Modeling Of Turbulent Heat Transfer Research Articles

A developed transition simulation model for turbulent plane jet impingement heat transfer

Jet impingement has been widely used due to its high heat transfer rate, but numerical simulation of this flow is highly challenging because of complex flow phenomena. In this paper, a turbulence model based on the physics of jet impingement is developed using the shear stress transport (SST) four-equation transition model and the SST with cross-diffusion correction (SSTCD) model. The proposed method is evaluated for plane jet impingement under various nozzle-plate spacings (2.6, 4 and 6) and different Reynolds numbers ranging from 10,200 to 20,000 in terms of heat transfer and flow fields. The results show that the developed model has the ability to capture the second peak of heat transfer and skin friction at low nozzle-plate spacing. Even at high nozzle-plate spacing, this approach also gives accurate trends for the above two features. However, without the cross-diffusion correction, the transition model provides too high energy and low velocity peaks. With the developed model in hand, the effects of pressure gradient on heat transfer and skin friction coefficient are further investigated. It is found that when the adverse pressure gradient becomes strong, the position of the secondary peak of skin friction occurs earlier than that of the secondary peak of heat transfer rate. Conversely, if the adverse pressure gradient disappears, the positions of these features coincide.

Study on coupled heat transfer model and enhanced heat transfer law of liquid metals and supercritical fluids

ABSTRACT The supercritical carbon dioxide Brayton cycle system is being considered for application in the power conversion system of advanced liquid metal fast reactors. One important research topic is the coupled heat transfer characteristics and enhanced heat transfer laws between liquid metals and supercritical fluids. However, the traditional Reynolds analogy hypothesis with a constant turbulent Prandtl number is difficult to satisfy the numerical conjugate heat transfer research of liquid metals and supercritical fluids. Therefore, based on the open-source computational fluid dynamics program OpenFOAM, a numerical method suitable for the coupled heat transfer calculation of liquid metals and supercritical fluids was developed, which can achieve precise conjugate heat transfer solutions by applying different turbulence models and heat flux models to liquid metals and supercritical fluids. Subsequently, based on this method, the coupled heat transfer behavior of liquid metals and supercritical fluids in the straight channel of a typically printed circuit heat exchanger was studied. The focus was investigating the conjugate heat transfer characteristics of liquid heavy metal lead-bismuth eutectic and liquid metal sodium with supercritical carbon dioxide. Some sensitive results, including the inlet temperature and Reynolds number of liquid metals and supercritical fluids, were qualitatively and quantitatively analyzed.

Direct Numerical Simulation of liquid metal forced and mixed convection in a square rod bundle

This paper reports results of Direct Numerical Simulations of fully developed, forced and mixed convection of Liquid Lead Bismuth Eutectic (LBE) around four vertical cylindrical rods arranged in a square lattice at Pr = 0.031. The solutions provided here are placed in a context where very few data are available for low-Prandtl flows, especially in mixed convection conditions, and can hence be useful for the development and validation of advanced turbulent heat transfer models. The equations are discretized using a Finite Volume implementation of a second order projection method. The irregular cylindrical boundaries are handled with an original Immersed Boundary technique. A single friction Reynolds number value is set (Reτ = 180) and buoyancy effects are accounted for by imposing the Rayleigh number, under the Boussinesq approximation. A Ra-value Ra = 2.5 ×104 is selected in order to investigate the main differences between forced and mixed convection at low Prandtl number values. Time-averaged velocity and temperature fields are shown, in order to discuss the main features of the flow and thermal fields. First order statistics are also presented, highlighting the effect of aiding buoyancy on turbulent heat and momentum transport.

