Liquid-liquid Extraction has emerged as a major technique for radioisotope extraction in recent years. This technique is particularly advantageous in the microscale as the surface-volume ratio is much larger. Since some of these radioisotopes have short half-lives, parallel flow in the microscale is used to extract them as it eliminates the need for separating the two fluids. Though such a configuration has been experimentally studied, dimensionless numbers have not been employed to understand the mass transfer mechanisms. This study uses three dimensionless numbers—the Biot, Peclet and Damkohler numbers—to delve deeper into mass transfer with a chemical reaction at the interface. Mass transfer simulations are performed using a Finite Difference model to solve the 2D Convection-Diffusion Equation with a first-order reaction at the interface, and these numbers are varied. The Damkohler number was observed to have the maximal impact on the extraction efficiency, and this was confirmed to be the case when the extraction efficiency didn’t change much as long as the Damkohler number was kept constant. In general, a higher Damkohler number results in a higher extraction efficiency and a correlation was proposed to quantify this influence.

This paper presents an experimental study for the transient growth of an ice layer in a square channel under laminar flow conditions and a mixed convection heat transfer regime. The ice layer was grown from a cold plate located at the bottom of the channel, capable of reaching temperatures between 0 and −20 °C. The onset of ice formation was marked by a sudden sharp increase of the cold plate temperature followed by a rapid spreading of the ice over the cold plate surface. This was attributed to subcooling effects within the thermal boundary layer of the flow. The flow field was measured using particle image velocimetry (PIV) and the ice profiles were measured at several instances of time after the onset of freezing by a visual tracing of the solid–liquid interface. In addition, a parametric study was performed regarding the effect of the cold plate temperature and the flow rate on the ice growth rate. Suitable approximations to the experimental boundary conditions were found after a detailed analysis of the cold plate's transient temperature response, which could be readily implemented in numerical software. An important novelty of the present work is the measurement of the transient ice development of the ice-layer near the inlet of the channel, in addition to the centre of the channel where the flow is more developed. As such, a comprehensive and well-described experimental data set was generated for transient freezing in laminar internal flow. With this approach, a very good agreement was obtained between the experimental results and numerical simulations which were included to indicate the suitability of the current experimental campaign for numerical benchmarking purposes.

This work presents two color LIF temperature measurements for the transient freezing in a square channel under laminar flow conditions. This is the first time non-intrusive temperature measurements were performed within the thermal boundary layer during the transient growth of an ice layer in internal flow. A combination of a local outlier factor algorithm and a smoothing operation was used to remove the top to bottom striations and reduce the other measurement noise. The temperature uncertainty in our measurements was between σ=0.3∘C and σ=0.5∘C. For the largest temperature difference between the bulk and the melting point of 14.6 °C, good results were obtained. As such, the current campaign demonstrates the potential of LIF as a non-intrusive temperature measurement technique for solid–liquid phase change experiments. However, some artefacts were present within the vicinity of the ice-layer due to the scattering of the laser light, especially near the inlet of the channel where the ice-layer is curved instead of flat. LIF measurements taken within a short time span prior to the onset of ice freezing showed approximately 2 °C of subcooling, consistent with previous findings. In addition, an anomalous behavior within the thermal boundary layer was observed, with a much smaller temperature gradient within the first few mm above the cold plate and a point of inflection in the temperature profile. The anomalous temperature behavior is possibly attributed to enhanced natural convection as a result of the subcooling at the cold plate surface.

The lattice-Boltzmann method (LBM) is becoming increasingly popular for simulating multi-phase flows on the microscale because of its advantages in terms of computational efficiency. Many applications of the method are restricted to relatively simple geometries. When a more complex geometry is considered—circular and inclined microchannels—some important physical phenomena may not be accurately captured, especially at low capillary numbers. A Y-Y micro-fluidic channel, widely used for a range of applications, is an example of a more complex geometry. This work aims to capture the various flow phenomena, with an emphasis on parallel flow and leakage, using the Rothman–Keller (RK) model of the LBM. To this purpose, we modify the forcing term to implement the surface tension for use at low capillary numbers. We compare the simulation results of the RK model with and without the force modification with experiments, Volume of Fluid and the phase field method and observe that the modified forcing term is an improvement over the current RK model at low capillary numbers, and it also captures parallel flow and leakage more accurately than the other simulation techniques.

