Natural Convection Heat Transfer Correlations Research Articles

Improved natural convection heat transfer correlations for reactor cavity cooling systems of high-temperature gas-cooled reactors: From computational fluid dynamics to Pronghorn

The reactor cavity cooling system (RCCS) is a common reactor safety system in high-temperature gas-cooled Reactors (HTGR) that removes heat from the reactor pressure vessel (RPV) by radiation (∼80%) and natural convection (∼20%). For the simulation of accident scenarios of HTGRs, intermediate fidelity and system codes models must be employed to limit the models’ execution time. While an accurate quantification of the radiative heat transfer is available in these models, the quantification of natural convection must rely on correlations of questionable accuracy for the Nusselt number. Commonly used correlations are based in experiments performed at low Rayleigh numbers and/or using isothermal walls in simplified geometries. This work improves on the accuracy of natural convection heat transfer correlations to support HTGR designs.These correlations include both local and average Nusselt numbers as a function of the global Rayleigh number, the local Rayleigh number, and the temperature profile at the hot wall of the RCCS. In the absence of dedicated experiments and the difficulty of performing high-fidelity simulations at realistic Rayleigh numbers, the data to fit the correlations are generated with computational fluid dynamics (CFD) using Reynolds Averaged Navier-Stokes (RANS) models. First, a careful selection of the RANS turbulence model is performed by comparing the results obtained with different RANS turbulence models against high-fidelity simulations of natural convection at Ra 1×1011 in a rectangular cavity. Next, the selected model is used to perform simulations of an HTGR cavity at different high Rayleigh numbers ∈[6.1×1011,2.9×1013] to encompass several HTGR designs, assuming an isothermal RPV wall. The results obtained are used to fit a correlation for the average and space-varying Nusselt number as a function of the global and local Rayleigh numbers via a sparsity-promoting, least-squares method. The selected RANS model is then used to perform simulations of a PBMR-400 (Pebble Bed Modular Reactor) HTGR cavity with the temperature profiles at the RPV wall obtained during a PLOFC (Pressurized loss of forced cooling) transient. We use the results obtained to fit a temperature-dependent correction to the space-varying Nusselt number with the sparsity-promoting, least-squares method. The results obtained in this work enable system-level codes, such as Pronghorn, to perform higher-fidelity simulations of the heat exchange process in the RCCS while still maintaining a low computational cost.

IVR-ERVC study of 1700 MW class PWR based on MAAP simulation and coupled analysis

As an effective severe accident mitigation strategy, in-vessel retention – external reactor vessel cooling (IVR-ERVC) has been applied to some advanced nuclear reactors. In the assessment of AP600-like reactor, the risk oriented accident analysis methodology (ROAAM) has been adopted based on a lumped parameter model, including sensitivity studies about key parameters and bounding scenarios during accident states. In the ROAAM method, the quantity of steel in the metallic layer and zirconium oxidized, and decay power is not deterministic. These three parameters result from reasonable analysis as presented in DOE/ID-10460 that has provided reasonable bounding distributions for AP600. This study has performed a MAAP4 simulation for 1700 MW class PWR and focused on core melting progress and bounding distributions of main parameters. The effectiveness of the IVR-ERVC for 1700 MW class PWR has been assessed in a coupled analysis based on a modified lumped model using MAAP simulation results. This analysis has considered the coupled relations about heat transfer between in- and ex-vessel. Also, this study has discussed the applicability of natural convection heat transfer correlations in molten pool and compared the results between the lumped parameter model and the modified lumped parameter model. The sensitivity analysis about the three parameters discussed above has been conducted. The methodology demonstrated in this paper can be used for severe accident analysis and advanced reactor design. The results obtained so far indicated that it is feasible to apply IVR-ERVC strategy to a large scale PWR.

Natural convective heat transfer of heated packed beds

Natural convection heat transfer of heated packed bed was investigated. Experiments were performed for a single heated sphere buried in unheated packed beds varying its locations and for packed beds with all heated spheres varying the heights of packed beds from 0.02m to 0.26m. Mass transfer experiments using a copper electroplating system were performed based upon the analogy between heat and mass transfer. The diameter of sphere was 0.006m, which corresponds to Rad of 1.8×107. For the single heated sphere cases, the measured results agreed well with the existing natural convection heat transfer correlations for packed beds and even with those for a single sphere in an open channel. For all heated sphere cases, the average heat transfers decrease with increasing packed bed heights.