Ignition characteristics of the high-velocity pulverized coal jet in MILD combustion mode: Experiments and prediction improvements

The influence of high jet velocity on the ignition characteristics of pulverized coal is very important for the Moderate or Intense Low-oxygen Dilution (MILD) combustion technology of pulverized coal. This paper conducts experimental and numerical simulation research on the ignition characteristics of the pulverized coal jet in a high-temperature environment based on the Hencken-type flat flame burner. The results show that when the ambient temperature is 1873 K and the ambient oxygen mole fraction is 5 %, the ignition delay distance of the pulverized coal jet decreases as the jet velocity increases from 15 m/s to 100 m/s for the formation of MILD combustion. The adoption of the turbulent particle heat transfer model and the non-spherical particle motion model effectively improves the prediction of particle dispersion, ignition delay, and reaction zone in the high-velocity coal jet flame. The enhancement of gas–solid heat transfer by turbulent fluctuation plays a dominant role in advancing the coal ignition in the high-velocity jet, while the non-spherical shape of coal particles mainly improves the uniformity of reaction distribution. The influence of ignition characteristics in the high-velocity jet on the MILD combustion formation of pulverized coal has been also analyzed in detail.

An inverse optimization of turbulent flow and heat transfer for a cooling passage with hierarchically arranged ribs in turbine blades

Owing to the limited cold-air amount and pressure in supply systems, high-efficient heat transfer with low-level friction loss is highly desired for cooling units of a turbine blade. To exploit the potential improvement of hierarchically arranged ribs in cooling passages proposed previously, multi-parameter optimizations for rib arrangements are implemented by integrating the simplified conjugate-gradient algorithm with the turbulent flow and heat transfer model. Rib heights as design variables are optimized with various performance indices as objective functions at a fixed Re. The optimizations confirm that using the wall temperature difference and Nu as the objective function, respectively, a limited heat transfer improvement is achieved with a greatly increased friction loss. Taking the overall performance factor as the objective function, different optimal designs at different constraint conditions possess hierarchical characteristics. A significant friction loss reduction of 52.1%, 54.7%, and 54.8%, is achieved with a moderate heat transfer loss of 10.9%, 7.0%, and 2.3%. Despite different thermal and friction performances, their overall performances are consistent with a remarkable increase of 13.9%, 21.2%, and 27.3%. Finally, the optimization strategy coupling the multi-parameter optimization and hierarchical scheme is confirmed as effective for enhancing the thermohydraulic performance of convective heat transfer systems with perturbation elements.

Model of multiphase flow, superheat transport, and particle capture in a steel continuous caster

A model of turbulent multiphase flow, heat transfer, and particle entrapment during continuous casting of steel is presented. The model includes the top 7m of the vertical and curved strand, and considers the effects of argon gas injection and thermal buoyancy. RANS model flow results are compared with LES. Lagrangian particle transport through the Eulerian-Eulerian multiphase flow field from the k-ɛ RANS model is based on random walk and features advanced particle capture criteria, improved from previous work by including anisotropic turbulent velocity fluctuations near the walls. Particle capture via 3 mechanisms is included: capture by solidified hooks at the meniscus, entrapment between dendrites, and engulfment by surrounding large particles. The fluid flow and bubble/inclusion capture results are validated with plant measurements, including nail board dipping tests and ultrasonic tests of particle locations, and good agreement is seen. The superheat has negligible effect on flow in the mold region but causes complex flow in the lower strand by creating multiple recirculation zones due to the thermal buoyancy. With high (30 K) superheat, this leads to less penetration, and slightly fewer and shallower capture of particles. Lower (10 K) superheat may enable significant top surface freezing, leading to very large internal defect clusters. Lower superheat also leads to deeper meniscus hooks, and more surface capture. Capture bands occur near the transition from vertical to curved, where downward liquid flow velocity balances the particle terminal velocity.

