Low Pr Fluids Research Articles

Domain partition leads to a manifold increase of heat transport in Rayleigh–Bénard convection at low Prandtl number

Results of an exploratory numerical study of Rayleigh–Bénard convection of a low-Pr fluid in a cylinder with a vertical partition are reported. It is shown that a partition may lead to a many-fold increase in the rate of convection heat transfer. The effect is associated with the formation of coherent hot and cold streams separated by the partition. The heat transfer enhancement is particularly strong in tall cylinders and requires that the partition penetrates into the thermal boundary layers near the top and bottom walls.

Magneto laminar mixed convection and entropy generation analyses of an impinging slot jet of Al2O3-water and Novec-649

In this study, the cooling capability and heat transfer characteristics in the mixed convective regime of a hot surface by a confined impinging slot jet in the presence of a uniform magnetic field have been investigated numerically. Besides, the second law of thermodynamics is applied to analyze the entropy generation inside the simulation medium. The simulations are for a two-dimensional slot jet that is directed vertically downward and impinges on a hot isothermal surface at the bottom. The set of non-dimensional governing equations is solved using ANSYS Fluent, which employs a finite volume approach in combination with a non-dimensionalization scheme. Flow patterns, isotherms, and entropy generation rates were calculated for various fluids (Air, Water, Novec-649, Al2O3-Water (3 %) nanofluid), that cover a wide range of Prandtl number values (Pr = 0.71–12.64), in the presence of a uniform magnetic field with Hartmann number values ranging from 0 (no magnetic field) to 100 (strong magnetic field). We prove that the Prandtl number plays a key role in determining heat transfer efficiency and entropy generation. Fluids with a high Pr number are more efficient for surface cooling, although they generate more entropy than low Pr fluids. Nanofluid with a high-volume fraction can be a better choice rather than air and water. On the other hand, we show that applying the magnetic field result in a very efficient method to reduce entropy generation although they degrade heat transfer efficiency. It is interesting that at a higher magnetic field, a high Prandtl number plays a better role. The percentage of reduction of Nuave by applying magnetic field is 28.5 % for air (Pr = 0.71), 45.2 % for water (Pr = 6.2), 43.4 % for Al2O3-water nanofluid (Pr = 4.91) and 48.3 % for Novec-649 (Pr = 12.64).We postulate that applying magnetic fields combined with high Pr number fluids, could provide an excellent balance between heat transfer efficiency and exergy destruction, thus providing efficient control options for thermal management and heat transfer.

Development and performance research of a helical longitudinal-groove tube with secondary flow reinforcement for heat transfer

The secondary flow has a strong promotion effect on heat transfer in the tube. In order to further utilize the secondary flow phenomenon to strengthen heat transfer of the helical tube, in this paper, a secondary flow enhanced heat transfer helical tube is developed, and stable secondary flow with high strength is obtained. The structure parameters are optimized with the highest comprehensive evaluation factor as the goal. The results show that compared with helical transverse-groove tube and helical grooved tube, helical longitudinal-groove tube has the best heat transfer performance. The new structure's enhanced heat transfer effect for high-Pr number fluid is better than that of low-Pr number fluid, and the enhanced heat transfer effect is not affected by the inlet Reynolds number. The helical angle of helical groove has a greater influence on the comprehensive evaluation factor, while the groove depth and the number of heads have a smaller influence on the comprehensive evaluation factor. The optimal parameter scheme is: The groove depth is 0.5 mm, the helical angle of helical groove is 82°, the head number of helical groove is 1, the comprehensive evaluation factor of helical longitudinal-groove tube compared with ordinary helical tube is 1.173

Numerical Study of Low Pr Flow in a Bare 19-Rod Bundle Based on an Advanced Turbulent Heat Transfer Model

Compared to assuming a constant turbulent Prandtl number model, an advanced four-equation model has the potential to improve the numerical heat transfer calculation accuracy of low–Prandtl number (Pr) fluids. Generally, a four-equation model consists of a two-equation k−ε turbulence model and a two-equation kθ−εθ heat transfer model. It is essential to analyze the influence of dissimilar turbulence models on the overall calculation accuracy of the four-equation model. The present study aims to study the effect of using different turbulence models on the same kθ−εθ heat transfer model. First, based on the open-source computational fluid dynamics software OpenFOAM, an advanced two-equation kθ−εθ heat transfer model was introduced into the solver buoyant2eqnFoam, which was developed based on the self-solver buoyantSimpleFoam of OpenFOAM. In the solver buoyant2eqnFoam, various turbulence models built into OpenFOAM can be conveniently called to close the Reynolds stress and an advanced two-equation heat transfer model can be utilized to calculate the Reynolds heat flux of low-Pr fluids. Subsequently, the solver buoyant2eqnFoam was employed to study the fully developed flow heat transfer of low-Pr fluids in a bare 19-rod bundle. The numerical results were compared and analyzed with the experimental correlations and other simulation results to validate the effectiveness and feasibility of the solver buoyant2eqnFoam. Furthermore, the influence of combining different turbulence models with the same two-equation kθ−εθ heat transfer model was also presented in this study. The results show that the turbulence model has a considerable influence on the prediction of turbulent heat transfer in the high Peclet number range, suggesting that it should be prudent when picking a turbulence model in the simulations of low-Pr fluids.

