Constant Turbulent Prandtl Number Research Articles

Countergradient turbulent transport in a plume with a crossflow

AbstractDirect numerical simulation of a turbulent forced buoyant plume in a crossflow is performed at a source Reynolds number $${\text{ Re }}_0=1000$$ Re 0 = 1000 , Richardson number $$\mathrm{{Ri}}_0=1$$ Ri 0 = 1 , Prandtl number $$\mathrm{{Pr}}=1$$ Pr = 1 and source-to-crossflow velocity ratio $$R_0=1$$ R 0 = 1 . The instantaneous and temporally averaged flow fields are assessed in detail, providing an overview of the flow dynamics. The velocity, temperature and pressure fields are used together with enstrophy fields to describe qualitatively the evolution of the plume as it is swept downstream by the crossflow, and the mechanisms involved in its evolution are outlined. The plume trajectory is determined quantitatively in a number of ways, and it is shown that the central streamline and the centre of buoyancy of the plume differ significantly—as with jets in crossflow, the central streamline is seen to follow the top of the plume, whereas the centre of buoyancy, by definition, describes the plume as a whole. We then investigate the turbulence properties inside the plume; in particular the eddy viscosity and diffusivity are presented, which are significant parameters in turbulence modelling. Assessment of turbulence production demonstrates the presence of regions where turbulence kinetic energy is redistributed to the kinetic energy of the mean flow, implying a negative eddy viscosity within certain regions of the domain. Similarly, the observation that the buoyancy flux and buoyancy gradient are anti-parallel in specific regions of the flow implies a negative eddy diffusivity in said regions, which must be realised in models of such flows in order to capture the countergradient transport of thermal properties. A characteristic eddy viscosity and diffusivity are presented, and shown to be approximately constant in the fully developed regime, resulting in a constant characteristic turbulent Prandtl number, in turn signifying self-similarity.

Numerical Study of Turbulent Heat Transfer of Annular Fuel Assembly in a Sodium-cooled Fast Reactor by a SST k-ω-kθ-εθ Model

ABSTRACT The annular fuel has two cooling surfaces inside and outside, which can fully take away the heat of the fuel assemblies, and have strong advantages in safety and economy. It is urgent to conduct research on sodium-cooled fast reactor annular fuel assemblies. The Prandtl number Pr of liquid sodium is much less than 1 (Pr˂˂1). The problem is that using the traditional constant turbulent Prandtl number Pr t of 0.85 ~ 0.9, which is generally derived from the Reynolds analogy hypothesis suitable for conventional fluids, will greatly affect the accuracy of the numerical prediction of the thermal-hydraulic properties of liquid sodium in annular fuel assemblies. In order to address this issue, the turbulent heat transfer characteristics of the bare 7-pin annular fuel assembly and the annular fuel assembly with wire spacers for a sodium-cooled fast reactor are investigated by a SST k-ω-k θ -ε θ model, which couples the SST k-ω turbulence model with a two-equation k θ -ε θ heat flux model as a way to transport the turbulent stress and turbulent heat flux of liquid sodium. The open-source CFD software OpenFOAM is used for this calculation. In order to verify the validity of the present calculation method, some classical liquid metal heat transfer correlations are used to compare and analyze the results of the present calculation method (k θ -ε θ model), the results of the Reynolds analogy hypothesis (Pr t = 0.85 model), and the results of the turbulent Prandtl number correlation (Pr t =kays model). It is shown that the SST k-ω-Pr t = 0.85 model overestimates the Nusselt number Nu of the internal flow field and sub-channels of the annular fuel assembly. The SST k-ω-k θ -ε θ model agrees well with the SST k-ω-Pr t =Kays model in the internal flow field and sub-channels of the bare 7-pin annular fuel assembly and the annular fuel assembly with wire spacers. It suggests that the numerical calculation results of the SST k-ω-k θ -ε θ model are reliable in both the simple fuel assembly models and complex fuel assembly models. In brief, the SST k-ω-k θ -ε θ model is more capable of predicting the turbulent heat transfer characteristics of the bare 7-pin annular fuel assembly and the annular fuel assembly with wire spacers in sodium-cooled fast reactors. In addition, the thermal-hydraulic characteristics of annular fuel assemblies with wire spacers for sodium-cooled fast reactors have been investigated. This research can provide a reference for the study of turbulent heat transfer characteristics of annular fuel assemblies in sodium-cooled fast reactor.

