Liquid Metal Heat Transfer Research Articles

Numerical investigation of turbulent aided mixed convection of liquid metal flow through a concentric annulus

Turbulent aided mixed convection of a liquid metal with Pr=0.021 in a concentric heated annulus is investigated by solving the Reynolds-Averaged-Navier-Stokes equations. This geometry approximates rod bundles heat exchangers at high pitch-to-diameter ratios. Two inner-to-outer radius ratios of 0.13 and 0.5 are considered and a constant uniform heat flux is applied only to the inner wall, only to the outer wall or to both walls. Constant thermo-physical properties are assumed and buoyancy is accounted for in the momentum equation using the Boussinesq assumption. Four different eddy-viscosity models are first assessed against the few available experimental data for a pipe flow. The turbulent heat fluxes are modeled with the Simple-Gradient-Diffusion-Hypothesis and the turbulent Prandtl number is locally evaluated either with a correlation or by solving one additional transport equation for the temperature variance and one for its dissipation rate. The first approach gives a better agreement with the experimental data. It is found that, compared to medium-to-high Prandtl number fluids, the Reynolds number has a much greater influence on the onset and magnitude of heat transfer impairment. Its extent and degree are less than for ordinary fluids. It is shown that, contrarily to a pipe flow where liquid metals with Pr≈0.025 behave similar to air or water, in the concentric annulus big differences exist. The reason is the considerable contribution of molecular heat transfer in liquid metals that compensates the reduced turbulent mixing due to buoyancy.

Colligation of Experimental Data on Heat Transfer in Liquid Metals*

The experimental data on heat emission in turbulent flow of a liquid metal in a tube, including data on mercury, sodium, and the alloys Na–K and Pb–Bi, are examined. A universal profile of the temperature distribution in the form of the dimensionless variables T+= f(y++), approximated by three equations of which one is logarithmic, is obtained. On the basis of these relations, a relation is found in the form Nu = f(Pe), which is accurate to within ±8%, for use in engineering calculations.

Enhancement of Heat Transfer in a Liquid Metal Flow past a Thermally Conducting and Oscillating Infinite Flat Plate

The effect of conjugation on the enhancement of heat transfer in a liquid metal flow past a thermally conducting and sinusoidally oscillating infinite flat plate, when a constant temperature gradient is superimposed on the fluid, is investigated. The plate is made up of the materials compatible with the liquid metals used and is considered to be of finite thickness. Analytical solutions for the velocity and the temperature of the fluid and the solid are obtained. The effects of thermal conductivity and the thickness of the plate on the total time averaged heat flux transported and the thermal boundary layer thickness are investigated in detail. It is found that the effects of wall thickness and wall thermal conductivity on the heat flux transported depend on their effects on the transverse temperature gradient at any frequency. The optimum value of wall thickness at which the net heat flux transported attains the maximum value, for each fluid and for each wall material under consideration, is reported. A maximum increase of 46.14 % in the heat flux transported can be achieved by optimizing the wall thickness. A maximum convective heat flux of 1.87 × 108W/m2 is achieved using Na with AISI 316 wall. All the results obtained have been compared with the experimental and analytical results reported in the literature and are found to be in good agreement. It is believed that the new insights gained will be of significant use while designing liquid metal heat transfer systems.

Heat transfer on HLM cooled wire-spaced fuel pin bundle simulator in the NACIE-UP facility

The NACIE-UP experimental facility at the ENEA Brasimone Research Centre (Italy) allowed to evaluate the heat transfer coefficient of a wire-spaced fuel bundle cooled by lead-bismuth eutectic (LBE). Lead or lead-bismuth eutectic are very attractive as coolants for the GEN-IV fast reactors due to the good thermo-physical properties and the capability to fulfil the GEN-IV goals. Nevertheless, few experimental data on heat transfer with heavy liquid metals (HLM) are available in literature. Furthermore, just a few data can be identified on the specific topic of wire-spaced fuel bundle cooled by HLM. Additional analysis on thermo-fluid dynamic behaviour of the HLM inside the subchannels of a rod bundle is necessary to support the design and safety assessment of GEN. IV/ADS reactors.In this context, a wire-spaced 19-pin fuel bundle was installed inside the NACIE-UP facility. The pin bundle is equipped with 67 thermocouples to monitor temperatures and analyse the heat transfer behaviour in different sub-channels and axial positions.The experimental campaign was part of the SEARCH FP7EU project to support the development of the MYRRHA irradiation facility (SCK-CEN). Natural and mixed circulation flow regimes were investigated, with subchannel Reynolds number in the range Re=1000–10,000 and heat flux in the range q″=50–500kW/m2.Local Nusselt numbers were calculated for five sub-channels in different ranks at three axial positions. Section-averaged Nusselt number was also defined and calculated. Local Nusselt data showed good consistency with some of the correlation existing in literature for heat transfer in liquid metals for rod bundles. Local Nusselt numbers in peripheral ranks are lower, due to the presence of the hexagonal external wrap which affects the temperature profile.The good accuracy of the instrumentation and the error analysis implemented in the post-processing routines guaranteed a good reliability of the results. The data set presented can be used also to validate computer codes for HLM-cooled rod bundles.