We present a finite volume adaptive mesh refinement method for solid-liquid phase change problems with convection. The refinement criterion consisted of three different error estimators for the solid-liquid interface, the flow field, and the temperature field respectively. For the solid-liquid interface, the cells undergoing phase change were refined based on the maximum difference in the liquid fraction over the cell faces. For the flow field and the temperature field, an error indicator was used based on the cell residual method. To maintain a high parallelization efficiency, a dynamic load balancing procedure was used. The adaptive mesh refinement strategy was verified through three different test cases, these are the gallium melting in both 2D and 3D cavities, and the molten salt reactor freeze valve. For all three cases, very good agreement was obtained between the adaptive mesh results and the reference solutions. In addition, more accurate results were obtained with the adaptive meshes compared to static meshes with a similar amount of mesh cells. This illustrated the potential of the current approach for developing computationally efficient numerical methods for solid-liquid phase change problems.

We present a discontinuous Galerkin method for melting/solidification problems based on the “linearized enthalpy approach,” which is derived from the conservative form of the energy transport equation and does not depend on the use of a so-called mushy zone. We use the symmetric interior penalty method and the Lax–Friedrichs flux to discretize diffusive and convective terms, respectively. Time is discretized with a second-order implicit backward differentiation formula, and two outer iterations with second-order extrapolation predictors are used for the coupling of the momentum and energy. The numerical method was validated with three different benchmark cases, i.e., the one-dimensional Stefan problem, octadecane melting in a square cavity and gallium melting in a rectangular cavity. The performance of the method was quantified based on the L ² norm error and the number of iterations needed to convergence the energy equation at each time step. For all three validation cases, a mesh convergence rate of approximately O(h) was obtained, which is below the expected accuracy of the numerical method. Only for the gallium melting case, the use of a higher-order method proved to be beneficial. The results from the present numerical campaign demonstrate the promise of the discontinuous Galerkin finite element method for modeling certain solid–liquid phase change problems where large gradients in the flow field are present or the phase change is highly localized, however, further enhancement of the method is needed to fully benefit from the use of a higher-order numerical method when solving solid–liquid phase change problems.

A method based on ultrasonic wave propagation is applied for the determination of the viscosity of low viscous liquids. A waveguide is used to remotely transmit the ultrasonic waves from a shear piezoelectric transducer into the liquid. At the solid-liquid interface, a guided wave mode, the shear mode, is used to extract the liquid viscosity. The energy of the reflected ultrasonic wave depends upon its operating frequency, the physical properties of the liquid (viscosity and density), and the waveguide (density and shear modulus). The results show that the attenuation of the waves, and thus the viscosity of the liquid, can be retrieved using this method. Measurements on water, ethanol, and mixtures of water/glycerol illustrate that the method can monitor changes in attenuation due to the viscosity of the liquid. The range of viscosities measured was between 0.8 and 60 mPa s. Compared to literature values, the relative error for these measurements was lower than 12% while the uncertainty in the measurements was lower than 5%. Besides its ability to measure low viscosities, this method offers advantages such as the capability to perform in-situ measurements of liquids in harsh environments, the omission of mechanical parts, and the possibility to handle small volumes of liquid. These features make this method suitable for low viscous liquids that are radioactive, corrosive and at high temperature.