Development and Assessment of an Isotropic Four-Equation Model for Heat Transfer of Low Prandtl Number Fluids

In the simple gradient diffusion hypothesis, the turbulent Prandtl number (Prt) with a constant of 0.85 is difficult to accurately predict for liquid metals having low Prandtl numbers (Pr), while a four-equation model can improve this solution by introducing the turbulence time-scale into the calculation of turbulent thermal diffusivity. However, the four-equation model’s transport form and numerical stability are so complex that suitable commercial code is lacking. Therefore, an isotropic four-equation model with simple Dirichlet wall boundary conditions is built in the present work. Based on the open-source computational fluid dynamics program OpenFOAM, the fully developed velocity, temperature, Reynolds stress, and heat flux of low Pr fluids (Pr = 0.01–0.05) in the parallel plane are obtained by numerical simulation. The results show that the time-average statistics predicted using the present four-equation model are in good agreement with the direct numerical simulation data. Then, the isotropic four-equation model is used to analyze the flow and heat of liquid metal (Pr = 0.01) in a quadrilateral infinite rod bundle. The numerical results are compared with the various and available experimental relationships. The Nusselt numbers calculated using the isotropic four-equation model are betweenness the available correlations, while the turbulent Prandtl number model using a constant of 0.85 over predicts heat transfer. More detailed local heat transfer phenomena and distribution of low Pr fluids are obtained using the present isotropic four-equation model.

Critical role of Prandtl number on multiple steady states during natural convection in square enclosures: Analysis of heat transfer rates, flow and thermal maps

The effect of Prandtl number (Pr) on the multiplicity of the steady states (flow and temperature maps) is investigated for the natural convection of Newtonian fluids within a square enclosure involving hot bottom wall, cold side walls and adiabatic top wall. The analysis is based on the steady state governing equations, which are solved by penalty Galerkin finite element method and Newton–Raphson solution scheme. A novel perturbation technique has been developed, which is applied in conjunction with an in-house continuation scheme for the initiation of various symmetric as well as asymmetric steady states. The current computation strategy involving perturbation and continuation schemes leads to a rich bifurcation diagram in the parameter space of Pr (0.01⩽Pr⩽10) for Ra (Rayleigh number) =106. It is found that the occurrence of multiple steady states depends on Pr. Only one symmetric solution is obtained in the high–Pr regime (Pr>0.42), while a highly populated bifurcation diagram consisting of 6 symmetric branches, 18 asymmetric branches and 4 isolas is obtained in the low–Pr regime (especially for Pr≲0.05). The solution branches correspond to a wide spectrum of flow structures involving single cell, multiple cells, reverse-cells, corner-cells, horizontally stacked cells, vertically stacked cells etc., which are reported for the first time. These flow structures result in a wide range of Nusselt numbers (average heat transfer rates) at a given Pr, especially for the low–Pr fluids (such as liquid metals). The flow structures are critically analyzed in terms of the location of the flow intensification and its impact on the overall heat transfer rates. It has been shown that the overall heat transfer rates for the low–Pr fluids can be significantly enhanced (80 –100% in few cases) based on corner-cells or single cell driven flow.

On the Simulation of Turbulent Heat Transfer for Low-Pr Fluid Cross-Flow in Tube Banks

On the Simulation of Turbulent Heat Transfer for Low-Pr Fluid Cross-Flow in Tube Banks

Influence of Prandtl number on bifurcation and pattern variation of non-isothermal annular Poiseuille flow