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 flow and heat transfer of supercritical water with different heat fluxes

The flow and heat transfer characteristics of supercritical water (SCW) are important considerations in the thermal-hydraulic design of the Supercritical Water-Cooled Reactor (SCWR). In the present study, the direct numerical simulation (DNS), developed with OpenFOAM, was utilized to investigate the effect of heat flux on the flow and heat transfer of SCW in a vertical circular pipe. The investigation involves detailed analyses of the wall temperature, velocity distribution, and turbulent statistics at various heat fluxes. It was found that buoyancy first impairs heat transfer, and then recovers heat transfer. This is attributed to the variation of buoyancy production and turbulence production, which are resulted from the buoyancy direct effect and indirect effect, respectively. As the heat flux increases, the recovery occurs earlier with higher magnitude. The vortex structures based on Q-criterion clearly illustrate the same process as well. Several heat-transfer correlations were assessed based on the DNS results. It indicates that Dittus and Boelter correlation (1930) cannot accurately predict the heat-transfer characteristics of SCW, while Chen and Fang correlation (2014) exhibits a higher level of predictive accuracy for Nusselt number. In addition, several turbulence models were evaluated against the DNS data. The results show significant deviations in predicting the heat transfer of SCW. The large discrepancy may be due to the inappropriate model coefficients, the failed predication of turbulence kinetic energy, as well as the constant turbulent Prandtl number commonly applied.

Coupling heat transfer study of liquid sodium and supercritical carbon dioxide in a PCHE straight channel based on a four-equation model

The Brayton cycle using supercritical carbon dioxide (S-CO2) as the working fluid is expected to be a thermo-power conversion technology for sodium-cooled fast reactors. Printed Circuit Heat Exchanger (PCHE) is the key heat transport structure to realize the above technology. The study of conjugate heat transfer characteristics of sodium (Na) with low Prandtl number turbulent heat transfer characteristics and S-CO2 with supercritical convective heat transfer behaviors in a PCHE channel are of great significance. However, the constant turbulent Prandtl number (Prt) model obtained by the general Reynolds analogy hypothesis may affect the conjugate heat transfer assessment between Na and S-CO2. Compared with the constant Prt model, the fluid’s Prt distribution can be obtained by four-equation models, introducing the transport of turbulent kinetic energy k, dissipation rate ε of k, temperature fluctuation kθ, and dissipation rate εθ of kθ. The four-equation model is expected to obtain more effective conjugate heat transfer characteristics between Na andS-CO2, while there are no available commercial codes. Therefore, in this paper, two kinds of four-equation model, which can effectively evaluate the heat transport performance of Na with low-Prandtl number and S-CO2 away from the pseudo-critical region, respectively, are first introduced into the conjugate heat transfer solver of OpenFOAM. Then the conjugate heat transfer experiment data of Na in a pipe and the simulation data of S-CO2 in a PCHE straight channel are used to verify the validity of the numerical model in this paper. The results show that the present calculation method can effectively reproduce the numerical conjugate heat transfer process of Na and S-CO2. Finally, based on four-equation models, the coupling heat exchange performance of Na/S-CO2 are studied to obtain the effects of mass rate and temperature on the conjugate heat transfer process between Na and S-CO2 in a PCHE straight channel.

Assessment of Computational Fluid Dynamic Modeling of Multi-Jet Impingement Cooling and Validation With the Experiments

Abstract The current study involves numerical and experimental investigations of circular in-line jets impinging on a heated flat plate. The generic configuration is characterized by nine jets, each with a diameter of D = 0.0152 m. The jets are influenced by a self-generating crossflow and are positioned at a nozzle-to-plate distance (H/D) of 5 and a jet pitch (p/D) of 5. The steady Reynolds-averaged Navier–Stokes (RANS) simulations are performed for turbulent jet Reynolds numbers with the in-house CFD code TRACE. The Menter k–ω shear stress transport (SST) model is applied for turbulence modeling and the turbulent scalar fluxes are modeled based on the Reynolds analogy for a constant turbulent Prandtl number. To gain a closer insight into the impingement jet physics, high-resolution near-wall velocity and thermal fields are obtained through large eddy simulations (LESs) and measurements from particle image velocimetry (PIV). Focus is laid on the comparison of RANS results with the LES data and the experimental data. The results exhibit a qualitative similarity between the simulations and the experiments. Furthermore, correlations of the Nusselt number from the literature are used to validate the simulation results.

