Turbulent heat transfer to longitudinal flow through a triangular array of circular rods

Temperature distribution and heat transfer to longitudinal turbulent, fully developed flow through triangular arrays of smooth circular rods are analysed for liquids with Prandtl number 1 and 1. Nusselt number is plotted versus pitch and turbulence for constant heat flow and for constant temperature on the rod surface, and the optimum pitch is determined. The influence of Prandtl number on Nusselt number is analysed.     

Computation of single- and two-phase heat transfer rates suitable for water-cooled tubes and subchannels

A computational method for predicting heat transfer, valid for a wide range of flow conditions (from pool boiling and laminar flow conditions to highly turbulent flow), has been developed. It correctly identifies the heat transfer modes and predicts the heat transfer rates as well as transition points (such as the critical heat flux point) on the boiling curve.The computational heat transfer method consists of a combination of carefully chosen heat transfer equations for each heat transfer mode. Each of these equations has been selected because of their accuracy, wide range of application, and correct asymptotic trends. Using a mechanistically-based heat transfer logic, these equations have been combined in a convenient software package suitable for PC or mainframe application. The computational method has been thoroughly tested against many sets of experimental data. The parametric and asymptotic trends of the prediction method have been examined in detail. Correction factors are proposed for extending the use of individual predictive techniques to various geometric configurations and upstream conditions.     

Direct-contact condensation heat transfer model in RELAP5/MOD3.2 with/without noncondensable gases for horizontally stratified flow

Direct-contact condensation experiments on atmospheric steam and steam/air mixture on subcooled water flowing co-currently in nearly-horizontal channels are carried out and the local heat transfer coefficients are obtained. Inlet air mass fraction in the mixture is varied by up to 50%. Based on previous and present experimental data, a direct-contact condensation database is constructed. The horizontally stratified condensation model of RELAP5/MOD3.2 overpredicts both co-current and counter-current experimental data. The correlation proposed by Kim predicts the database relatively well compared with that of RELAP5/MOD3.2. In the presence of noncondensable gases, RELAP5/MOD3.2 overpredicts the database with percentage errors of 55.1 and 61.1% for pipe inclination angles of θ=2.1° and θ=5.0°, respectively. The UCB correction factor is modified to consider the effects of noncondensable gases on heat transfer coefficients. When Kim's correlation is substituted with the Dittus–Boelter type correlation in RELAP5/MOD3.2 and a modified correction factor is used, the prediction errors are greatly reduced to 20.7 and 28.8% for inclination angles of θ=2.1° and θ=5.0°, respectively.     

Numerical simulation of heat transfer deterioration phenomenon in supercritical water through vertical tube

In this study, a numerical investigation of heat transfer deterioration (HTD) in supercritical water flowing through vertical tube is performed by using six low-Reynolds number turbulence models. All low-Reynolds models can be extended to reproduce the effect of buoyancy force on heat transfer and show the occurrence of localized HTD. However, most k–ε models seriously over-predict the deterioration and do not reproduce the subsequent recovery of heat transfer. The V2F and SST models perform better than other models in predicting the onset of deterioration due to strong buoyancy force. The SST model is able to quantitatively reproduce the two heat transfer deterioration phenomena with low mass flux which have been found in the present study.     

Modeling of condensation heat transfer for a PRHRS heat exchanger in a SMART-P plant