The relative influence of momentum diffusivity and thermal diffusivity, in terms of the Prandtl number (Pr), on the finite-amplitude instability of a non-isothermal annular Poiseuille flow (NAPF) is analyzed. The limiting value of the growth of instabilities under nonlinear effects is studied by deriving a cubic Landau equation. Emphasis is given especially on studying the impact of the low Prandtl number and the curvature parameter (C) on the bifurcation and the pattern variation of the secondary flow for both axisymmetric and non-axisymmetric disturbances. The finite-amplitude analysis predicts that in contrast to NAPF of water or fluid with Pr ≥ O(1) where the flow is supercritically unstable, the NAPF of low Pr fluids, particularly liquid metals, has shown both supercritical and subcritical bifurcation in the vicinity as well as away from the critical point. The nonlinear interaction of different harmonics for the liquid metal predicts a lower heat transfer rate than those by the laminar flow model, whereas for a fluid with Pr > 2, it is the other way. The maximum heat transfer takes place for the considered minimum value of C. For fluids with low Pr, a probable lower critical Rayleigh number is obtained. The corresponding variation in neutral stability curves as a function of wavenumber reveals that the instability that is supercritical for some wavenumber may be subcritical or vice versa at other nearby wavenumbers. The structural feature of the pattern of the secondary flow under the linear theory differs significantly from those of the secondary flow under nonlinear theory away from the bifurcation point. This is a consequence of the intrinsic interaction of different harmonics that are responsible for the stabilizing or the destabilizing nature of different components in the disturbance kinetic energy balance.

Modified turbulent Prandtl number model for helium–xenon gas mixture with low Prandtl number

Gas-cooled space nuclear-reactor systems generally adopt the helium–xenon mixture (He–Xe) as a working fluid and coolant, the Prandtl number (Pr) of which is low for recommended mixing ratios. Many studies have shown that the turbulent Pr (Prt) is not constant and that it is greater than 0.85 for low-Pr fluids. However, the Prt in the Reynolds-averaged Navier–Stokes model is generally set to 0.85 by default, which inevitably results in large prediction errors with respect to the flow and heat transfer of low-Pr He–Xe. In this paper, the Prt model of He–Xe is examined using theoretical analysis and numerical simulations. Based on the existing models applicable to liquid metals, the spatial distribution of the Prt model is modified. The Prt of turbulent core region is expressed as a function form, in which the local Reynolds number (Re) is introduced to characterize the trend of Prt in the near-wall region. With the undetermined coefficients obtained using numerical simulation, a new modified Prt model for low-Pr He–Xe is proposed. The results suggest that the new model can better reflect changes in Prt with Re, Pr, and the distance from the wall. The numerical predictions of Prt distribution at different radial positions are consistent with the analytical results, especially the distribution of the near-wall region. For the convective heat transfer simulation, the new Prt model has optimal numerical accuracy. In the future, the proposed Prt model can be used to further study the flow and heat transfer characteristics of He–Xe.

Linear instability of concentric annular flow: Effect of Prandtl number and gap between cylinders

The stability of non-isothermal Poiseuille flow in a coaxial annular domain is studied using normal mode analysis. The stably stratified flow (i.e., when buoyant force is in the direction of forced flow) is induced due to external pressure gradient and maintenance of linear variation of the temperature of the inner cylinder. We have emphasized the impact of the gap between cylinders in terms of curvature parameter (C) and Prandtl number (Pr) on the instability of the flow under axisymmetric as well as non-axisymmetric disturbances. In general, it has been found that the flow of low Pr fluids under axisymmetric disturbance is more stable in comparison with the flow under non-axisymmetric disturbance. When the gap between cylinders is relatively small (i.e. C is large), the flow under non-axisymmetric is most stable for the fluids having high Pr. It is known that the Newtonian pipe flow is linearly stable for all values of Reynolds number (Re). However, in the present study, we have seen the instability of the pipe flow with a thin rod placed at the center even for a very small value of heat source intensity (in terms of Rayleigh number) at Re=2000. Here the disturbance velocity is concentrated in the vicinity of the inner wall and instability is due to transfer of kinetic energy from the basic flow through Reynold’s stress. Depending on the value of controlling parameters, three types of instability: thermal-shear, interactive, thermal-buoyant have been observed. In general, for a fixed value of Pr, the type of instability is not affected by C and Re. The non-isothermal Poiseuille flow of low Pr (including mercury and gases) is governed by thermal-shear instability and the same of high Pr (including liquid and oil) is governed by thermal-buoyant instability.

CFD SIMULATIONS OF THE HELIUM-XENON MIXTURE FLOW AND HEAT TRANSFER

Helium-xenon gas mixtures are generally proposed for the working fluid of gas-cooled space nuclear reactors with Brayton cycle to achieve a compact design. The Prandtl number (Pr) of helium-xenon mixtures at certain mixing ratios can be significantly lower than that of pure gases, inducing problems in describing the turbulent heat transfer. In this paper, investigations are performed to study the feasibilities of different CFD methods which were used to simulate the flow and heat transfer of helium-xenon mixtures. The thermophysical properties that are used in the simulation are firstly re-examined. Then, various turbulent models are employed to test their applicability by comparing the simulations with experimental data. It shows that all calculations have a general consistent tendency with, but lower than, experimental data. The SST κ-ω model has a better prediction ability. Considering the fact that the turbulent Prandtl number (Prt) varies perpendicular to the wall surface for the low Pr fluids, the Kays-Crawford Prt model is introduced into the SST κ-ω model, and the simulation results prove to be improved significantly in various cases.

