High Pr Fluid Research Articles

Experimental investigation of the Reynolds analogy for high Prandtl number fluid with repeated rib roughness

Reynolds analogy describes the relationship between friction (f/2) and heat transfer (St) owing to their superficial resemblance. However, Reynolds analogy is limited to simple geometries with a Prandtl number (Pr) close to unity. To extend Reynolds analogy, we measured the St and f/2 simultaneously using a high Pr fluid in duct flow in vertical duct flow with repeated rib roughness. The experiments were performed at a fixed value of Pr, 2014, Reynolds number (Re) ranging from 9.1 × 103 to 9.6 × 104, and relative roughness (e/D) ranging from 0.01 to 0.04. In the high Pr fluid, the St was much lower than f/2, as most of heat exchange occurred in the conduction sublayer, resulting from a thin thermal boundary layer. On the rough surface, both f/2 and St were higher than on the smooth surface. However, the influence of Re and e/D was different. The differences stem from that the corresponding phenomenon to pressure drag in friction does not exist in heat transfer. The extended Reynolds analogy correlation was developed. In addition, the efficiency factor was defined as the ratio of the enhancement rates of St and f/2 on the rough surface to those on the smooth surface. The efficiency factor decreased with Re and e/D, while it increased with Pr.

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

Application of adjoint-based sensitivity analysis to natural circulation of high-Pr fluid inside heat transport system

Various passive safety systems have been developed for advanced nuclear reactors. The use of natural driving force for passive systems requires accurate assessment of reliability and performance. Sensitivity analysis is an efficient technique to test the reliability and performance of a safety system, and in order to improve the computational efficiency, the adjoint-based sensitivity method has been introduced. The present study aims to develop an adjoint-based sensitivity method to evaluate the sensitivity of natural circulation system using high-Pr fluid, and to assess its applicability to the experimental facility developed in UNIST. The conservation equations for a closed rectangular loop are written, and the corresponding adjoint system is developed based on the Lagrangian approach. Three different functionals are evaluated which represent thermal-hydraulics and heat transfer performance with respect to various input parameters. The developed adjoint method shows reasonable accuracy in the sensitivity analysis compared with other methods, while significantly reducing the computational time. Following sensitivity analyses using various design parameters assess the sensitivity of natural circulation mass flux, temperature distribution, and Nusselt number. Three different system conditions are imposed to investigate the effects of (i) the implementation of temperature-dependent fluid properties, (ii) the orientations of the heat exchanger and (iii) the operating temperature range, on the entire system reliability. It is found that the variation of fluid properties with respect to the temperature has an important effect on the stability of heat transfer performance in the system. Finally, the advantages in using high-Pr fluids for natural circulation heat transport system is verified by comparing the sensitivities of Nusselt number for different fluids with different Prandtl numbers. The outputs of this study are expected to provide the assessment of the reliability and performance of natural circulation system using molten salt, which can be used for further design studies on molten salt system with low computational burden. Furthermore, this paper demonstrate the applicability of the adjoint-based method for molten salt system applications.

Cascade-like and cyclic heat transfer characteristics affected by enclosure aspect ratios for low Prandtl numbers

For low Prandtl-number fluids, heat-transfer characteristics under the influence of the aspect ratio for buoyancy-driven recirculating flows in rectangular enclosures (with left hot, right cold, top/bottom insulated walls) behave differently from those for high-Pr fluids. At Ra=106 and Pr=0.025, as the enclosure widens, time-averaged and hot-wall-spatially-averaged heat transfer first decreases, then cascades downward. Locally, heat transfer peaks at a few locations, and these peaks travel cyclically as time elapses. For completeness, the present study serves as a sequel of a previous high-Pr investigation.