Direct numerical simulation of flow and heat transport in a closely-spaced bare rod bundle

Direct Numerical Simulation (DNS) of fully-developed flow and heat transfer is performed for a bare rod bundle with a low pitch-to-diameter ratio using the highly-scalabale spectral element code Nek5000. The simulation is performed at a Reynolds number, Reh, based on the bulk velocity and hydraulic diameter, of 9800, with iso-temperature and iso-flux thermal boundary conditions and Prandtl numbers 0.025, 1.0 and 2.0. The mean velocity and temperature statistics are first validated against the experimental measurements of Hooper et al. (1983) and complementary DNS results of Lai et al. (2019) which are reported in the literature at a higher Reh of 22,600. The mean flow and temperature are demonstrated a similar behaviour at the present low Renolds number and the higher Reynolds number of Lai et al. (2019), indicating the Reynolds number scaling of the mean flow. The anisotropy of the flow is illustrated using distribution of normal and Reynolds stresses, and the Lumley invariant map. It is shown that the turbulence in the subchannel region is characteristic of wall-bounded turbulent flows such as channel flows. In the narrow gap, however, turbulence is suppressed, only enhanced in the streamwise direction due to flow pulsations. Further, temperature statistics with both thermal boundary conditions are presented, demonstrating the effect of the Prandtl number on the mean and fluctuating quantities. The temperature statistics with iso-temperature wall boundary conditions, not reported in literature before, are shown to behave differently in the interstitial subchannel region and the narrow gap between two rods. The distribution of turbulent heat flux is also presented. The streamwise component of turbulent heat flux is again shown to be enhanced, in comparison to the same in the subchannel. The pulsating motion of flow across the narrow gap is discussed further. A frequency analysis of the velocity in the narrow gap elucidates the frequency of flow pulsations. Unlike mean flow statistics, the flow pulsations are shown to exhibit a low Reynolds number effect. The reference DNS data presented in the present work, complementary to that of Lai et al. (2019), serves as a benchmark against which lower order turbulence models may be further developed or improved. In particular, the newly presented anisotropy data and the turbulence heat flux data are essential for further development, improvement and validation of turbulent heat transfer models at different Prandtl numbers.

Numerical study on conjugate heat transfer characteristics of liquid lead-bismuth eutectic and supercritical carbon dioxide in a PCHE straight channel

The Printed Circuit Heat Exchanger (PCHE) is the optimal heat transfer structure of the fourth-generation advanced Lead–Bismuth Eutectic (LBE) cooled fast reactor coupling with the supercritical carbon dioxide (S-CO2) Brayton cycle system. It is of great significance to study the conjugate heat transfer characteristics between LBE with low Prandtl number turbulent heat transfer characteristics and S-CO2 with supercritical convective heat transfer characteristics. However, the conventional Reynolds analogy assumption will affect the numerical heat transfer precision of LBE and, thus, the accuracy of the coupled heat transfer of LBE and S-CO2. In the present work, an advanced two-equation turbulent heat transfer model, which can effectively correct the numerical heat transfer process of LBE, is introduced into the conjugate heat transfer solver of the open-source Computational Fluid Dynamics (CFD) program OpenFOAM, where the Reynolds analogy assumption is retained to reproduced the heat transfer of S-CO2 flow away from the pseudo-critical region. The currently developed model and numerical method are compared with the experimental data of an LBE-cooled pipe and the simulation data of conjugated heat transfer of S-CO2 and S-CO2 in a PCHE straight channel. The results show that the calculation method in this study can improve the numerical conjugate heat transfer accuracy of LBE compared with the Reynolds analogy assumption model and can reproduce the flow and heat transfer process of S-CO2 in a PCHE straight channel. Then, the conjugate heat transfer characteristics between LBE and S-CO2 in a PCHE straight channel are studied. The effects of inlet Reynolds number and inlet temperature are focused on to study the conjugate heat transfer law of LBE coupling S-CO2.