Experimental study of liquid metal heat transfer in a vertical heated channel affected by a coplanar magnetic field

Experimental study of liquid metal heat transfer in a vertical heated channel affected by a coplanar magnetic field

Experimental study of liquid metal heat transfer in a vertical heated channel affected by a coplanar magnetic field

Experimental study of liquid metal heat transfer in a vertical heated channel affected by a coplanar magnetic field

Study on the flow and heat transfer of liquid metal based nanofluid with different nanoparticle radiuses using two-phase lattice Boltzmann method

A two-phase lattice Boltzmann model considering the interaction forces of nanofluid has been developed in this paper. It is applied to investigate the flow and natural convection heat transfer of Cu–Ga nanofluid. The effects of different nanoparticle radiuses, interaction forces, aspect ratios of the enclosure, nanoparticle volume fractions, and Rayleigh numbers on the nanoparticle distributions and heat transfer characteristics are investigated. It is found that the nanofluid with small nanoparticle radius significantly improves the heat transfer compared with the nanofluid with big nanoparticle radius. The temperature difference driving force has the biggest effect on the nanoparticle distribution, followed by the Brownian force and drag force, and the other forces have the least effect. The average Nusselt number increases with the increasing aspect ratio of the enclosure, nanoparticle volume fraction and Rayleigh number.

Numerical simulation of liquid metal turbulent heat transfer from an inline tube bundle in cross-flow

Results of the numerical simulation of turbulent flow field and heat transfer of liquid metal in cross-flow over inline tube bundles consisting of smooth round tubes are presented. Computations have been performed with CFD-code ANSYS Fluent on the base of a two-dimensional unsteady RANS formulation using the SST turbulence model by Menter and assuming constant physical properties of a fluid with the Prandtl number equal to 0.023. The Reynolds number ranged from 26,200 to 52,400. Instantaneous and time-averaged velocity and temperature fields obtained for bundles of different intertube spacing with a variation of the bundle width (number of tube rows in the cross direction) were analyzed. Integral characteristics of heat transfer were compared with the experimental data.

CFD simulations in heavy liquid metal flows for square lattice bare rod bundle geometries with a four parameter heat transfer turbulence model

The study of heat transfer in heavy liquid metals has gained more attention in the last several years due to their applications in new advanced nuclear reactors. These fluids are characterized by low Prandtl numbers and a peculiar heat transfer that cannot be accurately reproduced with standard turbulence approximations, such as the Simple Eddy Diffusivity model (SED), commonly used in commercial codes. In this paper we report the results obtained for the SED and a more advanced κ–ϵ–κθ–ϵθ four parameter turbulence model for simulations in square lattice bare rod bundle geometries with different pitch-to-diameter ratios. We compare these numerical results with the available experimental data and correlations for the prediction of the Nusselt number.

A new solar fuels reactor concept based on a liquid metal heat transfer fluid: Reactor design and efficiency estimation

A new reactor concept for two-step partial redox cycles is presented and evaluated by transient simulation that considers heat and mass transfer along with reaction kinetics. The major difference between the reactor described herein and previous designs is that the conversion from solar to chemical energy is divided into two steps: sunlight-to-thermal energy conversion accomplished with a liquid metal based receiver, and the thermal-to-chemical conversion accomplished with a separately optimized array of reaction chambers. To connect these two conversion steps, liquid metal is used as a high temperature heat transfer fluid that feeds the solar energy captured in the receiver to the reactor. The liquid metal also facilitates efficient heat recuperation (∼80%) between the reaction chambers. The overall thermal-to-chemical efficiency from the thermal energy in the liquid metal to the chemical energy in the hydrogen fuel is estimated to be 19.8% when ceria is employed as the reactive oxygen storage material. This estimated efficiency is an order of magnitude higher than previous designs and the reactor concept discussed herein identifies important insights that apply to solar–fuel conversion in general.