Influence of Induced Magnetic Field on Thermal MHD Flow

This paper studies the influence of an induced magnetic field on the forced convective heat transfer from an isothermal sphere in the presence of an applied magnetic field. Irrespective of the choice of magnetic Reynolds number, the induced magnetic field is also taken into consideration and, therefore, we have solved the full-magnetohydrodynamic equations in (ψ-ω-A) formulation. We have used a higher order numerical scheme with compact stencil in spherical polar coordinates for discretization. We have observed that the application of magnetic field on the flow has a twofold effect. Firstly the recirculation bubble vanishes, and secondly it alters the heat transfer coefficient. In particular, the heat transfer gets enhanced near the top of the sphere, while in the upstream and downstream regions, it diminishes. We have also found that the magnetic Reynolds number aids in the reduction of heat transfer. Our results on the heat transfer coefficient in the liquid sodium flow problem concur with the available experimental data. Further, we have observed that the effect of magnetic Reynolds number on a low Pr fluid is negligible.

Marangoni flow in floating half zone of molten tin

Gravity affects the stability of Marangoni flow in floating half zone of low-Pr fluids through two different factors, i.e., the buoyancy and the static deformation of the free surface shape. In the present study, influence of these two factors are evaluated by unsteady three-dimensional (3D) simulations for a realistic model of floating half zone of molten tin (Pr=0.009) with an aspect ratio As=2.0 under a ramped temperature difference (1.19K/min) between the top and bottom ends of two iron supporting rods. The corresponding first critical conditions for the onset of 3D asymmetric non-oscillatory flows and the second critical conditions for the onset of 3D oscillatory flows are determined. Simulation results indicate that the fee surface deformation is the most influential factor for the critical conditions of the flow transitions. Buoyancy is less influential to the flow transitions. However, buoyancy causes multiple step transitions between different 3D asymmetric non-oscillatory flow modes.

Heat transfer to liquid metals in a hexagonal rod bundle with grid spacers: Experimental and simulation results

Thermal-hydraulics is a key scientific subject to be investigated for the development of innovative reactor systems. For applications using liquid metals as coolants this task is particularly challenging due to their very low Prandtl number (Pr), preventing the application of common analogies between the turbulent transport of momentum and heat. Thus specific models and validation data with low-Pr fluids are required for representing safety-related thermal-hydraulic scenarios, such as heat transfer in fuel assemblies.Aiming to achieve a better understanding of these flow scenarios, in the European FP7 cooperation project THINS (2010–2014) this subject is investigated at three complementary levels. An experimental campaign consisting of an electrically heated 19-pin hexagonal rod bundle cooled by lead-bismuth eutectic (LBE) is carried out at typical reactor conditions in terms of operating temperature, power density and velocity. Both pre- and post-test analyses using existing numerical tools are performed for evaluating the differential pressure and heat transfer characteristics of the test section. Moreover, advanced turbulence models and numerical techniques are developed and applied to this geometry.Overall, the goals of this project are achieved. The experiments show good degree of repeatability and provide reliable validation data. For intermediate flow rates a good agreement is observed with the results of the heat transfer simulations, based on a constant turbulent Prandtl number. Two advanced approaches for representing the turbulent heat transport considering look-up tables and a four-equation model are successfully tested and overcome the limitations of using a constant turbulent Prandtl number. Using a coarse-grid CFD approach the turbulent momentum transport along two bundles is studied, yielding a good accuracy with a 1000-fold mesh reduction.

Unsteady numerical simulation of flow and heat transfer in a uniformly Joule-heated rectangular pool

Based on the Joule heating nuclear waste treatment technology, a series of numerical simulation of fluid flow and heat transfer based on two-dimensional non-steady state model has been studied, the fluid is in a rectangular cavity with an aspect ratio of 2, the direct current contributes heat for heating the process medium by a pair of plate electrodes, the top wall is cooled with atmosphere and all the other walls are kept thermally insulated. For Pr=1 fluid, the thermally driven stable convection and the electromagnetically driven stable flow can be observed respectively or both gravitationally and electromagnetically driven stable convection exhibit. The threshold Hartmann number for the first transition from an ax symmetric 2 cells steady flow to a steady non-asymmetric state 1 roll flow is 159.687, where the Nusselt number exhibits a minimum value. And the second transition from non-asymmetric state 1 roll flow to a steady asymmetric 2 rolls flow is fixed at Ha=178.88. It is found that physically realizable periodic oscillation flow evolves for the low Pr fluid (Pr=0.01), which can significantly affect the heat transfer. These transient characteristics of velocity and temperature fields are presented graphically.