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.

Validation of a numerical model for hot-spot detection on the surface of a rotor pole using a scale model of a hydroelectric generator

To meet the ever-increasing demand for electricity, Hydro-Québec is investigating the viability of running its existing hydroelectric generators at higher power levels than their current operating limits. To assist in this investigation, numerical models capable of simulating the conjugate turbulent air flow and heat transfer phenomena in these generators were formulated and then validated, by using them to predict these phenomena within a scale model of a hydroelectric generator available at Hydro-Québec’s Research Institute and comparing the results to complementary experimental data. Reynolds-averaged governing equations were used, with turbulent stresses and heat fluxes approximated using eddy-viscosity and eddy-diffusivity approaches, in conjunction with the standard k − ɛ and a k − ω shear-stress-transport models, constant turbulent Prandtl number, and specialized treatments of the near-wall regions. Variable- and constant-fluid-property formulations (with coupled and decoupled solutions of the fluid flow and heat transfer) were assessed. The discretization of the complex geometry and the governing equations, and solutions of the discretized equations, were done using commercial codes. These numerical models gave favorable and comparable results, with predictions of global flow quantities (such as windage losses and overall mass flow rates) lying within 4%, and average and maximum temperatures of the pole surface within 5 °C and 3 °C, respectively, of the corresponding experimental data when using the constant-property, coupled, standard k − ɛ model with specialized wall functions. However, the equivalent decoupled model, which was the least computationally intensive, was also adequate for the task at hand. Numerical assessments of two alternate ventilation configurations in the scale model were also undertaken. They showed that increasing the surface area of the spider arms reduced the maximum temperature of the pole by 2.6 °C; and restricting the rotor inlet area reduced the windage losses and the maximum temperature of the pole by 4.7% and 1.5 °C, respectively. • 3D Conjugate heat transfer simulations of a hydroelectric generator scale model. • Validation of flow and temperature distributions by way of experimental measurements. • In contrast with design assumptions, flow across the rotor rim ducts is non-uniform. • Numerical predictions of hot-spots on the scale model’s rotor to within 2.7 °C. • Proposed modifications to the rotor design to reduce rotor pole hot-spot temperatures.

Thermal-hydraulic study in a wire-wrapped 19-rod bundle based on an isotropic four-equation model

The thermal–hydraulic performance of rod bundles with wire spacers is significant for studying Lead–Bismuth Eutectic (LBE) cooled fast reactor. The problem is that using the traditional constant turbulent Prandtl number of 0.85 ∼ 0.9, which is generally derived from the Reynolds analogy hypothesis suitable for conventional fluids, will greatly affect the numerical heat transfer accuracy of LBE having low Prandtl number properties. Thus, a great quantity of development work of four-equation models, which may improve the calculation accuracy of turbulent heat transfer in LBE flows, has been made by researchers, while no commercial code is available. The present work addresses an effort to study the thermal–hydraulic phenomenon in an LBE-cooled 19-rod bundle with wire spacers geometry on a self-compiled CFD solver (iso4eqnFoam), which is implemented by a standard finite volume method and C++ program and developed on OpenFOAM. In particular, the simulation aims to perform fully-developed turbulent stresses and turbulent heat fluxes by solving an isotropic four-equation model, which allows simple zero-fixed-value boundary conditions for turbulent variables and considers the difference between viscous and thermal boundary layer of LBE. The simulation results on a bare 19-rod bundle are first compared with heat transfer experimental data and other simulations to validate the effectiveness of the solver. Then, an LBE-cooled 19-rod bundle with wire spacers is presented with thermal–hydraulic simulations. The result shows that iso4eqnFoam can simulate the turbulent heat transfer of LBE under complex geometry. Finally, the distributions of temperature, temperature fluctuation, and turbulent Prandtl number in the channel of the wire-wrapped rod bundle are reported based on the isotropic four-equation model.

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.