A theoretical model using a heat and mass transfer analogy and a simple model using Lee and Kim's [Lee, K.-Y., Kim, M.H., 2008a. Experimental and empirical study of steam condensation heat transfer with a noncondensable gas in a small-diameter vertical tube. Nucl. Eng. Des. 238, 207-216] correlation were developed to investigate steam condensation in the presence of a noncondensable gas inside a vertical tube submerged in pool water. Rohsenow's correlation was used to consider the secondary pool-boiling heat transfer. Both models were assessed with the experimental data of Oh and Revankar [Oh, S., Revankar, S.T., 2005a. Investigation of the noncondensable effect and the operational modes of the passive condenser system. Nucl. Technol. 152, 71-86; Oh, S., Revankar, S.T., 2005b. Effect of noncondensable gas in a vertical tube condenser. Nucl. Eng. Des. 235, 1699-1712; Oh, S., Revankar, S.T., 2005c. Complete condensation in a vertical tube passive condenser. Int. Commun. Heat Mass Trans. 32, 593-602; Oh, S., Revankar, S.T., 2005d. Analysis of the complete condensation in a vertical tube passive condenser. Int. Commun. Heat Mass Trans. 32, 716-727; Oh, S., Revankar, S.T., 2006. Experimental and theoretical investigation of film condensation with noncondensable gas. Int. J. Heat Mass Trans. 49, 2523-2534; Oh, S., Gao, H., Revankar, S.T., 2007. Investigation of a passive condenser system of an advanced boiling water reactor. Nucl. Technol. 158, 208-218] for low pressure and Kim [Kim, S.J., 2000. Turbulent film condensation of high pressure steam in a vertical tube of passive secondary condensation system. Ph.D. dissertation, Korea Advanced Institute of Science and Technology] for high pressure, which were obtained from in-tube steam condensation with air in the pool water. These models predicted the data of Oh and Revankar well, but they slightly underestimated the data of Kim. The design of the Passive Residual Heat Removal System (PRHRS) condensation heat exchanger was evaluated with the theoretical model at real operating conditions (e.g., secondary pool-boiling, high system pressure). The PRHRS condensation heat exchanger designed was estimated to remove sufficiently the remaining heat in a reactor during a major accident.     

Conjugated heat transfer in a concentric annular pipe

Combined convection and radiation heat transfer for adsorbing-emitting gas in the entrance region of a finite length concentric annular duct is numerically investigated. The thermal boundary conditions imposed on the two duct walls are of a mixed type; a constant heat flux, attributed by both radiation and conduction, is imposed at the inner wall, and a constant temperature is imposed at the outer wall. An approximation model, namely the method of moments, is employed to consider the radiation contribution. The method of lines (MOL) is employed to discretize the nonlinear partial differential energy and radiation transport equations into a set of ordinary differential equations. The fifth-order Runge-Kutta-Verner method is used to solve the ordinary differential equation set. The effects of six major parameters on the conjugate behavior in the entrance region of a concentric annular duct are discussed. Compared to the isothermal boundary condition, the results indicate that the local Nusselt number exhibits many different behaviors for the mixed boundary condition.     

Supercritical-water heat transfer in a vertical bare tube

This paper presents selected results on heat transfer to supercritical water flowing upward in a 4-m-long vertical bare tube. Supercritical-water heat-transfer data were obtained at pressures of about 24 MPa, mass fluxes of 200-1500 kg/m² s, heat fluxes up to 884 kW/m² and inlet temperatures from 320 to 350 °C for several combinations of wall and bulk-fluid temperatures that were below, at or above the pseudocritical temperature.In general, the experiments confirmed that there are three heat-transfer regimes for forced-convective heat transfer to water flowing inside tubes at supercritical pressures: (1) normal heat-transfer regime characterized in general with heat transfer coefficients (HTCs) similar to those of subcritical convective heat transfer far from critical or pseudocritical regions, which are calculated according to the Dittus-Boelter type correlations; (2) deteriorated heat-transfer regime with lower values of the HTC and hence higher values of wall temperature within some part of a test section compared to those of the normal heat-transfer regime; and (3) improved heat-transfer regime with higher values of HTC and hence lower values of wall temperature within some part of a test section compared to those of the normal heat-transfer regime.This new heat-transfer dataset is applicable as a reference dataset for future comparison with supercritical-water bundle data and for a verification of scaling parameters between water and modeling fluids.Also, these HTC data were compared to those calculated with the original Dittus-Boelter and Bishop et al. correlations. The comparison showed that the Bishop et al. correlation, which uses the cross-section average Prandtl number, represents HTC profiles more correctly along the heated length of the tube than the Dittus-Boelter correlation. In general, the Bishop et al. correlation shows a fair agreement with the experimental HTCs outside the pseudocritical region, however, overpredicts by about 25% the experimental HTCs within the pseudocritical region. The Dittus-Boelter correlation can also predict the experimental HTCs outside the pseudocritical region, but deviates significantly from the experimental data within the pseudocritical region. It should be noted that both these correlations cannot be used for a prediction of HTCs within the deteriorated heat-transfer regime.     