Numerical study on conjugate heat transfer in a liquid-metal-cooled pipe based on a four-equation turbulent heat transfer model

Conjugate heat transfer between liquid metal and solid is a common phenomenon in a liquid-metal-cooled fast reactor's fuel assembly and heat exchanger, dramatically affecting the reactor’s safety and economy. Therefore, comprehensively studying the sophisticated conjugate heat transfer in a liquid-metal-cooled fast reactor is profound. However, it has been evidenced that the traditional Simple Gradient Diffusion Hypothesis (SGDH), assuming a constant turbulent Prandtl number (Prt, usually 0.85 - 1.0), is inappropriate in the Computational Fluid Dynamics (CFD) simulations of liquid metal. In recent decades, numerous studies have been performed on the four-equation model, which is expected to improve the precision of liquid metal’s CFD simulations but has not been introduced into the conjugate heat transfer calculation between liquid metal and solid. Consequently, a four-equation model, consisting of the Abe k−ε turbulence model and the Manservisi kθ−εθ heat transfer model, is applied to study the conjugate heat transfer concerning liquid metal in the present work. To verify the numerical validity of the four-equation model used in the conjugate heat transfer simulations, we reproduce Johnson’s experiments of the liquid lead-bismuth-cooled turbulent pipe flow using the four-equation model and the traditional SGDH model. The simulation results obtained with different models are compared with the available experimental data, revealing that the relative errors of the local Nusselt number and mean heat transfer coefficient obtained with the four-equation model are considerably reduced compared with the SGDH model. Then, the thermal-hydraulic characteristics of liquid metal turbulent pipe flow obtained with the four-equation model are analyzed. Moreover, the impact of the turbulence model used in the four-equation model on overall simulation performance is investigated. At last, the effectiveness of the four-equation model in the CFD simulations of liquid sodium conjugate heat transfer is assessed. This paper mainly proves that it is feasible to use the four-equation model in the study of liquid metal conjugate heat transfer and provides a reference for the research of conjugate heat transfer in a liquid-metal-cooled fast reactor.

Thermal-hydraulic study on the VHELP rod bundle of China initiative accelerator driven system

Wire-wrapped rod bundles are candidate fuel assembly forms for the Lead–Bismuth Eutectic (LBE) cooled reactor of China initiative Accelerator Driven System (CiADS). The hydraulic experiment of the 19-rod bundle has been completed on the Visual Hydraulic Experimental Loop Platform (VHELP) of CiADS. It is necessary to study the thermal–hydraulic behavior of VHELP 19-rod bundles, providing a reference for the safety design of CiADS. Since the wire structure forces the LBE coolant having low Prandtl number heat transfer characteristics to cross mixing in the channel, a turbulent heat transfer model that can simulate reasonably the Reynolds stress and Reynolds heat flux is needed in the numerical calculation. In the present work, an isotropic four-equation model, which considers the difference between the velocity field and the temperature field of LBE and allows simple zero-fixed-value boundary conditions to be imposed on the wall for turbulent kinetic energy k and its dissipation rate ε∼, temperature fluctuation kθ and its dissipation rate εθ∼, was applied to investigate the heat transfer phenomenon of VHELP rod bundles in CiADS project. Firstly, the flow pressure drop characteristics with different Reynolds numbers of the VHELP rod bundles were studied. The pressure drop data predicted by the present isotropic four-equation model agrees with the Cheng and Todreas relation but is higher than the hydraulic experimental results of unheated wire-wrapped rod bundles for the CiADS-VHELP project. Finally, the effects of flow rates and heat fluxes on the detailed thermal–hydraulic behavior of VHELP rod bundles with seven pitches were quantitatively analyzed. This study can reference the design and experimental project of the LBE-cooled wire-wrapped fuel assembly in CiADS.