A collaborative effort towards the accurate prediction of turbulent flow and heat transfer in low-Prandtl number fluids

This article reports the experimental and DNS database that has been generated, within the framework of the EU SESAME and MYRTE projects, for various low-Prandtl flow configurations in different flow regimes. This includes three experiments: confined and unconfined backward facing steps with low-Prandtl fluids, and a forced convection planar jet case with two different Prandtl fluids. In terms of numerical data, seven different flow configurations are considered: a wall-bounded mixed convection flow at low-Prandtl number with varying Richardson number (Ri) values; a wall-bounded mixed and forced convection flow in a bare rod bundle configuration; a forced convection confined backward facing step (BFS) with conjugate heat transfer; a forced convection impinging jet for three different Prandtl fluids corresponding to two different Reynolds numbers of the fully developed planar turbulent jet; a mixed-convection cold-hot–cold triple jet configuration corresponding to Ri = 0.25; an unconfined free shear layer for three different Prandtl fluids; and a forced convection infinite wire-wrapped fuel assembly. This wide range of reference data is used to evaluate, validate and/or further develop different turbulent heat flux modelling approaches, namely simple gradient diffusion hypothesis (SGDH) based on constant and variable turbulent Prandtl number; explicit and implicit algebraic heat flux models; and a second order turbulent heat flux model. Lastly, this article will highlight the current challenges and perspectives of the available turbulence models, in different codes, for the accurate prediction of flow and heat transfer in low-Prandtl fluids.

Numerical and experimental analysis of a planar jet with heated co-flow at medium and low Prandtl-number values

In the present work, we combine experiments and numerical simulations of a planar jet with heated co-flow with medium (air) and low-Prandtl (He-Xe gas mixture) fluids. Jets are recognized as representative test cases to be investigated in large components of pool-type liquid metal-cooled nuclear systems, like the Multi-purpose hYbrid Research Reactor for High-tech Applications (MYRRHA), currently under design at SCK•CEN. The present planar jet configuration mimics a closed wind tunnel that is designed and operated at VKI to generate an experimental database for velocity and temperature fields of a turbulent forced-convection flow regime. The performed experiments combine the Particle Imaging Velocimetry (PIV) (in characteristic planes) and thermocouple (single point) measurements. In parallel with experiments, comprehensive numerical simulations have been performed within the RANS modeling framework. Next to the standard eddy-viscosity based two-equation k-ε model, an extended variant based on the low-Reynolds elliptic relaxation concept (so-called ζ-f model) has been applied too. To investigate the low-Prandtl effects on the heat transfer, series of the turbulent heat transfer models have been applied, ranging from a conventional constant turbulent Prandtl number to a more elaborate kθ-εθ model. The combination of the low-Reynolds ζ-f and kθ-εθ models was explored for the first time in the content of nuclear engineering applications. The focus of the numerical studies is to address in details the effects of low-Prandtl fluid in the strongly forced convection flow (central planar cold jet) in presence of a strong shear (hot co-flow). We demonstrate the importance of the proper specification of the inlet boundary conditions in numerical simulations to mimic correctly experimentally observed asymmetrical distributions of the cross-wise profiles of stream-wise velocity, turbulent kinetic energy and temperature. Finally, the minor differences in results between the assumed constant turbulent Prandtl number and more advanced kθ-εθ model of the turbulent heat flux confirmed the overly dominant mechanisms of the strong convection and molecular diffusion in the present configuration.

On the turbulence structure of deep katabatic flows on a gentle mesoscale slope.

A comprehensive analysis of the turbulence structure of relatively deep midlatitude katabatic flows (with jet maxima between 20 and 50 m) developing over a gentle (1°) mesoscale slope with a long fetch upstream of the Meteor Crater in Arizona is presented. The turbulence structure of flow below the katabatic jet maximum shows many similarities with the turbulence structure of shallower katabatic flows, with decreasing turbulence fluxes with height and almost constant turbulent Prandtl number. Still stark differences occur above the jet maximum where turbulence is suppressed by strong stability, is anisotropic and there is a large sub‐mesoscale contribution to the flux. Detecting the stable boundary‐layer top depends on the method used (flux‐ vs. anisotropy‐profiles) but both methods are highly correlated. The top of the stable boundary layer, however, mostly deviates from the jet maximum height or the top of the near‐surface inversion. The flat‐terrain formulations for the boundary‐layer height correlate well with the detected top of the stable boundary layer if the near‐surface and not the background stratification is used in their formulations; however, they mostly largely overestimate this boundary‐layer height. The difference from flat‐terrain boundary layers is also shown through the dependence of size of the dominant eddy with height. In katabatic flows the eddy size is semi‐constant with height throughout the stable boundary‐layer depth, whereas in flat terrain, eddy size varies significantly with height. Flux‐gradient and flux‐variance relationships show that turbulence data from different stable boundary‐layer scaling regimes collapse on top of each other showing that the dominant dependence is not on the scaling regime but on the local stability.