Hydrothermal waves in two-dimensional liquid layers with sudden changes in the available cross-section

PurposeHydrothermal waves represent the preferred mode of instability of the so-called Marangoni flow for a wide range of liquids and conditions. The related features in classical rectangular containers have attracted much attention over recent years owing to the relevance of these oscillatory modes to several techniques used for the production of single crystals of semiconductor or oxide materials. Control or a proper knowledge of convective instabilities in these systems is an essential topic from a material/product properties saving standpoint. The purpose of this study is to improve our understanding of these phenomena in less ordinary circumstances.Design/methodology/approachThis short paper reports on a numerical model developed to inquire specifically about the role played by sudden changes in the available cross-section of the shallow cavity hosting the liquid. Although accounting for the spanwise dimension would be necessary to derive quantitative results, the approach is based on the assumption of two-dimensional flow, which, for high-Pr fluids, is believed to retain the essence of the involved physical processes.FindingsResults are presented for the case of a fluid with Pr = 15 filling an open container with a single backward-facing or forward-facing step on the bottom wall or with an obstruction located in the centre. It is shown that the presence of steps in the considered geometry can lead to a variety of situations with significant changes in the local spectral content of the flow and even flow stabilization in certain circumstances. The role of thermal boundary conditions is assessed by considering separately adiabatic and conducting conditions for the bottom wall.Originality/valueAlthough a plethora of studies have been appearing over recent years motivated, completely or in part, by a quest to identify new means to mitigate these instabilities and produce accordingly single crystals of higher quality for the industry, unfortunately, most of these research works were focusing on very simple geometries. In the present paper, the causality and interdependence among all the kinematic and thermal effects mentioned above is discussed.

Analysis of energy management via entropy generation approach during natural convection in porous rhombic enclosures

Analysis of ‘entropy generation’ is an important strategy to optimize the natural convection process in order to achieve efficient heat transfer within the system. Rhombic enclosures of various inclination angles (φ=30°, 45° and 75°) filled with porous media and bounded by adiabatic top wall, cold side walls, isothermally (case 1) and non-isothermally (case 2) heated bottom wall have been considered for the analysis of thermal processing of various fluids (Pr=0.015, 0.7, 7.2 and 1000) in the range of Darcy number (Da=10−5– 10−3). At Da=10−5, the total entropy generation, Stotal, is found to be significantly high for φ=30° and low for φ=75° and is dominated by heat transfer irreversibility (Sθ) for all Pr in case 1 whereas the distributions of Stotal for φ=45°, 75° and 90° closely follow the distributions of φ=30° for all Pr in case 2. Cup mixing temperature (Θcup) is higher for φ=75° and 90° whereas overall heat transfer rate, Nu¯, is higher for φ=30° compared to other φs in both heating cases except at high Pr (0.7−1000) fluids at Da=10−5. On increase of Da to 10−3, fluid friction irreversibility, Sψ also increases for all φs irrespective of Pr in both cases. Increase in Stotal with Da is small for lower φ(φ=30°) due to insignificant Sψ of Stotal and large for higher φ(φ=75°) due to significant Sψ of Stotal at Da≥10−4 irrespective of Pr in both cases. Also, Θcup slightly decreases at Da≥10−4 and further, that reaches a constant value at higher Da as well as Stotal in both cases irrespective of φ for all Pr except Pr=0.015. Maximum Nu¯ occurs for φ=30° cavities at Da=10−3 for all Pr in case 1 due to less available energy loss corresponding to less Sψ. Current work attempts to analyze energy efficient thermal convection strategies within porous rhombic enclosures based on entropy generation minimization vs enhanced thermal mixing or heat transfer rates for various fluids in porous media.

Space experiment on the instability of Marangoni convection in large liquid bridge - MEIS-4: effect of Prandtl number -

Microgravity experiments on the thermocapillary convection in liquid bridge, called Marangoni Experiment in Space (MEIS), are carried out in "KIBO" of ISS. Three series of experiments, MEIS-1, 2, and 4, have been conducted so far. This paper reports the results obtained from MEIS-4, in which 20cSt silicone oil (Pr = 207) is used to generate large liquid bridges. They are suspended between coaxial disks that are 50mm in diameter, with their maximum length equal to 62.5mm. MEIS-4 aims at (1) determining the critical temperature difference for the onset of oscillatory flow; (2) realizing high Marangoni number conditions for high Pr fluid; (3) clarifying the effects of volume ratio, heating rate, hysteresis, and cooled disk temperature; and (4) observing whether the hydrothermal wave with azimuthal mode number m = 0 appears or not. The main results are presented and compared with those obtained in MEIS-1 and 2, which utilized liquid bridges of 5cSt silicone oil (Pr = 67).