Fluid flows through rod bundles are observed in many nuclear applications, such as in the core of Gen IV liquid metal fast breeder nuclear reactors (LMFBR). One of the main features of this configuration is the appearance of flow fluctuations in the rod gaps due to the velocity difference in the sub-channels between the rods. On one side, these pulsations are beneficial as they enhance the heat exchange between the rods and the fluid. On the other side, the fluid pulsations might induce vibrations of the flexible fuel rods, a mechanism generally referred to as Flow Induced Vibrations (FIV). Over time, this might result in mechanical fatigue of the rods and rod fretting, which eventually can compromise their structural integrity. Within the SESAME framework, a joint work between Delft University of Technology (TU Delft), Ghent University (UGent), and NRG has been carried out with the aim of performing experimental measurements of FIV in a 7-rods bundle and validate numerical simulations against the obtained experimental data. The experiments performed by TU Delft consisted of a gravity-driven flow through a 7-rods, hexagonal bundle with a pitch-to-diameter ratio P/D=1.11. A section of 200 mm of the central rod was made out of silicone, of which 100 mm were flexible. Flow measurements have been carried out with Laser Doppler Anemometry (LDA) whereas a high-speed camera has measured the vibrations induced on the silicone rod. The numerical simulations made use of the Unsteady Reynolds-averaged Navier-Stokes equations (URANS) approach for the turbulence modelling, and of strongly coupled algorithms for the solution of the fluid-structure interaction (FSI) problems. The measured frequency of the flow pulsations, as well as the mean rod displacement and vibration frequency, have been used to carry out the benchmark.

Axial flow in tube bundles with small pitch-to-diameter ratio, a geometry encountered in nuclear reactor cores and heat exchangers, often displays periodic fluctuations. A significant velocity discrepancy between the inter-cylinder gap and subchannel center originates from the difference in through-flow area, feeding an instability. As it is associated with velocity-shear, it is similar to the Kelvin-Helmholtz type and the term 'gap instability' is adopted. A vortex street arises and structural vibration of the cylinders might develop due to the fluctuating pressure. Numerical simulations of this phenomenon were performed. The computational domain was constructed to match the most important geometrical features of an experimental setup. The bundle consists of 7 steel tubes in triangular array, placed in a hexagonal conduit. A flexible segment made of silicone is embedded in the central tube, with both extremes clamped to the steel parts of the cylinder. In the experiment, data of the fluctuating velocity was gathered using laser Doppler anemometry measurements. As first step, a completely rigid structure was considered. Unsteady Reynolds-averaged Navier-Stokes (URANS) simulations were used to test if this particular geometry also triggers the gap vortex street, which was the case. The phenomenon clearly appears as oscillations of the velocity components. Subsequently, fluid-structure interaction (FSI) simulations, taking into account the flexible part, allowed to assess the effect of the fluctuating flow field on the structure. A comparison between one-way and two-way coupled simulations was made.

This paper focuses on the freeze-plug, a key safety component of the Molten Salt Fast Reactor, one of the Gen. IV nuclear reactors that must excel in safety, reliability, and sustainability. The freeze-plug is a valve made of frozen fuel salt, designed to melt when an event requiring the core drainage occurs. Melting and draining must be passive, relying on decay heat and gravity, and must occur before the reactor incurs structural damage. In this work, we preliminarily investigate the freeze-plug melting behavior, assessing the influence of various design configurations and parameters (e.g., sub-cooling, recess depth). We used COMSOL Multiphysics® to simulate melting, adopting an apparent heat capacity method. Results show that single-plug designs generally outperform multi-plug ones, where melting is inhibited by the formation of a frozen layer on top of the metal grate hosting the plugs. The layer thickness strongly depends on sub-cooling and recess depth. For multi-plug designs, the P/D ratio has a negligible influence on melting and can therefore be chosen to optimize the draining time. The absence of significant mixing in the pipe region above the plug leads to acceptable melting times (i.e., <1000 s) only for distances from the core up to 0.1 m, considered insufficient to host all the cooling equipment on the outside of the draining pipe and to protect the plug from possible large temperature oscillations in the core. Consequently, we conclude that the current freeze-plug design based only on decay heat to melt is likely to be unfeasible. A design improvement, preserving passivity and studied within the SAMOFAR project (http://samofar.eu/), consists in accelerating melting via heat stored in steel masses adjacent to the draining pipe.