A Turbulence Closure Study of the Flow and Thermal Fields in the Ekman Layer

We assess the performance of turbulence closures of varying degrees of sophistication in the prediction of the mean flow and the thermal fields in a neutrally-stratified Ekman layer. The Reynolds stresses that appear in the Reynolds-averaged momentum equations are determined using both eddy-viscosity and complete differential Reynolds-stress-transport closures. The results unexpectedly show that the assumption of an isotropic eddy viscosity inherent in eddy-viscosity closures does not preclude the attainment of accurate predictions in this flow. Regarding the Reynolds-stress transport closure, two alternative strategies are examined: one in which a high turbulence–Reynolds–number model is used in conjunction with a wall function to bridge over the viscous sublayer and the other in which a low turbulence–Reynolds-number model is used to carry out the computations through this layer directly to the surface. It is found that the wall-function approach, based on the assumption of the applicability of the universal logarithmic law-of-the-wall, yields predictions that are on par with the computationally more demanding alternative. Regarding the thermal field, the unknown turbulent heat fluxes are modelled (i) using the conventional Fourier’s law with a constant turbulent Prandtl number of 0.85, (ii) by using an alternative algebraic closure that includes dependence on the gradients of mean velocities and on rotation, and (iii) by using a differential scalar-flux transport model. The outcome of these computations does not support the use of Fourier’s law in this flow.

Status and perspectives of turbulent heat transfer modelling in low-Prandtl number fluids

Thermal-hydraulics is recognized as a key safety challenge in the development of liquid metal cooled reactors. At nominal operating conditions, the Prandtl number of liquid metals which are used as primary coolants, such as lead and sodium, is very low: typically of the order of 0.025–0.001. Obtaining an accurate prediction of the turbulent heat transfer at such a low Prandtl number is not an easy task for the standard turbulence models and has challenged the modellers over several decades. In the framework of the EU SESAME project, an effort has been put forward to assess and/or further develop/calibrate different turbulent heat flux closures. In this regard, the present article reports an assessment of four different turbulent heat flux closures for applications involving low-Prandtl fluids. These closures include: (i) the Reynolds analogy based on a constant turbulent Prandtl number (ii) a four-equation explicit algebraic heat flux model (AHFM) (ii) a three-equation implicit AHFM called AHFM-NRG and (iv) a non-linear second-order heat flux model called Turbulence Model for Buoyant Flows (TMBF). The performance of these turbulence models has been assessed in three different test cases against high-fidelity numerical reference data been generated within the SESAME project. The three test cases are: a natural Rayleigh-Bénard convection flow, a mixed convection planar channel flow and a forced convection impinging jet flow. The shortcomings of the classical Reynolds analogy approach for low-Prandtl fluids in all flow regimes are highlighted; hence, more advanced and well-calibrated closures are recommended.

Development of a model for unsteady conjugate heat transfer simulations

Recent developments in CFD simulations go towards higher accuracy by using time-resolved simulations instead of steady RANS simulations and adding solid structures to the simulation instead of assuming constant wall temperatures or heat fluxes at wall boundaries. This means a very large number of time steps are necessary to both accurately resolve the turbulent fluctuations in the fluid parts and have a converged temperature field in the solid parts of the computational domain. Another problem in near-wall heat transfer is the often used assumption of a constant turbulent Prandtl number, which is not correct for many flow configurations. The present work therefore focuses on the development of a methodology for accelerated unsteady conjugated heat transfer simulations. Furthermore, the implementation of a near-wall heat transfer model that does not rely on a constant turbulent Prandtl number was evaluated. The models are implemented in the CFD solver ANSYS CFX. The validation of the turbulent heat transfer model shows improved agreement with the experimental results compared to a constant turbulent Prandtl number approach. The improved unsteady conjugate heat transfer methodology gives the same accuracy of the results as the implicit unsteady conjugate heat transfer model but with considerable reduction of the computational time.