Direction of scalar transport in turbulent channel flow

The concept of reverse diffusion, introduced by Corrsin to describe the motion of particles as they move towards a location in the flow field, is fundamental to the understanding of mixing. In this work, direct numerical simulations in conjunction with the tracking of scalar markers are utilized in infinitely long channels to study the principal direction of transport of heat (or mass) for both forwards and backwards single particle dispersion. The viscous sub-layer, the transition region (between the viscous sub-layer and the logarithmic region), and the logarithmic region of a Poiseuille flow and a plane Couette flow channel are studied. Fluctuating velocities of scalar markers captured in these regions are used to obtain the full autocorrelation coefficient tensor forwards and backwards with time. The highest eigenvalue of the velocity correlation coefficient tensor quantifies the highest amount of turbulent heat transport, while the corresponding eigenvector points to the main direction of transport. Different Prandtl number, Pr, fluids are simulated for the two types of flow. It is found that the highest eigenvalues are higher in the case of backwards dispersion compared to the case of forwards dispersion for any Pr, in both flow cases. The principal direction for backwards and forwards dispersion is different than for forwards dispersion, for all Pr, and in all flow regions for both flows. Fluids with lower Pr behave different than the higher Pr fluids because of increased molecular diffusion effects. The current study also establishes an interesting analogy of turbulent dispersion to optics defining the turbulent dispersive ratio, a parameter that can be used to identify the differences in the direction of turbulent heat transport between forwards and backwards dispersion. A spectral analysis of the auto-correlation coefficient for both forwards and backwards dispersion shows a universal behavior with slope of −1 at intermediate frequencies.

Heat Transfer Experiments Using a High Prandtl Number Fluid Flowing in Sphere-Packed Channels for Flibe Blanket Design

Flibe blanket, which uses molten salt Flibe as coolant and tritium breeder, is considered as one of the candidates of advanced liquid blanket for fusion reactors. Although Flibe has low heat transfer performance which comes from high Pr, sufficient heat removal can be achievable by using sphere-packed pipe (SPP) as heat transfer promoter.In this study, heat transfer correlations of SPP which can be available for high Pr fluids are derived from experimental analysis inserting various size and materials of spheres into the pipe. Further, heat transfer performance in a rectangular channel is simulated by using sphere-packed annular channel. Based on these results, heat transfer performance of Flibe blanket is evaluated and some design window with pressure drop of less than 1 MPa/m was confirmed.

A Complete Heatline Analysis on Visualization of Heat Flow and Thermal Mixing during Mixed Convection in a Square Cavity with Various Wall Heating

A wide range of applications involving mixed-convection studies can be found in various engineering processes such as thermal discharge of water bodies, float glass production, heat exchangers, nuclear reactors, and crystallization process. The present study focuses on understanding the thermal mixing scenarios for mixed-convection lid-driven flow in a square cavity using heatlines. Thermal mixing is analyzed for four different thermal boundary conditions, and heat flow patterns in mixed convection are analyzed using Bejan’s heatlines concept for wide ranges of parameters (Pr = 0.015–7.2, Re = 1–100, and Gr = 103–105, where Pr, Re, and Gr denote the Prandtl, Reynolds, and Grashof numbers, respectively). The results indicate that, at low Pr values (Pr = 0.015), the transport is conduction-dominant irrespective of the values of Gr and Re. The trends of heatlines and streamlines are identical near the core for high-Re cases. A single circulation cell was observed in the streamlines for any Pr ≥ 0.7 at high Re and low Gr values for uniform heating of the bottom surface with cold side walls. It was observed that thermal mixing increased significantly with subsequent rises in Gr for high-Pr fluids. Patterns of heatlines and multiple circulation cells of heatlines were found to lead to enhanced thermal mixing, with the thermal boundary layer much compressed toward the walls for linearly heated side walls. The heat-transfer rates along the walls are illustrated by the local Nusselt number distribution based on gradients of heatfunctions for the first time in this work. Nusselt numbers with infinitely large magnitudes were observed at hot–cold junctions, illustrating high heat-transfer rates. An oscillatory distribution in the local heatfunction rate was observed as a result of sinusoidal heating of the bottom surface for high-Pr fluids. Negative heat-transfer rates or local Nusselt numbers were observed along the side walls when side wall(s) was/were linearly heated, as explained based on negative heatfunction gradients. Also, the effect of Gr on the local and average Nusselt numbers in different cases can be adequately explained based on heatlines. Dense heatlines signifying higher overall heat-transfer rates along the bottom surface and side walls were observed for uniform bottom surface heating, whereas lower heat-transfer rates were observed for sinusoidal heating. Nonmonotonic distributions in overall heat-transfer rates along the bottom surface and left wall were observed when both walls were linearly heated, whereas a smooth and exponential increase was observed when the right wall was isothermally cooled.

