RANS simulations for transition and turbulent flow regimes in wire-wrapped rod bundles

Internal flows through rod assemblies are commonly found in heat exchangers, steam generators, and nuclear reactors. One of the fuel assembly designs considered for liquid metal-cooled reactors utilizes wires helically wrapped around each fuel rod as spacers. The wires keep the fuel pins separated, enhancing the turbulent mixing, and heat transfer, but also affecting the pressure drop. It is of interest the understanding of the fluid flow phenomena in the sodium-cooled fast reactor as it is one of the Generation IV advanced reactor designs and it has been a motivating topic of research for the last decade. A wire-wrapped fuel assembly replica with 61-pins has been in operation at the Thermal-Hydraulic Research Laboratory of Texas A&M University. This facility produced high-fidelity velocity and pressure drop data for validation of computational fluid dynamics codes. This study investigates the effects of geometrical features and operating conditions on the flow behavior of the 61-pin wire wrapped bundle using Reynolds-Averaged Navier-Stokes (RANS) models to predict the axial and transverse pressure drops for a range of Reynolds numbers from 1,270 to 100,000. The friction factor predictions were in satisfactory agreement with the experimental data and the Upgraded Chen and Todreas correlation. The internal subchannel velocity results were compared with experimental data and Large Eddy Simulations (LES) and found in reasonable agreement. This study demonstrates that RANS is a suitable approach in predicting velocity and pressure fields in wire-wrapped rod bundles, with a relatively low computational effort.     

Experimental study of convective heat transfer from a rotating finned tube in transverse air flow

 The convective heat transfer from fins to air has been evaluated using rotating annular fins subjected to an air flow parallel to the fins. The fin cooling is studied using infrared thermography. The thermal balance in a fin during its cooling process allows us to obtain the heat transfer coefficient from the temperature time evolution of the fin. Moreover, Particle Image Velocimetry allows us to obtain the flow field in the mid-plane between two fins. The influence of the fin spacing on the convective heat transfer is studied for various velocities of the superposed air flow and various fin rotational speeds. These tests were carried out for air flow Reynolds numbers (based on the shaft diameter and the velocity of the superposed air flow) between 2550 and 18200 and rotational Reynolds numbers (based on the shaft diameter and the peripheral speed) between 800 and 2.9 × 10⁴, for different fin spacings. Received: 14 May 1999/Accepted: 8 October 1999     

Numerical investigation of flow and combined natural-forced convection from an isothermal square cylinder in cross flow

Unsteady flow and heat transfer from a horizontal isothermal square cylinder is studied numerically using a three-dimensional computational model to investigate the influence of buoyancy on the forced flow and heat transfer characteristics. The numerical model is based on a horizontal square cylinder subjected to laminar fluid flow in an unconfined channel. The governing equations in 3D form are solved using a fractional step method based on the finite difference discretization in addition to a Crank–Nicholson scheme employed to the convective and the viscous terms. Two working fluids–air (Pr = 0.7) and water (Pr = 7)–are considered, and the flow and heat transfer simulations were carried out for the Reynolds and Richardson numbers in the intervals 55 ≤ Re ≤ 250 and 0 ≤ Ri ≤ 2, respectively. The flow characteristics such as time-averaged drag/lift, rms drag/rms lift coefficients as well as Strouhal number were computed. The heat transfer from the cylinder is assessed by mean Nusselt number (and rms Nusselt number) over the total heated cylinder walls. As the buoyancy increases, the mass and the velocity of the fluid flowing underneath the cylinder increases. The fluid is injected into the near wake region with an upward motion which significantly alters the flow field in the downstream as well as upstream regions. The effects of Reynolds, Richardson and Prandtl numbers on the flow field and temperature distributions are discussed in detail. It is shown that the flow and heat transfer characteristics are influenced more for air than water. To fill the void in the literature, useful empirical correlations of practical importance are derived for pure forced and pure natural as well as mixed convection. The mixed convection correlations, in terms of the ratio of pure forced convection, are also developed, and their implications are discussed.     