Experimental development of natural convection heat transfer correlations for spiral-helical surface water heat exchangers (1385-RP)

Surface water heat pump systems utilize surface water bodies, such as lakes, reservoirs, and rivers, as heat sources and heat sinks. Closed-loop surface water heat pumps use submerged heat exchangers to extract or reject heat from the surface water body. Heat transfer between the heat exchanger and the lake is generally governed by buoyancy driven natural convection. One form of surface water heat exchanger is the spiral-helical heat exchanger, which is usually fabricated from high-density polyethylene tubing. Though the exterior convective resistance is an important part of the design calculation, convection correlations suitable for spiral-helical surface water heat exchangers are not available. In the current article, the authors cover an experimental study involving heat rejection experiments and heat extraction experiments on nine different spiral-helical configurations with three different high-density polyethylene tube sizes. Standard high-density polyethylene and thermally enhanced high-density polyethylene heat exchangers were also tested and compared. Convection correlations for spiral-helical heat exchangers were developed for heat extraction and heat rejection conditions. Heat transfer rate predicted with the correlations is compared against experimental data.

New natural convection heat transfer correlations in enclosures for building performance simulation

ABSTRACTThis paper presents new correlations to calculate natural convection heat transfer coefficients (CHTC) in enclosures for building performance simulation. Current work related to the development of correlations is not oriented to building enclosures, and the influence of high numbers of Rayleigh (Ra) and aspect ratio on the CHTC has not been studied in detail. In this work, two new correlations have been developed for a vertical wall, one in laminar regime (Ra < 107) and another one in turbulent regime (107<Ra<1011). Moreover, two new correlations have been developed for floor and ceiling, one in laminar regime (Ra < 106) and another one in turbulent regime (Ra > 106). All correlations have been developed as function of the aspect ratio (H/L) and Ra numbers calculated from the enclosure average air temperature and wall surface temperature. By contrast, in previous works the Ra numbers have been calculated from the temperature difference of opposite walls. Computer Fluid Dynamics (CFD) simulations for different aspect ratios (H/L = 0.5–1–2) and Ra numbers (103–1011) have been carried out in order to obtain these correlations. The SIMPLE algorithm has been used for the solution of the Navier–Stokes equations and the realizable turbulence k- model with an enhanced wall-function treatment has been used. The correlations developed follow the expected trend for the low number of Ra in comparison with the expressions developed by other authors. For a high number of Ra, our correlations improve the previous correlations, because it is a function of the aspect ratio of the enclosure and the average air temperature of the enclosure. This approach is simple to implement in the construction of thermal simulation programs with low computational cost.

Natural convection heat transfer in a uniformly heated horizontal pipe

Natural convection heat transfers inside horizontal pipes were measured. The Rayleigh numbers were varied from 6.8 × 108 to 1.5 × 1012, while the Prandtl number was fixed at 2,094. Based on the analogy concept, a copper sulfate electroplating system was adopted to measure mass transfer rates in place of heat transfer rates. Test results using single-piece electrodes were in good agreement with the work of Sarac and Korkut. The angle-dependent mass transfer rates, measured using piecewise electrodes, were compared with the results of studies on natural convection in concentric annuli, and showed similar trends. The experiments were expanded to the turbulent region, and a transition criterion was proposed. Angle-dependent natural convection heat transfer correlations for the laminar and turbulent regions were derived.

수직 원형관내 자연대류 물질전달실험에서 양극의 면적과 위치가 한계전류에 미치는 영향

Natural convection heat transfer rates in a vertical pipe were measured for number from 2.1x to 1.2x. Using the analogy concept, heat transfer experiments were replaced by mass transfer experiments. A cupric acid - copper sulfate () electroplating system was adopted as the mass transfer system and the mass transfer rates were measured. Comparison of the results with the existing laminar and turbulent natural convection heat transfer correlations on a vertical plate showed very good agreements except for the high case, where the boundary layer inside the vertical pipe interferes. The agreements showed the usefulness of the analogy experiment method. Using 3 different anode size and 6 different geometrical configurations, the effects of the anode size and position were explored. As expected, the anode size and position do not affect the limiting currents for most cases. These results will be used as the experimental background for the positioning and sizing of the anodes for a more complex experiment.

Experimental study of natural convection heat transfer in a microencapsulated phase change material slurry

Abstract A new microencapsulated PCM (Phase Change Material) slurry (MEPCS) at high concentration (45% w/w) was developed based on microencapsulated Rubitherm RT6. Its heat storage and heat transfer characteristics have been experimentally investigated in order to assess its suitability for integration into a low temperature heat storage system for solar air conditioning applications. Differential scanning calorimetry tests have been conducted to evaluate the cold storage capacity and phase change temperature range. An experimental setup was built in order to quantify the natural convection heat transfer occurring from a vertical helically coiled tube immersed in the MEPCS. First, tests were carried out using water in order to obtain natural convection heat transfer correlations and then a comparison was made with the results obtained for the MEPCS. It was found that inside the phase change interval the values of the heat transfer coefficient for the MEPCS were significantly higher than for water, under identical temperature conditions.