Visualization of heat flow due to natural convection within triangular cavities using Bejan’s heatline concept

Natural convection and flow circulation within a cavity has received significant attention in recent times. The wide range of applicability of flow inside a cavity (food processing industries, molten metal industries, etc.) requires thorough understanding for cost efficient processes. This paper is based on comprehensive analysis of heat flow pattern using Bejan’s heatline concept. The key parameters for our study are the Prandtl number, Rayleigh number and Nusselt number. The values of Prandtl number (0.015, 0.026, 0.7 and 1000) have been chosen based on wide range of applicability. The Rayleigh number has been varied from 10 2 to 10 5. Interesting results were obtained. For low Rayleigh number, it is found that the heatlines are smooth and perfectly normal to the isotherms indicating the dominance of conduction. But as Ra increases, flow slowly becomes convection dominant. It is also observed that multiple secondary circulations are formed for fluids with low Pr whereas these features are absent in higher Pr fluids. Multiple circulation cells for smaller Pr also correspond multiple cells of heatlines which illustrate less thermal transport from hot wall. On the other hand, the dense heatlines at bottom wall display enhanced heat transport for larger Pr. Further, local heat transfer ( Nu l , Nu t ) are explained based on heatlines. The comprehensive analysis is concluded with the average Nusselt number plots. A correlation for average heat transfer rate and Ra has been developed and the range of Rayleigh number is also found, to depict the conduction dominant heat transfer.

Analysis of heat recovery and thermal transport within entrapped fluid based on heatline approach

The wide applications of indirect heating and cooling processes have opened scope for various researchers to explore in-depth analysis and applications of systems involving heat exchange processes. This paper targets the analysis and visualization of heat transfer in entrapped triangular cavities within adjacent square tubes forming a system of practical application especially in pollution control with hot fluid flowing through the stack and entrapped cold fluid confined within the triangular cavities. Also, efficient heat recovery has been examined for the entrapped fluid in the system. The parameters for this study are the Prandtl number ( Pr), Rayleigh number ( Ra) and Nusselt number ( Nu). Complete details of heating patterns in both triangular cavities have been analyzed with heatline approach for visualization of heat flow. At low Rayleigh number, it is found that the heatlines are smooth and perfectly normal to the isotherms indicating the dominance of conduction for both the triangles. But as Ra increases, flow slowly becomes convection dominant. Multiple secondary circulations within the upper triangle are formed for fluids with low Pr, whereas this is absent in higher Pr fluids. Multiple circulation cells for smaller Pr also correspond to multiple cells of heatlines which illustrate less thermal energy transport from hot wall. On the other hand, the dense heatlines at bottom wall display enhanced heat transport for larger Pr. But interestingly for lower triangle there is hardly any variation of patterns with the increase in Prandtl number in the system. Analysis is concluded with the average Nusselt number plots. It is found that fluid with higher Pr may be recommended for upper triangle, but fluid with all ranges of Pr may be used for lower triangle.