Liquid metal reactors typically employ wire wraps as spacers between the fuel pins. In the past, design and safety calculations were largely one-dimensional and based on experimental data. Nowadays, with modern state-of-the-art computer power and tools, three-dimensional Computational Fluid Dynamics (CFD) simulations allow designers and safety specialists to obtain much more detailed information on the flow and heat transport in liquid metal cooled fuel assemblies, obviously in close collaboration with experimental campaigns. This may lead to new insights possibly decreasing the safety margins. This paper intends to provide an overview on the activities in the frame of design and safety support for wire-wrapped fuel assemblies. It all starts with validation. Therefore, validation efforts will be shown for fuel assemblies as they are designed on the drawing board for ‘cold’ conditions. Such analyses will profit from the quantification of uncertainties and determination of most influencing parameters. Nevertheless, in reality a fuel assembly will not be employed as designed in ‘cold’ conditions. Therefore, they will probably deform. This requires an assessment of the effect of deformations. Another aspect possibly occurring during operational conditions is vibrations. State-of-the-art coupled CFD and finite element method fluid structure interaction techniques have been developed and applied to a wire wrapped fuel pins, providing insights in the vibration behavior of such assemblies. Apart from that, vibration experiments have been performed at complete fuel assembly scale providing important insights to safety analysts and designers. However, design and safety analysts will not only have to cope with operational conditions, but also have to show the heat transport behavior under accident conditions. Assessments of the effect and formation of blockages are necessary. In all above cases, it should be clear that experiments and numerical simulations go hand-in-hand. Numerical simulations are used to design the experiment, the experiment is used to validate the simulations, and the simulations are used to interpret the experimental results.

Abstract: The feasibility of particle image velocimetry (PIV) in a thermally convective supercritical fluid was investigated. Hereto a Rayleigh–Bénard convection flow was studied at pressure and temperature above their critical values. The working fluid chosen was trifluoromethane because of its experimentally accessible critical point. The experiments were characterized by strong differences in the fluid density from the bottom to the top of the cell, where the maximum relative density difference was between 17 and 42%. These strong density changes required a careful selection of tracer particles and introduced optical distortions associated with strong refractive index changes. A preliminary background oriented schlieren (BOS) study confirmed that the tracer particles remained visible despite significant local blurring. BOS also allowed estimating the velocity error associated with optical distortions in the PIV measurements. Then, the instantaneous velocity and time-averaged velocity distributions were measured in the mid plane of the cubical cell. Main difficulties were due to blurring and optical distortions in the boundary layer and thermal plumes regions. An a posteriori estimation of the PIV measurement uncertainty was done with the statistical correlation method proposed by Wieneke (Measure Sci Technol 26:074002, 2015). It allowed to conclude that the velocity values were reliably measured in about 75% of the domain. Graphic abstract: [Figure not available: see fulltext.].

The core of a Liquid Metal Fast Reactor (LMFR) has wires wrapped helicoidally around the fuel pins. This solution prevents damage of the cladding by fretting, and pushes the coolant flow through the gaps between the pins, thus, enhancing the heat exchange. The wires make the flow through the core very complex to understand and model. The goal of this study is, thus, twofold: it aims to obtain insight into the physics of the flow field near the wire and to provide high-fidelity data for benchmarking numerical simulations. Water at room temperature flowing inside a 7 rods, wire-wrapped hexagonal bundle is studied within a Reynolds number range of 4000−14000 using the Particle Image Velocimetry (PIV) technique. The measured quantities are the axial and lateral velocity components, and their root mean square. The measurement area is close to the wire around the central rod. Fluorinated ethylene propylene (FEP), which is a refractive index-matching (RIM) material, provides optical access to the measured region without disturbance of the light beam. The flow direction below the wire follows the wrapping path, as expected. However, if the flow is measured at the front of the wire, the streamlines bend in the opposite direction. The Euler equations applied to the streamlines show that this effect is caused by the pressure gradient across the wire. These findings deepens the physical understanding of the rod bundle flow in the presence of wire spacers, improving the LMFR designs. Moreover, the generated data will support validation of numerical codes for Gen-IV nuclear reactors.

