to generate mean temperature profiles as a function of the entry distance in the case of a step change in heat or mass flux at the walls of the channel. The heat transfer coefficient and the Nusselt number ratio, Nu( x)/ Nu( x→∞), downstream from the step change in the wall flux are determined for the range of Pr or Sc fluids examined. Relations between the heat or mass transfer coefficient at the fully developed part of the channel and Pr or Sc are proposed for low and high Pr or Sc cases. Finally, unified correlations, which provide the heat or mass transfer coefficient for all Pr or Sc, in the Reynolds number range examined, are proposed. Also, the exponent of the asymptotic dependence of the eddy diffusivity close to the wall is obtained.

Oscillatory Marangoni flow in half-zone liquid bridge of molten tin supported between two iron rods

Two series of three-dimensional (3-D) numerical simulations were conducted in order to understand 3-D Marangoni convection in half-zone liquid bridges of molten tin. In one series, we determined the second critical Marangoni number for liquid bridges of low-Prandtl-number fluid ( Pr=0.009) at different aspect ratios, As, based on the well-known simple bridge geometry which assumes the liquid bridge is supported between two differentially heated isothermal solid discs. A new type of oscillatory flow was first observed in a simulation of a tin liquid bridge of As=2.0 under highly supercritical conditions at Ma=1.4 Ma c2 , the whole flow and temperature fields with an azimuthal wave number m=1, exhibiting an apparently twisting oscillations back and forth around the axis, rotates very slowly in the azimuthal direction. In the second series, we conducted numerical simulations based on much realistic bridge geometry. Special emphasis was placed on the effects of less conductive supporting rods on the stability limit of the axisymmetric steady flow and the onset of flow oscillations. Present simulations reveal that the 3-D flow causes non-uniform temperature distributions in the supporting rods. We proposed a new definition of effective temperature difference (Δ T e) acting on the liquid surface to evaluate the Marangoni number. Thus determined first and second critical Marangoni numbers fall close to, but slightly larger than, those predicted by the simple model. However the deviations are less than 3%. On the other hand, present simulations revealed that very small spatial offsets of temperature measuring points cause significant error in Δ T measurement because of the conduction resistance in the rod under large heat flux. This effect is very important for any liquid bridge experiments using low- Pr fluid. A simple conduction dominant model provides reasonable estimate of Δ T e from the temperature difference measured by thermocouples.

Transport properties for turbulent dispersion from wall sources

AbstractThe dispersion of a passive contaminant by turbulence is not only intrinsically interesting, but also is fundamental to practical heat‐ and mass‐transfer problems. The mechanism of turbulent dispersion from the wall and effects of the molecular Prandtl number are examined. Transport properties for scalar dispersion from an instantaneous line source at the wall of a parallel‐plate channel in which fully developed turbulent flow occurs, as well as from a continuous line source, are studied. Numerical experiments using a direct numerical simulation (DNS) of the flow, combined with Lagrangian scalar tracking (LST) of trajectories of thermal markers in the flow field, are conducted. The method is applied for a wide range of molecular Prandtl (Pr) or Schmidt (Sc) number fluids (0.1⩽Pr⩽50,000, which corresponds to liquid metals, gases, refrigerants, lubricants and electrochemical fluids). Results from the DNS/LST method are compared with experimental data, which are available for low Pr or Sc fluids. The turbulent diffusivity and turbulent Prandtl number for the plume that results from a line source are calculated, and an appropriate scaling is proposed. Finally, a model is developed for the prediction of the mean temperature or mean concentration profile as a function of Pr or Sc.

Approaches of fusion science to global warming from the perspective of thermofluid research

Scientific interest in the environmental and meteorological fields has been focused on the estimation of the temperature rise on the earth in the near and far future. The temperature rise is estimated by a gas transfer flux. It is very difficult to measure and estimate the gas transfer rate resulting from the air–sea interaction because of very high Schmidt number ( Sc) turbulent fluid flow with free surface deformation. On the other hand, the utilization of high Prandtl number ( Pr) fluid flows, like a Flibe, with free surface as a coolant in an advanced magnetic fusion reactor and as a chamber protection scheme in an inertial confinement fusion reactor have been considered. From the perspective of thermofluid research, it would be very important to discuss on some common aspects between fusion nuclear technology and global warming problem. Since the thermal diffusivities of high Pr or Sc fluids are very small, when the high temperature or concentration regions appear on the free surface caused by plasma radiation or carbon-dioxide gas absorption, respectively, the scalar transport from the free surface to the bulk flow must be very slow compared with the fluid motion. In this paper, some common aspects between the heat transfer of high Pr free surface flow in fusion engineering and the mass transfer of high Sc free surface flow in the global warming problem are discussed.