Understanding migratory flow caused by helicoid wire spacers in rod bundles: An experimental and theoretical study

The core of a Liquid Metal Fast Breeder Reactor (LMFBR) consists of cylindrical fuel rods that are wrapped by a helicoidally-wound wire spacer to enhance mixing and to prevent damage by fretting. It is known that the liquid metal close to the rod is forced to follow the wires, and that liquid metal further away from the rod crosses the wires (called: migratory flow). This work aims at gaining more insight into the physics behind migratory flow and to provide a model for its bending angle. To this purpose, the flow field in a 7-rods, wire-wrapped, hexagonal bundle with water is studied within the Reynolds number range of 4990–16330 by using Particle Image Velocimetry (PIV). Refraction of the light is minimized by using Fluorinated Ethylene Propylene (FEP), which is a refractive index-matching (RIM) material. These measurements confirm that liquid near the rod follows the helicoid path and bends cross-wise with respect to the wire further away from the rod. A theoretical model for the bending angle of the flow is derived from the Euler equations and shows that the bending is primarily caused by the pressure gradient field induced by the wire. The model shows a very good correspondence with the experimentally obtained PIV data. These findings improve our understanding of the physics at play in rod bundle flows with wrapped wires and can be of assistance in developing practical correlations for frictional pressure losses and heat transfer in such bundles.     

Effect of an axial throughflow on buoyancy-induced flow in a rotating cavity

In this paper large-eddy simulation is used to study buoyancy-induced flow in a rotating cavity with an axial throughflow of cooling air. This configuration is relevant in the context of secondary air systems of modern gas turbines, where cooling air is used to extract heat from compressor disks. Although global flow features of these flows are well understood, other aspects such as flow statistics, especially in terms of the disk and shroud boundary layers, have not been studied. Here, previous work for a sealed rotating cavity is extended to investigate the effect of an axial throughflow on flow statistics and heat transfer. Time- and circumferentially-averaged results reveal that the thickness of the boundary layers forming near the upstream and downstream disks is consistent with that of a laminar Ekman layer, although it is shown that the boundary layer thickness distribution along the radial direction presents greater variations than in the sealed cavity case. Instantaneous profiles of the radial and azimuthal velocities near the disks show good qualitative agreement with an Ekman-type analytical solution, especially in terms of the boundary layer thickness. The shroud heat transfer is shown to be governed by the local centrifugal acceleration and by a core temperature, which has a weak dependence on the value of the axial Reynolds number. Spectral analyses of time signals obtained at selected locations indicate that, even though the disk boundary layers behave as unsteady laminar Ekman layers, the flow inside the cavity is turbulent and highly intermittent. In comparison with a sealed cavity, cases with an axial throughflow are characterised by a broader range of frequencies, which arise from the interaction between the laminar jet and the buoyant flow inside the cavity.     

Experimental study on convective heat transfer coefficient around a vertical hexagonal rod bundle

Research on convective heat transfer coefficient around a rod bundle has many diverse applications in industry. So far, many studies have been conducted in correlations related to internal and turbulent fully-developed flow. Comparison shows that Dittus-Boelter, Sieder-Tate and Petukhov have so far been the most practical correlations in fully-developed turbulent fluid flow heat transfer. The present study conducts an experimental examination of the validity of these frequently-applied correlations and introduces a manufactured test facility as well. Due to its generalizibility, the unique geometry of this test facility (hexagonal arranged, 7 vertical rods in a hexagonal tube) can fulfil extensive applications. The paper also studies the major deviation sources in data measurements, calibrations and turbulence of fluid flow in this. Finally, regarding to sufficient number of experiments in a vast fluid mean velocity range (3,800?<?Re?<?40,000), a new curve and correlation are presented and the results are compared with the above mentioned commonly-applied correlations.     

Heat transfer measurements and correlations for air–water flow of different flow patterns in a horizontal pipe

Heat transfer coefficients were measured and new correlations were developed for two-phase, two-component (air and water) heat transfer in a horizontal pipe for different flow patterns. Flow patterns were observed in a transparent circular pipe using an air–water mixture. Visual identification of the flow patterns was supplemented with photographic data, and the results were plotted on the flow regime map proposed by Taitel and Dukler and agreed quite well with each other. A two-phase heat transfer experimental setup was built for this study and a total of 150 two-phase heat transfer data with different flow patterns were obtained under a uniform wall heat flux boundary condition. For these data, the superficial Reynolds number ranged from 640 to 35,500 for the liquid and from 540 to 21,200 for the gas. Our previously developed robust two-phase heat transfer correlation for a vertical pipe with modified constants predicted the horizontal pipe air–water heat transfer experimental data with very good accuracy. Overall the proposed correlations predicted the data with a mean deviation of 1.0% and an rms deviation of 12%.     