RANS Modeling of Turbulent Flow and Heat Transfer in a Droplet-Laden Mist Flow through a Ribbed Duct

The local structure, turbulence, and heat transfer in a flat ribbed duct during the evaporation of water droplets in a gas flow were studied numerically using the Eulerian approach. The structure of a turbulent two-phase flow underwent significant changes in comparison with a two-phase flow in a flat duct without ribs. The maximum value of gas-phase turbulence was obtained in the region of the downstream rib, and it was almost twice as high as the value of the kinetic energy of the turbulence between the ribs. Finely dispersed droplets with small Stokes numbers penetrated well into the region of flow separation and were observed over the duct cross section; they could leave the region between the ribs due to their low inertia. Large inertial droplets with large Stokes numbers were present only in the mixing layer and the flow core, and they accumulated close to the duct ribbed wall in the flow towards the downstream rib. An addition of evaporating water droplets caused a significant enhancement in the heat transfer (up to 2.5 times) in comparison with a single-phase flow in a ribbed channel.

Proposal of a turbulent Prandtl number model for Reynolds-averaged Navier–Stokes approach on the modeling of turbulent heat transfer of low-Prandtl number liquid metal

Because of their high molecular heat conductivity, low-Prandtl number liquid metal is a promising candidate coolant for various designs of advanced nuclear systems such as liquid metal–cooled fast reactors and accelerator-driven sub-critical system (ADS). With the fast-growing computational capacity, more and more attention has been paid to applying computational fluid dynamics (CFD) methods in thermal design and safety assessment of such systems for a detailed analysis of three-dimensional thermal–hydraulic behaviors. However, numerical modeling of turbulent heat transfer for low-Prandtl number liquid metal remains a challenging task. Numerical approaches such as wall-resolved large eddy simulation (LES) or direct numerical simulation (DNS), which can provide detailed insight into the physics of the liquid metal flow and the associated heat transfer, were widely applied to investigate the turbulent heat transfer phenomenon. However, these approaches suffer from the enormous computational consumption and are hence limited only to simple geometrical configurations with low to moderate Reynolds numbers. The Reynolds-averaged Navier–Stokes (RANS) approach associated with a turbulent Prandtl number Prt accounting for the turbulent heat flux based on Reynolds analogy is still, at least in the current state in most of the circumstances, the only feasible approach for practical engineering applications. However, the conventional choice of Prt in the order of 0.9∼unity in many commercial computational fluid dynamics codes is not valid for the low-Prandtl number liquid metal. In this study, LES/DNS simulation results of a simple forced turbulent channel flow up to a friction Reynolds number Reτ of 2000 at Pr of 0.01 and 0.025 were used as references, to which the Reynolds-averaged Navier–Stokes approach with varying Prt was compared. It was found that the appropriate Prt for the RANS approach decreases with bulk Peclet number Peb and approaches a constant value of 1.5 when Peb becomes larger than 2000. Based on this calibrated relation with Peb, a new model for Prt used in the RANS approach was proposed. Validation of the proposed model was carried out with available LES/DNS results on the local temperature profile in the concentric annulus and bare rod bundle, as well as with experimental correlations on the Nusselt number in a circular tube and bare rod bundle.

Validation of turbulent heat transfer models against eddy covariance flux measurements over a seasonally ice-covered lake

Abstract. In this study we analyzed turbulent heat fluxes over a seasonal ice cover on a boreal lake located in southern Finland. Eddy covariance (EC) flux measurements of sensible (H) and latent heat (LE) from four ice-on seasons between 2014 and 2019 are compared to three different bulk transfer models: one with a constant transfer coefficient and two with stability-adjusted transfer coefficients: the Lake Heat Flux Analyzer and SEA-ICE. All three models correlate well with the EC results in general while typically underestimating the magnitude and the standard deviation of the flux in comparison to the EC observations. Differences between the models are small, with the constant transfer coefficient model performing slightly better than the stability-adjusted models. Small difference in temperature and humidity between surface and air results in low correlation between models and EC. During melting periods (surface temperature T0>0 ∘C), the model performance for LE decreases when compared to the freezing periods (T0<0 ∘C), while the opposite is true for H. At low wind speed, EC shows relatively high fluxes (±20 W m−2) for H and LE due to non-local effects that the bulk models are not able to reproduce. The complex topography of the lake surroundings creates local violations of the Monin–Obukhov similarity theory, which helps explain this counterintuitive result. Finally, the uncertainty in the estimation of the surface temperature and humidity affects the bulk heat fluxes, especially when the differences between surface and air values are small.