Experimental study on transition to oscillatory thermocapillary flow in a low Prandtl number liquid bridge

The transition behavior from stationary to oscillatory thermocapillary flow was experimentally studied with a liquid bridge of molten tin (Prandtl number Pr=0.01) of 1.5 mm in radius. The experimental difficulties such as preventing oxidation of the melt surface and detecting a small amplitude of surface temperature fluctuation without any external disturbances on the flow field were successfully solved by employing a high vacuum condition, ion etching to remove the oxide film on the surface and a high resolution radiation thermometer. A temperature fluctuation was first observed at a Marangoni number Ma of 43.3. Frequency and amplitude of the fluctuation were 0.08 Hz and 0.3 K, respectively, which is significantly larger than temperature resolution of the radiation thermometer used. The temperature oscillation developed with increasing temperature difference imposed between the upper and lower ends of the liquid column and then observed a standing wave of 0.42 Hz with very strong amplitude at a Marangoni number of 91. The flow transition was directly proved by a surface flow visualization experiment. Tin-oxide particles, which were pre-mixed with molten tin, were observed to repeat oscillatory movement along the circumferential direction with 0.5 s interval after the onset of the oscillation. Those results are the first and clear experimental evidence for the transition to oscillatory flow in a low Pr fluid by a non-contact diagnostic, which has never been observed yet. Validity of the experimentally determined critical Marangoni number and the frequency of the standing wave were discussed by comparing with a numerical result.

Numerical simulation of oscillatory Marangoni flow in half-zone liquid bridge of low Prandtl number fluid

A set of numerical simulations was conducted using a finite difference method to understand the general feature of oscillatory Marangoni convection in half-zone liquid bridges of low Prandtl number fluids (Pr=0, 0.01, 0.02) with a cylindrical liquid surface over a wide aspect ratio range (As=0.6 to 2.2). The simulation results indicated that under smaller temperature differences the flow in the liquid bridge was axisymmetric but it became unstable against three-dimensional (3-D) disturbances beyond a certain threshold value of temperature difference, i.e., the flow became steady 3-D flow at and beyond the first critical Reynolds number Re c1. This steady 3-D flow became unstable against time-dependent 3-D disturbances beyond a second critical condition, Re c2. The numerical simulations revealed the critical conditions and flow structures in detail for Pr=0 fluid and rough sketches for fluids of Pr=0.01 and 0.02. The present results of Re c1 and Re c2 showed good agreements with those of linear stability analyses and with available numerical results. A stability map for low Pr fluids (Pr=0, 0.01 and 0.02) was proposed.

Limiting Values for Free-Convection Induced Flow Rates in Vertical Eccentric Annuli with an Isothermal Boundary

Fully developed laminar natural convection in vertical eccentric annuli has been investigated under fundamental thermal boundary conditions of the first and third kinds. For conditions of the first kind, numerical solutions are presented showing the effect of eccentricity on the velocity profiles and the local Nusselt number in an annulus of radius ratio 0.5. Limiting values for the induced flow rate and the average Nusselt numbers are presented for a fluid of Pr = 0.7 over wide ranges of eccentricity and annulus radius ratio (0.1-0.9). Closed-form analytical solutions are obtained for fundamental conditions of the third kind and the corresponding variations in the limiting induced flow rates with eccentricity are presented.

Direct numerical simulation of turbulent free-surface high Prandtl number fluid flows in fusion reactors

A high Pr fluid flow, such as FLiBe, has less heat transport capability because of low thermal conductivity and very thin thermal boundary layer. Until today, turbulent flow and heat transfer feature of high Pr fluid, especially as for a free-surface flow configuration, is not so clear because of the difficulties in velocity and temperature measurements in such a very thin boundary layer. In the present study, Direct Numerical Simulation (DNS) of turbulent free-surface flow of various Pr fluids has been carried out with a constant heat flux from the free surface and an adiabatic condition imposed on the wall. From the DNS, turbulent statistics have been obtained and the flow structure has been investigated via computational flow visualization technique. One of the highlights of this study is that the turbulent diffusivity near the free-surface increases when Pr increase and it leads to a very high-temperature region which could appear there, and then eventually a “laminarization” of fluid flow could occurr because of less turbulent heat flux there. This means that it is necessary to consider some turbulent heat transfer and thermal mixing augmentation for high Pr fluid flows.

Critical conductivity ratio for conjugate heat transfer in eccentric annuli

Conjugate laminar forced convection heat transfer in the entry region of eccentric annuli is numerically investigated. Heat transfer parameters are presented for a fluid of Pr = 0.7 flowing in an annulus of radius ratio 0.5 for four values of dimensionless eccentricity ranging from 0.1 to 0.7. Solid‐fluid conductivity ratio (KR) is varied to cover the range for practical cases with commonly encountered inner and outer tube thickness. Boundary conditions applied are isothermal heating of the inner surface of the core tube, while the outer surface of the external tube is maintained at the inlet fluid temperature. Limits for KR above which the conjugation can be neglected are obtained.