Influence of non-uniform flow distribution on overall heat transfer in convective bundle of circulating fluidized bed boiler

In the paper the results of comparative investigations on heat transfer performance of boiler convective bundle and its additional surface, i.e. membrane water wall are presented. For this purpose the non-uniform flow field was modelled in an isothermal test stand operated in self-modeling mode. Then the heat transfer characteristics of such arrangement were estimated by means of naphthalene heat/mass transfer analogy technique. The bundle samples in the shape of round bars (rods) were cast with naphthalene and placed in 27 locations in the bundle while water-wall-modeling samples were coated with naphthalene by painting. Both types of samples were exposed to cold air flow. The results were then compared to the mean heat transfer performance of the same bundle exposed to uniform flow field. The differences of approximately 10% were noticed. Moreover, the heat transfer coefficients for additional surface were even three times lower than those of the bundle. In view of results obtained in the work, the commonly made assumption of equality of heat transfer coefficients for both the bundle and its additional surface may lead to certain errors in heat transfer calculations and discrepancies between the calculated values of heating surfaces area and later operational needs of steam generator.     

A simultaneous PIV and heat transfer study of bubble interaction with free convection flow

Whole field velocity and point temperature and surface heat flux measurements were performed to characterise the interaction of a single rising ellipsoidal air bubble with the free convection flow from a heated flat surface immersed in water at different angles of inclination. Two thermocouples and a hot film sensor were used to characterise heat transfer from the surface, while a time-resolved digital particle image velocimetry technique was used to map the bubble induced flow in a plane parallel to the surface. Heat flux fluctuations, preceding and following the bubble passage, were shown to correlate with the variation in both local flow velocities and fluid temperatures. The largest increases in heat transfer were recorded when both flow and temperature effects combined to enhance the convective cooling simultaneously. Such conditions were shown to be most likely met when the block was inclined at 45°, thus forcing the bubble to slide closer to the heated surface and hence to the thermal boundary layer.     

Turbulence structure and heat and mass transfer mechanism at a gas-liquid interface in a wind-wave tunnel

Turbulence structure and heat and mass transfer mechanism across a wavy sheared gas-liquid interface are fluid-mechanically investigated in a wind-wave tunnel. Heat and mass transfer velocities are reported and the relationship between the scalar transfer velocities and the turbulence structure is discussed. In addition, three-dimensional direct numerical simulation is carried out to investigate the flow structure over a rigid-wavy wall similar to that over the wave. The results show that the organized motion in the air flow intermittently appears on the front side of the wave crest, and its structure is rather similar to the flow structure over the rigid-wavy wall. The organized motion in the air flow induces the organized motion in the water flow and the organized motion renews the air-water interface. The scalar transfer across a wavy sheared gas-liquid interface is controlled by the organized surface-renewal motion in the water flow     

Characteristics of air and water velocity fields during natural convection

Air and water velocity fields have been simulated during natural convection, using a two-dimensional volume of fluid (VOF) model. The results have shown that during unstable thermal stratification, the root-mean-square (RMS) airside velocities are an order of magnitude higher than the RMS waterside velocities, whereas, during the stable thermal stratification, the velocity magnitudes are comparable for air and water sides. Furthermore, the magnitude of the air velocity changed more rapidly with the change in the bulk air–water temperature difference than the water velocity, indicating that the air velocities are more sensitive to the bulk air and water temperature difference than the water velocities. A physical model of the heat and mass transfer across the air–water interface is defined. According to this model, the vortices on the air and water sides play an important role in enhancing the heat and mass transfer. Due to the significance of the flow velocities in the transport process, it has been proposed that the correlations for the heat and mass transfer during natural convection should be improved by incorporating the flow velocity as a parameter.     