This technical paper presents results of an air-cooled supercritical CO2 (sCO2) finnedtube sink heat exchanger (HX) performance test comprising wide range of variable parameters (26-166 C, 7-10 MPa, 0.1-0.32 kg/s). The measurement covered both supercritical and subcritical pressures including transition of pseudocritical region in the last stages of the sink HX. The test was performed in a newly built sCO2 experimental loop which was constructed within Sustainable Energy (SUSEN) project at Research Centre Rez (CVR). The experimental setup along with the boundary conditions are described in detail; hence, the gained data set can be used for benchmarking of system thermal hydraulic codes. Such benchmarking was performed on the open source Modelica-based code ClaRa. Both steady-state and transient thermal hydraulic analyses were performed using the simulation environment DYMOLA 2018 on a state of the art PC. The results of calculated averaged overall heat transfer coefficients (using Gnielinski correlation for sCO2 and IPPE or VDI for the air) and experimentally determined alues shows reasonably low error ofp25% and - 10%. Hence, using the correlations for the estimation of the heat transfer in the sink HX with a similar design and similar conditions gives a fair error and thus is recommended.

Being able to quantify mechanical vibrations is of key importance for the safety of nuclear power plants, as they are able to induce damage. In this work, numerical simulations are used to compute water flow and vibration in a densely packed bundle of 7 rods, mimicking an experimental setup. This flow configuration is chosen to resemble the coolant flow through a nuclear reactor core. Because of the wall proximity, a considerable velocity difference between the narrow gaps and the subchannels exists, with an inflection point in the velocity profile. This yields an unstable situation, and large vortices are continuously created through a mechanism similar to the Kelvin–Helmholtz instability. The vortex streets in between the rods are associated with a fluctuating pressure field, causing vibrations of the rods. The experimental setup contains 7 steel cylinders, encased in a hexagonal duct. The central rod contains a section where the steel is replaced by a water-filled silicone tube, clamped at both extremes to the steel rod, and the vibrations of this section are examined. The numerical approach consists of coupled fluid–structure interaction (FSI) simulations, with the flow being modelled using computational fluid dynamics (CFD) and the structure using computational solid mechanics (CSM). The available experimental data consist of Laser Doppler Anemometry (LDA) measurements and high-speed camera footage of the wall movement of the silicone rod. Equivalent data is collected from the numerical simulations. The simulations are repeated for different flow rates. The frequency spectrum of the coherent structures, and the frequency and amplitude of the wall movement are compared for each operating point, as well as their trend as a function of the flow rate. The dominant frequencies found in the simulation results were similar to the experimental results, although slightly higher. They also showed a linear trend, just like the experiments. A larger mismatch was present for the structural response, the frequencies found using the FSI model being more than twice as high.

A new friction-heat transfer analogy for the prediction of heat transfer to turbulent fluids at supercritical pressure is presented. This analogy is based on the observation that the predominent events that determine the turbulent heat flux known as hot ejections and cold sweeps have different thermophysical properties. This observation is used to derive a new friction-heat transfer analogy, which we call the ejection-sweep analogy. It is shown that the ejection-sweep analogy yields very good results with respect to predicting heat transfer coefficients for different fluids (water, CO ₂ , Helium, R22 and R134a) that are heated at supercritical pressure at low heat flux to mass flux ratios. Furthermore, the new analogy performs much better than the Chilton-Colburn analogy. The new analogy was also compared with two well-known relations from literature. It was found that the ejection-sweep analogy predictions are more consistent with respect to the investigated fluids than the relations from literature and that the analogy can be applied to at least all fluids studied in this work. The ejection-sweep analogy can be used in the development of more advanced heat transfer models that include buoyancy and acceleration effects.