低 Pr 流体液柱内の3次元マランゴニ対流の数値シュミレーション

低 Pr 流体液柱内の3次元マランゴニ対流の数値シュミレーション

Towards the development of a Reynolds-averaged algebraic turbulent scalar-flux model

Abstract In order to derive a possible direction for developing Reynolds-averaged algebraic turbulent scalar-flux models, a priori explorations are attempted by processing the LES data presently performed for channel flows under several flow-boundary conditions including shear-free boundaries. The present calibration has elucidated that the turbulent scalar-flux vectors obtainable from the simple generalized gradient-diffusion hypothesis (GGDH) hardly align with the simulation results in wall-shear flows at Pr ⩾0.71. However, the GGDH form returns a quite reasonable approximation in shear-free flow regions and/or lower Pr fluid cases. In the former flow cases, it has been found that an introduction of quadratic products of the Reynolds-stress tensor into the gradient diffusion model may improve the predictive performance.

Transitions and chaos in natural convection of a fluid with Pr = 0.1 in a horizontal annulus

Bifurcation sequence to chaos in natural convection in a horizontal annulus is numerically investigated for the fluid of Pr = 0.1. As Ra is increased, a transition from a steady unicellular flow to an oscillatory multicellular flow with a counter-rotating eddy on the top of the annulus occurs. After the first Hopf bifurcation from steady to monoperiodic flow, a period-3 solution first appears. Quasi-periodic flow and two period-doubling bifurcations are recorded before chaos, and a window of period 4 is observed between chaotic states.

Free Convective Transition of Intermediate Prandtl-Number Fluids in a Wide-Gap Horizontal Annulus

Natural convection in a wide-gap horizontal annulus is considered, and the transition of flows and the bifurcation phenomenon are investigated for the fluids with Pr=0.2 and 0.3. At Pr=0.2, a bicellular flow pattern is observed at high Rayleigh number, and the solution is unique. At Pr=0.3, both the steady unicellular and bicellular flows exist above a certain critical Rayleigh number. For the fluids of Pr=0.2, the bicellular flow can be obtained by the impulsive heating of the inner cylinder, but it is not obtained from the zero initial condition for Pr=0.3. Hysteresis phenomena have not been observed. A transition from a bicellular flow to a unicellular flow occurs for Pr=0.3.

CONJUGATE NATURAL CONVECTION HEAT TRANSFER IN AN OPEN-ENDED VERTICAL CONCENTRIC ANNULUS

This paper is concerned with the steady conjugate heat transfer problem in vertical open-ended concentric annuli under the laminar natural convection flow regime. A finite difference technique has been used to solve the governing equations, with the outer surface of the outer tube wall being isothermally heated while the inner surface of the inner tube is kept adiabatic. Numerical results are presented for a Newtonian fluid of Pr = 0.7 in a fluid annulus of radius ratio 0.5. We present the effect of solid-fluid conductivity ratio on the induced flow behavior and some engineering parameters, such as the heat absorbed and the mixing-cup temperature.

Spreadsheet numerical simulation for developing laminar free convection between vertical parallel plates

A detailed spreadsheet simulation for laminar free convection with simultaneously thermally and hydrodynamically developing boundary layer in the entrance region between two vertical parallel plates is presented. The boundary layer governing equations are expressed in an implicit finite difference form. This results in sets of algebraic equations. These sets of algebraic equations are solved simultaneously using a non-iterative scheme. Spreadsheet setup for the developing fluid and heat flow problems, the powerful abilities of the spreadsheet and macro creation for automated solutions are emphasized. Plots of the results are presented using the spreadsheet-built-in powerful graphical facilities. The spreadsheet simulation results are compared with presently obtained results for the same problem via a FORTRAN code. Moreover, the numerically obtained developing axial velocity and temperature profiles at large distance downstream the entrance, for high enough channels, show excellent agreement with the available fully-developed analytical profiles. Flow and heat transfer parameters such as the channel height required to naturally induce a specific flow rate, the local and averaged Nusselt number and the amount of heat absorbed by the fluid through the channel have been calculated for a fluid of Pr=0.7, air, under two types of thermal boundary conditions. These boundary conditions are namely boundary conditions of the first and third kind.

Transient combined natural convection-conduction in open-ended vertical concentric annuli

Transient conjugate natural convection heat transfer in open-ended vertical concentric annuli is investigated numerically. The governing equations of an induced laminar flow for a fluid of Pr=0.7 are solved using a finite-difference technique. The heating is achieved by a step change in the temperature of the outer surface of the outer tube while the inner surface of the inner tube is kept adiabatic. The range of Grashof number considered is 500≤Gr*≤105. The effects of solid-fluid conductivity ratio and diffusivity ratio on the transient induced flow characteristics are presented.