A study of thin water film flow down an inclined plate without and with countercurrent air flow

Characteristics of thin water film flow down an inclined plane surface without as well as with superposed countercurrent air flow were studied experimentally. Three different angles of inclination of the channel with horizontal were investigated. At each inclination angle, five film Reynolds numbers were studied. Experiments were performed beginning at zero air flow and then increasing the air flow rate in steps until water entrainment occurred. Visual observation of the film surface was carried out as were film thickness measurements by means of capacitance probes. Results presented include mean film thickness and distribution, frequency spectra and propagation velocities of interfacial disturbances, and the incipience condition for entrainment of water from the film into the air stream.     

Numerical simulation of effects of flow maldistribution on heat and mass transfer in a PEM fuel cell stack

A 3D numerical study was carried out to analyze flow, heat and mass transfer first in a single half-cell cathode channel of proton exchange membrane (PEM) fuel cell. From practical point of view, it is necessary to put the appropriate number of cells in a stack. Hence, the above study on a single half-cell is extended to a stack of channels. Due to stacking, the assumption of uniform flow distribution would no longer hold true. Therefore, the channel flow-maldistribution is considered. The water formed at the active surface due to the electrochemical reaction diffuses through the porous layer and eventually enters the gas flow duct. The higher gas velocities in the duct result in faster water vapour removal which leads to a lower value of water vapour into the duct and hence a lower Nusselt number.     

Experimental investigation on flow and heat transfer performance of a novel heat fin-plate radiator for electronic cooling

Within the electronics industry, high degree of integration and enhanced performance has led to high heat dissipation electronic devices. This has identified the future development of very high heat flux components. In this paper, a novel and high efficient diffusion welded heat fin-plate radiator (HFPR) was proposed and designed. Various parameters affect the thermal performance of HFPR. The effect of three parameters: the working fluid filling ratios (8% < FR < 70%), the vacuum degrees (0.001 Pa < VD < 0.1 Pa), and the air flow velocities (0.5 m/s < u < 6 m/s) were investigated experimentally. Using distilled water and ethanol as working fluids, a series of tests were carried out to find the influence of the above parameters on steady-state heat transfer characteristics of HFPR. The experimental results indicated that the filling ratio and vacuum degree had a significant influence on thermal performance of HFPR. Also compared with cooling performance using distilled water and ethanol, the HFPR cooling component using distilled water had a stronger heat dissipation capacity for the same filling ratio. The results also can provide a basis for optimal design of HFPR structure.     

Cold flow experiments in an entrained flow gasification reactor with a swirl-stabilized pulverized biofuel burner

Short particle residence time in entrained flow gasifiers demands the use of pulverized fuel particles to promote mass and heat transfer, resulting high fuel conversion rate. The pulverized biomass particles have a wide range of aspect ratios which can exhibit different dispersion behavior than that of spherical particles in hot product gas flows. This results in spatial and temporal variations in temperature distribution, the composition and the concentration of syngas and soot yield. One way to control the particle dispersion is to impart a swirling motion to the carrier gas phase. This paper investigates the dispersion behavior of biomass fuel particles in swirling flows. A two-phase particle image velocimetry technique was applied to simultaneously measure particle and gas phase velocities in turbulent isothermal flows. Post-processed PIV images showed that a poly-dispersed behavior of biomass particles with a range of particle size of 112–160 µm imposed a significant impact on the air flow pattern, causing air flow decelerated in a region of high particle concentration. Moreover, the velocity field, obtained from individually tracked biomass particles showed that the swirling motion of the carrier air flow gives arise a rapid spreading of the particles.     