Prandtl and capillary effects on heat transfer performance within laminar liquid–gas slug flows

This paper investigates a two-phase non-boiling slug flow regime for the purposes of enhancing heat transfer in microchannel heat sinks or compact heat exchangers. The primary focus is upon understanding the mechanisms leading to enhanced heat transfer and the effect of using different Prandtl number fluids, leading to variations in Capillary number. Experimental work was conducted using Infrared thermography and results are presented in the form of Graetz solution, spanning both the thermal entrance and fully developed flow regions. Nusselt numbers enhancements were observed throughout when data was reduced to account for void fraction. However, the gaseous void was also noted to demonstrate an artificial increase with greater thicknesses of the liquid film, due to higher Capillary numbers. Up to 600% enhancement in heat transfer rates were observed over conventional Poiseuille flow. This was verified through Nusselt number measurements over inverse Graetz number ranges from 10 −4 to 1 and slug length to channel diameter ratios from 0.88 to 32. Varying Prandtl and Capillary numbers caused notable effects in the transition region between entrance and fully developed flows. Significant Nu oscillations were observed for low Pr fluids due to internal circulation within the slug. However, these oscillations are observed to be damped out when higher Prandtl number fluids are employed. The thickness of the liquid film surrounding the gas bubbles is shown to have a significant influence on heat transfer performance. Overall, this study provides a greater understanding of the mechanisms leading to significant enhancements in heat exchange devices employing two-phase gas–liquid flows without boiling.

Analysis of entropy generation for distributed heating in processing of materials by thermal convection

Analysis of entropy generation has been carried out for square cavities with distributed heated sources filled with various materials involving wide range of Pr(=0.015, 0.7, 10, 1000) during the conduction and convection regime within Ra(=10 3 − 10 5). Entropy generation terms involving thermal and velocity gradients are evaluated accurately based on elemental basis set via Galerkin finite element method. Local entropy maps are analyzed in detail for various cases and the dominance of thermal and frictional irreversibilities is studied via average Bejan number. The heat transfer irreversibility is found to dominate during conduction regime while the fluid friction irreversibility dominates the entropy generation in the convection regime, except for the low Pr fluid based on the heating configuration of the cavity. Further, the variation of total entropy generation has been observed to be similar for different heating configurations for higher Pr fluids (=10, 1000) whereas, the configuration of cavity has been found to have little effect on total entropy generation for fluids with Pr = 0.7 during both conduction and convection regimes. Thermal mixing and degree of temperature uniformity due to distributed heating in various cases are also reported and optimum cases for processing of various fluids are presented based on minimum entropy generation.

Magnetic field effect on the cooling of a low-Pr fluid in a vertical cylinder

Results of direct numerical simulations are presented for the transient and turbulent natural convection cooling of an initially isothermal quiescent liquid metal placed in a vertical cylinder in the presence of a vertical magnetic field. The electrically conductive low-Prandtl number fluid is put to motion when the cylindrical wall is suddenly cooled to a uniform lower temperature. For this particular cooling process, the flow is characterized by three sequential almost discrete stages: (a) development of momentum and thermal boundary layers along the cylindrical cold wall, (b) intrusion of the cooled fluid into the main fluid body, and (c) flow and thermal stratification. The selected Rayleigh numbers in the present study are high enough so that turbulent convection is established. The numerical results show that the magnetic field has no observable effect at the initial stage of the vertical boundary layer development and conduction heat transfer is favored during the intrusion stage. An interesting effect of the magnetic field during the stratification stage is the deceleration of the cooling process for low Rayleigh numbers and its acceleration for high ones. This dependence of the magnetic field effect on the Rayleigh number was found to be related to the cold vortices emanating from the vertical boundary layer. In contrast with the hydrodynamic cooling, the magnetic field was also found to accelerate the cooling near the bottom of the cylinder.

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.

Oscillatory Transition of Axisymmetric Flow in Partially Confined Thermo-capillary Bridges of Low-Pr Fluids: Effect of Centrifugal and Elliptic Instability Mechanisms

Oscillatory Transition of Axisymmetric Flow in Partially Confined Thermo-capillary Bridges of Low-Pr Fluids: Effect of Centrifugal and Elliptic Instability Mechanisms