Convection heat transfer of NaK-78 liquid metal in a circular tube and a tri-lobe channel

Computational Fluid Dynamics (CFD) analysis of turbulent convection heat transfer of NaK-78, liquid metal alloy in a uniformly heated circular tube are performed and the results are compared to reported experimental measurements. Also presented are the results for a tri-lobe channel, of the same heated length, equivalent hydraulic diameter, wall heat flux, liquid mass flux, setup and the inlet and exit bulk temperatures as in the circular tube experiments. The tri-lobe channel has 28% larger cross-sectional and surface areas than the circular tube. Examined are the effect of using the two-layer realizable k–ε, the Shear Stress Transport (SST) k–ω, and the SST Detached Eddy Simulation (DES) turbulence models on the computation time and the accuracy of the results. The calculated axial distribution of the wall temperature for the circular tube compares favorably to reported measurements at Pe=163 and 796. This agreement confirms the soundness of the implemented methodology and the numerical meshing grid. The calculated and experimental Nu values for fully developed flows in the uniformly heated circular tube, covering a wide range of Pe values, are correlated to within ±10%, as:Nu=5.6+0.013Pe0.863Although the calculated Nu values using the different turbulence models are well within the ±10% of the experimental data, the computation time using the DES turbulence model is 13 and 14 time that using the k–ω and the k–ε model, respectively. Unlike for the circular tube, the local Nu in the tri-lobe channel varies azimuthally with the values in the corners are much lower than in the concavities of the tri-lobe channel. The calculated average values of Nusselt number, N¯u for the fully developed flows of liquid NaK-78 in the tri-lobe channel are correlated, to within ±5% as:N¯u=6.6+0.007Pe0.94For Pe<100, the N¯u values for the tri-lobe channel are ∼15% higher than for the uniformly heated circular tube, but the difference gradually decreases with increasing Pe.

Liquid metal heat transfer in heat exchangers under low flow rate conditions

The present paper describes the liquid metal heat transfer in heat exchangers under low flow rate conditions. Measured data from some experiments indicate that heat transfer coefficients of liquid metals at very low Péclet number are much lower than what are predicted by the well-known empirical relations. The cause of this phenomenon was not fully understood for many years. In the present study, one countercurrent-type heat exchanger is analyzed using three, separated countercurrent heat exchanger models: one is a heat exchanger model in the tube bank region, while the upper and lower plena are modeled as two heat exchangers with a single heat transfer tube. In all three heat exchangers, the same empirical correlation is used in the heat transfer calculation on the tube and the shell sides. The Nusselt number, as a function of the Péclet number, calculated from measured temperature and flow rate data in a 50 MW experimental facility was correctly reproduced by the calculation result, when the calculated result is processed in the same way as the experiment. Finally, it is clarified that the deviation is a superficial phenomenon which is caused by the heat transfer in the plena of the heat exchanger.

Assessment and calibration of an algebraic turbulent heat flux model for low-Prandtl fluids

Turbulent heat transfer is an extremely complex phenomenon, which has challenged turbulence modellers over various decades. The limitations of the commonly used eddy diffusivity approach have become more evident specially for innovative nuclear reactor applications with low-Prandtl fluids like liquid metals. One of the objectives of the THINS (Thermal Hydraulics of Innovative Nuclear Systems) project sponsored by the European Commission is to push forward the validation and adoption of more accurate closures for single-phase turbulence for innovative reactors in engineering codes. As a part of this THINS project, CD-adapco has implemented in its commercial code STAR-CCM+ an algebraic turbulent heat flux model. In the present work, this implemented model has been widely tested and further calibrated for the application to natural, mixed and forced convection flow regimes at low-Prandtl number. As an outcome, a modelling correlation is proposed in combination with a newly proposed set of model coefficients. This proposed correlation shows dependency of Reynolds and Prandtl numbers in a logarithmic manner to accommodate the wall-normal temperature gradient for the heat flux term. The use of this correlation brings significant improvements in the prediction of heat transfer in liquid metals in all flow regimes.

Review of data and correlations for turbulent forced convective heat transfer of liquid metals in pipes

Within the present work the dataset of experimental points and the heat transfer correlations available in literature for liquid-metal fully-developed, forced-convective heat transfer in pipes are reviewed and critically analyzed. Over 1,100 data points from 21 different sources are considered for constant heat flux, covering a wide range of operating conditions (velocity, heat flux, diameter, among others). Among 15 evaluated correlations, four appropriate ones are recommended for forced turbulent convection: one covering all the data points and the other three respectively related to alkali liquid metals, lead alloys and mercury. Moreover, a new correlation has been derived as a best fit of the limited number of available data points for constant wall temperature, while an alternative evaluation method is also described for this boundary condition.