Experimental assessment of heat storage properties and heat transfer characteristics of a phase change material slurry for air conditioning applications

A new microencapsulated phase change material slurry based on microencapsulated Rubitherm RT6 at high concentration (45% w/w) was tested. Some heat storage properties and heat transfer characteristics have been experimentally investigated in order to assess its suitability for the integration into a low temperature heat storage system for solar air conditioning applications. DSC tests were conducted to evaluate the cold storage capacity and phase change temperature range. A phase change interval of approximately 3 °C and a hysteresis behaviour of the enthalpy were identified. An experimental set-up was built in order to quantify the natural convection heat transfer occurring from a vertical helically coiled tube immersed in the phase change material slurry. First, tests were carried out using water in order to obtain natural convection heat transfer correlations. Then a comparison was conducted with the results obtained for the phase change material slurry. It was found that the values of the heat transfer coefficient for the phase change material slurry were higher than for water, under identical temperature conditions inside the phase change interval.

Effect of Relative Humidity on the Prediction of Natural Convection Heat Transfer Coefficients

Results of an investigation into the sensitivity of natural convection heat transfer correlations with respect to relative humidity are presented. Given the relatively small values of natural convection heat transfer coefficients, small changes in the thermophysical properties can have a significant impact on the values predicted by theoretical/empirical correlations. In this study, the thermophysical properties are assumed to be those of a dry air and water vapor mixture. The mole fractions are determined as a function of relative humidity. Several widely used natural convection heat transfer correlations have been examined to determine the impact of varying the relative humidity on the predicted Nusselt number. The results show a general trend of an increasing Nusselt number with relative humidity. The results presented in this paper provide an engineering tool for obtaining accurate values of natural convection heat transfer coefficients for a moist air environment using only the thermophysical properties of dry air.

Transient Natural Convection Heat Transfer Correlations for Tube Bundles Immersed in a Thermal Storage

A scale analysis of the transient discharge of a fully mixed thermal storage vessel with an immersed single-tube heat exchanger is extended to provide a generalized expression for the transient natural convection Nusselt number for heat exchangers comprising many tubes. The transient Nusselt number is expressed in terms of the Rayleigh number at the initiation of the discharge (or charge) process and easily measured geometric parameters. Nusselt numbers measured for a 240-tube heat exchanger immersed in a fully mixed 126L storage vessel are well correlated in the proposed form. The applicability of the approach to thermally stratified storage fluids is evaluated for both a single-tube and the 240-tube bundle. For heat exchangers of practical size for solar systems, for example the 240-tube bundle, buoyancy driven flow within the storage is sufficient to mix an initially stratified fluid. In this case, Nusselt numbers during the discharge process are predicted accurately by the proposed transient formulation. However, if the storage fluid remains stratified during discharge, as is the case for an initially stratified vessel with a single-tube heat exchanger, the transient formulation is not recommended.

Heat transfer enhancement from enclosed discrete components using pin–fin heat sinks

Computational modeling, temperature measurements, and flow visualizations were conducted to investigate the enhancement of combined natural convection, conduction, and radiation heat transfer from a 25.4 mm×25.4 mm discrete heat source in a 127 mm×127 mm and 41.3 mm high enclosure, using pin–fin heat sinks. The pin–fin array was attached to the heated component, which was flush mounted on the enclosure base. Effects of flow confinement by enclosure walls on heat transfer from the pin–fin heat sink were found prominent. The existing natural convection heat transfer correlations for pin–fin arrays in free space showed large deviations from present measurements. Radiation was also found to contribute significantly to the overall heat transfer. Experimental results show that enhancement of heat transfer using pin–fin heat sinks was significantly different for horizontally and vertically heated orientations of the enclosure.

Bulk phase and intrinsic interfacial resistances to evaporation under vacuum

To assess the importance of bulk phase heat transfer resistances in vacuum evaporation processes, measurements are made of the evaporation rate of triethanolamine at subatmospheric pressures. Spontaneous interfacial convection at the evaporating vapor:liquid surface is suppressed by the addition of sufficient amounts of a surface-active solute. At pressures of 100 and 21 Pa the contribution of kinetic mobility of molecules at the interface is negligible and the experimental results are predicted by accounting for the heat transfer resistance in the bulk liquid phase only. Furthermore, these results confirm the validity of published natural convection heat transfer correlations for this system. Next, experimental measurements of evaporative flux are made at low pressures (≤0.1 Pa), for which the limited kinetic mobility of molecules adds a significant resistance. Results are seen to, be consistent only with an evaporation coefficient E = 0.3, suggesting that even trace quantities of a soluble surface-active agent can dramatically alter the interfacial character of triethanolamine.