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.

Discharge effectiveness of thermal energy storage systems

The use of air as heat transfer fluid and a packed bed of rocks as storage medium for a thermal energy system (TES) can be a cost-effective alternative for thermal applications. Here, a porous media turbulent flow (standard k-ε) and heat transfer (local thermal non-equilibrium) model is used to simulate the discharge cycle of such system. Temperature fields of corresponding charging cycles are used as initial conditions. Effects of varying mass flow rates (Re number), porosity, permeability (Da number), thermal conductivity ratio and thermal capacity ratio on the effectiveness of the discharge are compared. The examination of these effects indicated that increasing the mass flow rate improved the effectiveness of the discharge, which was not seen for the charging cycle. Also, increasing porosity improved discharge efficiency more significantly than it did in the charging cycle. In both charge and discharge cycles the effect of permeability is significant and reducing Da number improved temperature stratification and efficiencies. The effect of the thermal conductivity ratio was mostly seen on the outlet temperatures, where lower ratios allowed for higher temperature values. Increasing the thermal capacity ratio improved charging effectiveness but, on the discharge cycle, cycle this effect was reduced. Moreover, for lower Re number flows, increasing this ratio reduced efficiency indicating that the mass flow rate should be matched carefully with the thermal capacity of the system. All these effects have important implications which should be taken into consideration when designing an effective thermal energy storage system.

Study on the flow and heat transfer characteristics of liquid sodium in a hexagonal 7-rod bundle

The flow and heat transfer characteristics of liquid metal sodium are different from the ordinary fluids, which brings great challenges to the CFD simulation in the sodium-cooled fast reactor (SFR). Therefore, the accurate flow and heat transfer models are particularly significant in the high fidelity three dimensional analysis of liquid metal reactors. In this paper, the OpenFOAM solver implemented with k – ε – kθ – εθ turbulent heat transfer model was developed and used to study the flow and heat transfer characteristics of liquid metal sodium. Firstly, the proposed thermal hydraulic models were validated against the thermal hydraulic experiment of single-phase liquid sodium in a 7-rod bundle. The key thermal hydraulic parameters, such as the Nusselt number, pressure drop and frictional coefficient, were compared with the experimental data. Results show that the developed OpenFOAM solver with new implemented model performs well and the simulated results were in good agreement with the experimental data. Then the thermal–hydraulic characteristics of liquid sodium in the bend rod bundle were investigated. The effects of bending angle, Reynolds number on peak wall temperature and Nusselt number were investigated. CFD results suggest that the heat transfer in the bend rod bundle is highly sensitive to the bending angle but not to Reynolds number. Two opposite-direction cross flows were formed in the sections before and after the maximum bend position, which reveals the formation and disappearance of hot spot in the narrow gap.

Generalized semi-mechanistic model of impinging jet quenching heat transfer

In the present analysis, a semi-mechanistic maximum heat flux (qmhf) model has been developed for sub-cooled jet impingement cooling of the heated surface. The model for evaporative heat flux is based on the work of Katto's Model of Helmholtz instability theory of liquid thin film. While the convective heat transfer is derived from the model of bubble-induced turbulent heat transfer using integral analysis. Subsequently, the semi-mechanistic model of maximum heat flux is developed utilizing the assumption of infinite thermal conductivity of heated surface. In addition, experiments were performed on a heated vertical stainless steel foil of 0.15 mm thickness (SS-304) by circular horizontal impinging jets. Number of experimental parameters were studied including, initial surface temperature, nozzle to plate distance, flow rate, and effect of additives like surfactants and nanofluids. Finally, a generalized model for the maximum heat flux of sub-cooled jet is presented by incorporated different empirical parameters into the model using regression analysis with test data. Various modeling parameters are identified in the present investigation and comparisons of the present model with present tests data and previous findings are presented.