Post-dryout heat transfer in a multi-dimensional porous bed

Post-dryout behavior of a particulate debris bed was investigated numerically. A separate flow model using the concepts of relative permeabilities and the Leverett function was used to describe two-phase flow and heat transfer in the bed. The saturation distribution, liquid and vapor pressures and flows were calculated when heat generation rate (decay rate) was less than a critical value called the 'dryout heat flux'. When the heat generation rate was greater than the dryout heat flux, a dry zone was defined by extrapolating two-phase flow calculations. This is accomplished by solving the nonlinear partial differential equations governing pressures and temperature using an alternating direction implicit (ADI) method with an upwind scheme. Conduction, convection and radiation are taken into account in the dry zone. The maximum temperature in the bed, the melting heat fluxes, and the fractional contribution to heat transfer by conduction, convection and radiation for various bed configurations were investigated.     

Magnetohydrodynamically enhanced heat transfer in a liquid metal system

The phenomena of liquid metal flow under the influence of magnetic and electric fields are important in the development and design of nuclear and metallurgical plants, such as the blanket cooling systems of fusion or fast breeder reactors and electromagnetic stirring devices. In this study, a computer code that models recirculating flows in two dimensions using a k − ε turbulence model is expanded to include the magnetohydrodynamic (MHD) effects of applied electric and magnetic fields. This modified code is then used to examine the effect of MHD stirring on the heat transfer characteristics of a liquid metal cooling system. Using liquid sodium properties, various thermophysical properties are investigated. The results indicate that a significant increase in the rate of heat transfer is obtainable when the heat transfer system is operated in the presence of MHD stirring.     

On the analysis of containment heat transfer following a LOCA

This paper is concerned with containment heat removal by steam condensation on passive heat sinks following a loss-of-coolant accident. A literature search and survey of technical publications including both experimental and analytical results that are relevant to the heat transfer mechanism inside the containment are summarized. Several small-scale experiments that relate to correlations used in licensing calculations as well as the large-scale Carolinas Virginia Tube Reactor Containment (CVTR) test data are discussed in detail. A theoretical model is then developed to predict the heat transfer rate. It is found that for the post-accident containment conditions, the heat transfer rate can be approximated by a closed form equation. The predictions compare favourably with various existing experimental data and offer logical explanations for the discrepancies among the data. It is observed that several crucial containment parameters are absent in the heat transfer correlations which are currently used for containment licensing calculations.     

Analysis of radiant heat transfer in a BWR fuel assembly

A computer code ‘CIDER’ was developed which analyzes radiant heat transfer in a BWR fuel rod bundle under loss of coolant conditions. In the code, (1) a channel box and fuel rods are considered to be gray bodies, (2) reflection and absorption of radiation beams in the atmosphere is neglected, (3) a fuel rod is approximated by a regular polygonal rod, and (4) radiant heat flux is calculated considering circumferential temperature distribution on each fuel rod surface, which is determined from radial and circumferential heat conduction calculations in a fuel rod. It was found that the conventional model with uniform cladding temperature overestimated heat flux about 30% in a typical situation, or correspondingly underestimated the temperature rises.     