Numerical Simulation of Flow and Heat Transfer during Filling Process Based on SPH Method

Expected to the non-grid characteristics and pure Lagrangian properties of SPH, the simulation of casting’s filling process would be simpler and precise. In this study, the implementations of SPH method are studied for liquid metal flow and heat transfer during the filling process. The temperature based thermophysical parameters are fitted and add into flow-heat coupling program. The temperature recovery method is included to consider the effect of latent heat. The validation of one-directional heat transfer problem shows that the SPH results have good agreement with the analytical results. The maximum relative error is less than 3%. Finally a circular part is calculated and proved that the SPH model used here works well and has enough precision to capture the behavior of the filling process.

Specific features of liquid metal heat transfer in a TOKAMAK reactor

Specific features of liquid metal heat transfer in a TOKAMAK reactor

Mould Filling Ability Characterisation of Cast Aluminium Alloys Using Design of Experiments

Mould filling ability characteristic has been influencing the liquid metal flow, heat transfer, and solidification there by affecting the quality of aerospace castings. Mould filling is a critical parameter in the production of sound and quality castings, especially in the case of complex-shaped castings where section thickness is varying considerably. The mould filling ability of aluminium alloys LM6 and LM25 has been studied in the present investigation. Experimentation has been carried out using orthogonal array experimental layout. The process parameters studied in the present investigation are alloy composition, sand fineness, mould coating, and pouring temperature. The mould filling ability of selected aluminium alloy has been studied using pin test piece with cylindrical cores. The results from experimentation are analyzed to find the influence of the process parameters on mould filling ability. Based on the above, LM6 alloy has been found to have better mould filling ability characteristics and the analysis of variance has also revealed the same optimum factor combination.

Experimental investigation of the turbulent heavy liquid metal heat transfer in the thermal entry region of a vertical annulus with constant heat flux on the inner surface

The thermally developing turbulent lead bismuth (Pb45Bi55) flow within a vertical annulus with the inner surface uniformly heated is experimentally investigated. The ratio between internal and external diameter is 0.136. The investigated Reynolds numbers vary between 1.48×104 and 2.37×105 and the applied heat flux from 135kW/m2 to 905kW/m2, covering both the forced and mixed convection regime. For forced convection, the local heat transfer convective coefficient is evaluated and compared with literature correlations for low Prandtl number fluids. Additionally, a new empirical relation for the local Nusselt number in the thermal entry region is proposed. The applicability of criteria addressing the forced to mixed convection transition in medium to high Prandtl number fluids is reviewed and extended to account also for low Prandtl number fluids such as heavy liquid metals. Here, the transition from turbulent-diffusion to molecular-diffusion dominated mixed convection is clearly shown.

An innovative method for prediction of liquid metal heat transfer rate for rod bundles based on annuli

An annulus can be seen as a rod bundle with a single rod, which has no thermal–hydraulic interaction with other rods. Thus the interaction in rod bundles can be obtained with the help of certain annuli. The heat transfer rates of both triangular and square lattices were studied based on the correlation of annuli, and modifications were done to take into account the influences of temperature difference, hydraulic diameter, interaction and shape difference, etc. The temperature difference correction was calculated with the section temperature distribution experimental data for annuli, while the other three were determined with geometric parameters. Correlations for both lattices were compared with available experimental data and the results showed good agreement. Comparison of these two correlations indicated that there were important differences between the two arrangement patterns if the pitch-to-diameter ratio was less than 1.25. Furthermore, the interaction correction was found to be generally equal to the thermal mixing length scale used in the sub-channel analysis, which may be used as a new correlation for the interaction correction.

Heat transfer in SiC compact heat exchanger

For development of a compact SiC heat exchanger, numerical heat transfer analysis was conducted to investigate its performance for a wide range of thermal media, liquid LiPb and helium gas, flow rates. The numerical model used was based on the heat exchanger test module developed by the authors. Within the authors’ experimental range, the heat quantity transferred from high temperature liquid LiPb to helium gas and the overall heat transfer coefficients obtained numerically are in agreement with the experimental results. Therefore, the numerical model has proved to be valid for estimation of heat transfer phenomena in the heat exchanger in incompressible regime. The heat quantity transferred from LiPb to He amounts up to 3.7 kW at helium pressure of 0.5 MPa. On the basis of the numerical results, a correlation for helium forced convection heat transfer in the heat exchanger is presented, which describes numerical results with an error of 1%. For heat transfer in LiPb, the Nusselt numbers calculated from an existing correlation for liquid metal heat transfer agree well with the present numerical results. The heat transfer of LiPb in the SiC compact heat exchanger would possibly be predicted from the conventional correlations based on the studies of liquid metal convective heat transfer. A concept of SiC compact heat exchanger studied could be applied to a design of intermediate heat exchangers operating at high temperatures in fusion reactor, as well as HTTR and VHTR systems.