Turbulent flow through a high aspect ratio cooling duct with asymmetric wall heating

We present well-resolved large-eddy simulations of turbulent flow through a straight, high aspect ratio cooling duct operated with water at a bulk Reynolds number of $Re_{b}=110\times 10^{3}$ and an average Nusselt number of $Nu_{xz}=371$. The geometry and boundary conditions follow an experimental reference case and good agreement with the experimental results is achieved. The current investigation focuses on the influence of asymmetric wall heating on the duct flow field, specifically on the interaction of turbulence-induced secondary flow and turbulent heat transfer, and the associated spatial development of the thermal boundary layer and the inferred viscosity variation. The viscosity reduction towards the heated wall causes a decrease in turbulent mixing, turbulent length scales and turbulence anisotropy as well as a weakening of turbulent ejections. Overall, the secondary flow strength becomes increasingly less intense along the length of the spatially resolved heated duct as compared to an adiabatic duct. Furthermore, we show that the assumption of a constant turbulent Prandtl number is invalid for turbulent heat transfer in an asymmetrically heated duct.

Variable Turbulent Prandtl Number Model for Shock/Boundary-Layer Interaction

Interaction of shock waves with turbulent boundary layers can enhance the surface heat flux dramatically. Reynolds-averaged Navier–Stokes simulations based on a constant turbulent Prandtl number often give grossly erroneous heat transfer predictions in shock/boundary-layer interaction flows. This is due to the fact that the underlying Morkovin’s hypothesis breaks down in the presence of shock waves; thus, the turbulent Prandtl number cannot be assumed to be a constant. In this paper, a new variable turbulent Prandtl number model based on linearized Rankine–Hugoniot conditions applied to shock–turbulence interaction is developed. The turbulent Prandtl number is a function of the shock strength, and a shock function is proposed to identify the location and strength of shock waves. The shock function also simulates the postshock relaxation of the turbulent heat flux, which is akin to that observed in canonical shock–turbulence interaction. The model is combined with the well-validated shock-unsteadiness model and is applied to the complex shock topology observed in oblique shock/turbulent boundary-layer interactions. Comparison with experimental data shows significant improvement in the surface heat transfer rate in the interaction region, both for attached and separated shock/boundary-layer interaction cases. The shock function is also used to propose a robust form of the existing shock-unsteadiness model that simplifies the numerical implementation enormously.

Large eddy simulation of upward co-current annular boiling flow using an interface tracking method

Towards the full understanding of the mechanism of boiling in annular flow regime, a computational fluid dynamics method with interface tracking has been developed. Smagorinsky model is used for the sub-grid scale turbulence, the constant turbulent Prandtl number being used to model the turbulent thermal conductivity. A sharp-interface phase change model is used to simulate heat and mass transfer phenomenon at the liquid-vapor interface. The developed numerical method is applied to a simulation of vertical upward co-current boiling flow in the annular flow regime. The experiment of Barbosa et al. is selected for validation: the mass flow rate is 30kg/m2·s with the heat flux 159kW/m2 under the system pressure of 1.9bar. The computed results clearly show how the disturbance waves are generated: the waves are caused from inhomogeneous shear stress acting on the liquid-vapor interface, which is amplified by flow separation in the vapor phase. Subsequently, the interaction between the disturbance waves, the mass transfer and the temperature distribution over the heat-transfer surface is investigated. The temperature gradient in the normal direction to the heat-transfer surface is larger in the thin liquid film than that in the disturbance wave, and consequently, mass transfer rate is also higher there. The higher temperature region is observed underneath the disturbance waves resulting from lower temperature gradient (i.e. heat flux). The computed results imply that the bubble nucleation observed in the experiment may be caused by the higher temperature underneath the disturbance wave on the heat-transfer surface.

Investigation on the applicability of turbulent-Prandtl-number models in bare rod bundles for heavy liquid metals

The study of turbulent heat transfer in heavy liquid metals has been undertaken till now as promising coolants for advanced nuclear fast reactors. However, the low Prandtl number property of liquid metals makes their heat transfer differ from traditional coolants and a constant turbulent Prandtl number is proven to be inappropriate for complex conditions. In this paper, in order to assess the applicability of different turbulent-Prandtl-number models in the bundle flow, turbulent heat transfer in triangular and square lattices with different pitch-to-diameter ratios are simulated. The low Reynolds k-∊ Launder and Sharma turbulence model is adopted for turbulent momentum transport, and different turbulent-Prandtl-number models are used to solve turbulent heat transport. Deviations of these models on overall Nusselt number and local temperature distributions are analyzed. Based on the results achieved, turbulent-Prandtl-number models of Kays and Aoki are recommended for heat transfer simulation in bundle flow. A constant turbulent Prandtl number of 1.5 seems to be also acceptable compared with the recommended turbulent-Prandtl-number models.