Direct numerical simulation of fluid flow in a 5x5 square rod bundle

Characterization of parallel flow through rod bundles is of key importance in assessing the performance and safety of several engineering systems, including a majority of nuclear reactor concepts. Inhomogeneities in the bundle cross-section can present complex flow phenomena, including varying local conditions of turbulence. With the ever-increasing capabilities of high-performance computing, Direct Numerical Simulation (DNS) of turbulent flows is becoming more feasible. Through resolving all scales of turbulence, DNS can serve as a “numerical experiment,” and can provide substantial insight into flow physics, but at considerable computational cost. Thus to date, the DNS in open literature for rod bundle flows is relatively scarce, and largely limited to unit-cell domains. Since wall effects are important in rod bundle flows, a multiple-pin DNS study can expand understanding of rod bundle flows while providing valuable reference data for evaluating reduced-resolution techniques. In this work, DNS of a 5x5 square bare rod bundle representative of typical light water reactor fuel dimensions was performed using the spectral element code Nek5000. Turbulent microscales based on an advanced Reynolds-Averaged Navier–Stokes model were used to establish the required DNS resolution. Velocity and Reynolds stress fields are analyzed in detail, and invariant analysis is used for further investigation into flow physics. The results show stark changes in the structure of turbulence in the edge gaps, suggesting the presence of gap vortices in these regions. In addition, turbulent kinetic energy budgets are presented to more fully illustrate the various turbulent processes. These data can prove useful for rigorous evaluation of lower-fidelity turbulence modeling approaches.     

Stabilization of flow boiling in a micro tube with air injection

Air injection as a stabilization method is evaluated for flow boiling in a micro tube. Pyrex glass tube coated by ITO film is employed as a test tube for flow visualization with water as a working fluid. Air bubble and liquid slug lengths are controlled by changing air and liquid mass velocities. Wall temperatures and inlet/outlet pressures show very large fluctuations during flow boiling without air injection. Severe reverse flow is also observed from flow visualization. On the other hand, wall temperature and inlet/outlet pressures as well as visualized flow patterns become very stable with air injection. In addition, much higher heat transfer coefficients are obtained for air injected cases. It is observed from the flow visualization that the flow becomes much stable and shows regular patterns.     

A general heat transfer correlation for non-boiling gas–liquid flow with different flow patterns in horizontal pipes

A general heat transfer correlation for non-boiling gas–liquid flow with different flow patterns in horizontal pipes is proposed. In order to overcome the effect of flow pattern on heat transfer, a flow pattern factor (effective wetted-perimeter) is developed and introduced into our proposed correlation. To verify the correlation, local heat transfer coefficients and flow parameters were measured for air–water flow in a pipe in the horizontal position with different flow patterns. The test section was a 27.9 mm ID stainless steel pipe with a length to diameter ratio of 100. A total of 114 data points were taken by carefully coordinating the liquid and gas superficial Reynolds number combinations. The heat transfer data were measured under a uniform wall heat flux boundary condition ranging from about 3000 W/m² to 10,600 W/m². The superficial Reynolds numbers ranged from about 820 to 26,000 for water and from about 560 to 48,000 for air. These experimental data including different flow patterns were successfully correlated by the proposed general two-phase heat transfer correlation with an overall mean deviation of 5.5%, a standard deviation of 11.7%, and a deviation range of −18.3% to 37.0%. Ninety three percent (93%) of the data were predicted within ±20% deviation.     

Flow pattern transition for gas-liquid flow in a vertical rod bundle

Experimental and analytical studies are presented directed to the prediction of flow pattern transitions in a vertical rod bundle array. The test section used consists of a 24 rod matrix on a square pitch in a cylindrical shell. Analytical models are given based on physical interpretation of the transition mechanisms. Data on rise velocities of small and large bubbles in rod bundles are also presented.     

Numerical experiments on convective heat transfer in water-saturated porous media at near-critical conditions

Fluid and heat flow at temperatures approaching or exceeding that at the critical point (374 °C for pure water, higher for saline fluids) may be encountered in deep zones of geothermal systems and above cooling intrusives. In the vicinity of the critical point the density and internal energy of fluids show very strong variations for small temperature and pressure changes. This suggests that convective heat transfer from thermal buoyancy flow would be strongly enhanced at near-critical conditions. This has been confirmed in laboratory experiments. We have developed special numerical techniques for modeling porous flow at near-critical conditions, which can handle the extreme nonlinearities in water properties near the critical point. Our numerical simulations show strong enhancements of convective heat transfer at near-critical conditions; however, the heat transfer rates obtained in the simulations are considerably smaller than data reported from laboratory experiments by Dunn and Hardee. We discuss possible reasons for this discrepancy and develop suggestions for additional laboratory experiments.