Phase change heat transfer device for process heat applications

The next generation nuclear plant (NGNP) will most likely produce electricity and process heat, with both being considered for hydrogen production. To capture nuclear process heat, and transport it to a distant industrial facility requires a high temperature system of heat exchangers, pumps and/or compressors. The heat transfer system is particularly challenging not only due to the elevated temperatures (up to ∼1300 K) and industrial scale power transport (≥50 MW), but also due to a potentially large separation distance between the nuclear and industrial plants (100+ m) dictated by safety and licensing mandates.The work reported here is the preliminary analysis of two-phase thermosyphon heat transfer performance with alkali metals. A thermosyphon is a thermal device for transporting heat from one point to another with quite extraordinary properties. In contrast to single-phased forced convective heat transfer via ‘pumping a fluid’, a thermosyphon (also called a wickless heat pipe) transfers heat through the vaporization/condensing process. The condensate is further returned to the hot source by gravity, i.e., without any requirement of pumps or compressors. With this mode of heat transfer, the thermosyphon has the capability to transport heat at high rates over appreciable distances, virtually isothermally and without any requirement for external pumping devices. Two-phase heat transfer by a thermosyphon has the advantage of high enthalpy transport that includes the sensible heat of the liquid, the latent heat of vaporization, and vapor superheat. In contrast, single-phase forced convection transports only the sensible heat of the fluid. Additionally, vapor-phase velocities within a thermosyphon are much greater than single-phase liquid velocities within a forced convective loop. Thermosyphon performance can be limited by the sonic limit (choking) of vapor flow and/or by condensate entrainment. Proper thermosyphon requires analysis of both.     

Laminar combined convection heat transfer of liquid sodium flowing through a single horizontal row of cooling tubes in the direction of gravity

The laminar combined convection heat transfer of the liquid sodium which flows through a single horizontal row of cooling tubes in the direction of gravity are studied using numerical analysis. The heat transfer characteristics at large Reynolds numbers are improved when Richardson numbers (= GR/Re²) are increased and the improvement rate is enlarged with an increase in value. The temperature field at small Reynolds numbers does not exhibit much change even when the Richardson number reaches a high value. Consequently the Nusselt numbers do not differ from those of forced convection. In other words, in a decay heat removal system at a low velocity, there is a possibility that an improvement in the heat transfer characteristics by combined convection cannot be expected even in a system with a large Richardson number.     

Evaporation and condensation heat transfer with a noncondensable gas present

To evaluate the system pressure of an external water wall type containment vessel, which is one of the passive systems for containment cooling, the evaporation and condensation behavior under a noncondensable gas presence has been experimentally examined. In the system, steam evaporated from the suppression pool surface into the wetwell, filled with noncondensable gas, and condensed on the containment vessel wall. The system pressure was the sum of the noncondensable gas pressure and saturated steam pressure in the wetwell. The wetwell temperature was, however, lower than the supression pool temperature and depended on the thermal resistance on the suppression pool surface. The evaporation and condensation heat transfer coefficients in the presence of air as noncondensable gas were measured and expressed by functions of steam/air mass ratio. The evaporation heat transfer coefficients were one order higher than the condensation heat transfer coefficients because the local noncondensable gas pressure was much lower on the evaporating pool surface than on the condensing liquid surface. Using logal properties of the heat transfer surfaces, there was a similar trend between evaporation and condensation even with a noncondensable gas present.     

MHD flow past a semi-infinite flat plate with heat transfer

Exact numerical solutions to the boundary layer similarity equations of MHD flow and heat transfer past a semi-infinite flat plate of an incompressible viscous fluid have been presented. The velocity of the fluid U and the magnetic field H₀ at a distance from the plate are both assumed to be uniform and parallel to the plate which is considered as isothermal. Velocity, magnetic and temperature fields have been shown graphically whereas the numerical values of ƒ′(0) and {−θ′(0)} are entered in tables. We observe that both ƒ′(0) and {−θ′(0)} decrease with increasing S (magnetic field parameter) and increase with increasing λ (ratio of magnetic diffusivity and viscous diffusivity).