Numerical study on the effect of heat loss upon the critical marangoni number in a half-zone liquid bridge

In a half-zone (HZ) liquid bridge, flow exhibits a transition from a two-dimensional steady to a three-dimensional oscillatory flow if the Marangoni number Ma exceeds a critical value Mac, or ΔT>ΔTc. In case of high Prandtle number fluids, the Mac obtained in the numerical simulations deviated significantly from the ones by the experiments. One of the causes of the difference is due to the heat loss over the free surface. Most of past researches neglected effects of the heat loss through an interface of the liquid bridge. Recently several experimental and analytical works reported that the critical condition is significantly affected by the heat loss. The present study aims to include the effects of the heat loss upon the Mac. As the result, the calculated Mac agrees well with the experiment for a high Pr fluid.

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.

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.

The Prandtl Number Effect on the Transition in Natural Convection Along a Vertical Surface

As is often the case, the decision to embark on a new project was triggered by a set of coincidental and mutually reinforcing observations: (i) There is a definite lack of information (theoretical, numerical, experimental) on natural convection in low-Pr fluids (Lykoudis, 1989). This observation was stressed recently also by Wolff et al. (1988). (ii) Georgiadis (1989) drew attention to the line of work represented by Chao et al. (1982) and Bertin and Ozoe (1986), who showed numerically that the onset of Benard convection appears to be influence by the Prandtl number in the Pr < 1 range. (iii) The authors were struck by Bertin and Ozoe's (1986) discovery that they were unable to obtain numerically a steady flow below a certain Prandtl number (Pr = 0.001), even though the Rayleigh number based on height seemed sufficiently low (Ra = 2,800). The present study was motivated by these observations and the apparent suggestion that in low-Pr fluids the laminar flow expires at unexpectedly low Rayleigh numbers. This idea is particularly interesting if they think of the natural convection boundary layer near a vertical wall, for which the textbook teaches to associate the constant Ra {approx} 10{sup 9} with the heightmore » of transition to the turbulent flow, regardless of the Prandtl number (e.g., Incropera and DeWitt, 1985, p. 427). In order to test this idea, the authors reexamined the experimental record of observations on transition in vertical natural convection boundary layer flow. Indeed, the empirical data described next show that the Prandtl number has a strong influence on the transition Rayleigh number. In low-Pr fluids the transition occurs at Rayleigh numbers much lower than the often-mentioned Ra {approx} 10{sup 9}, while in high-Pr fluids the transition Rayleigh number is higher than 10{sup 9}. It appears that the constant Grashof number Gr {approx} 10{sup 9} (i.e., not Ra {approx} 10{sup 9}) marks the transition in the wide Pr range 0.001-1000.« less

Natural Convective Boundary-Layer on Two-Dimensional and Axisymmetric Surfaces in High-Pr Fluids or in Fluid-Saturated Porous Media

In natural convective boundary layers on inclined surfaces, the surface-normal component of the buoyancy force induces a pressure gradient across the boundary layer. For the class of flows in which inertial effects are unimportant (including flows at high Prandtl number as well as flow through fluid-saturated porous media), a local nonsimilarity analysis indicates that the effects of the surface-normal pressure gradient on the temperature profile can be characterized by a single local configuration-parameter which depends on the local geometry and on the Rayleigh Number. Under Mangler’s transformation the reported computational results become applicable to axisymmetric as well as two-dimensional geometries of arbitrary contour. In contrast to the single-parameter dependence of the temperature profiles, the velocity profiles depend upon two local geometric parameters, as illustrated for the example of an inclined flat plate.

Experimental study on heat transfer of combined free and forced laminar convection in thermal entrance region of horizontal rectangular ducts.

Experimental studies by the electrochemical method were made to investigate the heat transfer problems of combined free and forced laminar convection for high Pr fluid in the thermal entrance region of rectangular ducts with the aspect ratio Υ=0.5, where the boundary condition of uniform wall temperature has been used. Experimental data for the local and mean Nu were compared with analytical solutions obtained by developing Leveque''s method and the numerical one, and the following conclusions were reached: i) for the region of forced convection in which the effect of free convection approaches zero, the experimental results are well-correlated with the analytical results obtained by developing Leveque''s method; ii) for the region where the effect of free convection exists, the experimental results are in satisfactory agreement with the numerical ones; and iii) for the onset of free convection effects, both experimental and numerical results are also in good agreement with the original correlative equation suggested by Ou et al.