Direct Numerical Simulation of natural, mixed and forced convection in liquid metals: selected results

Selected results of three Direct Numerical Simulations are presented, on relevant test cases for the thermal hydraulics of liquid–metal-cooled nuclear reactors, encompassing a wide spectrum of turbulent convection regimes. The first test case is a Rayleigh-Bénard cell at a Grashof number Gr=5×107, representative of the conditions in the unstably stratified layer of coolant in a reactor pool in both standard operating conditions and emergency situations, e.g. shutdown of the cooling system. The second case is the mixed convection in a cold-hot–cold triple jet configuration, representative of liquid streams exiting from the core into the pool, and relevant for the modeling of thermal striping and thermal fatigue phenomena on the vessel containment walls. The third case is the fully-developed flow in a vertical bare rod bundle with triangular arrangement and a pitch-to-diameter ratio P/D=1.4, in both forced and mixed convection conditions. These regimes respectively represent normal operation or decay heat removal conditions in reactor cores. The availability of these numerical databases will allows for an in-depth analysis of the turbulent flow and heat transfer in liquid metals under different convection regimes, and is also relevant for the development, calibration and validation of turbulent heat transfer models.

RANS modeling of turbulent flow and heat transfer of non-Newtonian viscoplastic fluid in a pipe

A mathematical model of the movement and heat transfer of a turbulent non-isothermal non-Newtonian fluid through a pipe wall with a cold surrounding space has been developed and simulated numerically. Fluid turbulence is described in the framework of the isotropic two-parameter k– ε˜ model. The Newtonian properties of the fluid in the initial cross-sections of the pipe transformed gradually into a viscoplastic non-Newtonian Bingham-Schwedoff fluid state due to heat transfer through the pipe wall between the heated fluid and a cold environment. The value of its streamwise velocity in the axial zone increased significantly when the fluid moved along the pipe. On the contrary, it decreased in the near-wall zone and the height of the region with a zero fluid velocity increased. This occurred due to the viscoplastic properties of a non-Newtonian fluid. The height of the region with a zero fluid velocity in the pipe increased gradually as the non-Newtonian fluid (waxy crude oil) moved through the pipe. A noticeable increase in the level of turbulent kinetic energy in the axial zone of the pipe and its noticeable decrease in its near-wall region were observed. A significant increase in the average dynamic viscosity and yield stress in the near-wall part of the pipe was shown. The boundary of the area of existence of Newtonian properties of fluid was determined. The height of the region with a zero fluid velocity in the pipe increased gradually as waxy crude oil moved through the pipe and reached y/R ≈ 0.1 at x/D = 15.

Computational model for turbulent heat transfer in buoyancy-influenced flows at supercritical pressures in circular tubes

Turbulent heat transfer at supercritical pressures in fluids flowing upward in heated circular tubes is very likely to be affected by buoyancy and, when this buoyancy is stronger than a certain value, mixed convection occurs. The turbulent mixed convection heat transfer is very complex, and none of the existing turbulence models can adequately simulates the experimental or DNS data including mixed convection. A hybrid turbulence model that blended two turbulence models, which used the Kolmogorov velocity scale and wall shear stress, respectively, has shown a good performance in predicting experiments or DNS. However, even the blended model has not been satisfactory for large buoyancy parameter (Bu). It is judged that the inadequacy is due to the treatment of the coefficient of the production term in the dissipation rate equation as a constant. The semi-local scaling concept has been found to be inadequate. As a remedy, the coefficient associated with the production term in the dissipation rate equation is treated as a function of turbulent boundary layer deformation and Bu, and an integrated density concept instead of local density is used in calculating friction velocity. The computational model improved from the previous blended turbulence model by introducing the two concepts satisfactorily predicts the DNS data.