Numerical study on thermal hydraulic performance of a Printed Circuit Heat Exchanger

Very High Temperature Reactors (VHTRs) require a high-temperature and high integrity Intermediate Heat Exchanger (IHX) with high effectiveness to efficiently transfer the core thermal output to a secondary fluid for electricity generation, hydrogen production, and/or other industrial process heat applications. A class of compact plate-type heat exchanger, namely, Printed Circuit Heat Exchanger (PCHE), is one of the leading candidate IHX configuration being considered for VHTR applications. In the current study, simplified computational models of PCHE are investigated using Fluent™ software. The geometry of the models considered in the study replicate the PCHEs that were fabricated using Alloy 617 plates for use in a High-Temperature Helium Facility (HTHF) at The Ohio State University. The computational cases investigated are based on the design conditions of the HTHF, i.e., a maximum operating pressure of 3 MPa, hot and cold side inlet temperatures of 1173 K and 813 K, respectively, and mass flow rates varying from 10 to 80 kg/h. This range of mass flow rates correspond to laminar and laminar-to-turbulent transition flows in the PCHE flow channel passages. The laminar-to-turbulent transition behavior has been numerically investigated for the semicircular and circular channel geometries. The numerical study showed that the transition is observed at Reynolds numbers of 2300 and 3100 for the circular and semicircular channels, respectively. Heat transfer and pressure drop characteristics are evaluated to provide preliminary performance data for the PCHEs fabricated at operating temperatures similar to those of the VHTRs. Local convective heat transfer coefficients are calculated for the hot and cold sides and compared with the available correlations for the circular and semicircular ducts. Overall performance characteristics of the PCHE computational model are computed and described in terms of the thermal effectiveness, number of transfer units, and overall heat transfer coefficient.     

Flow and pressure drop fluctuations in a vertical tube subject to low frequency oscillations

Heat transfer and other equipment mounted on off-shore platforms may be subjected to low frequency oscillations. The effect of these oscillations, typically in the frequency range of 0.1–1 Hz, on the flow rate and pressure drop in a vertical tube has been studied experimentally in the present work. A 1.75 m-long vertical tube of inner diameter 0.016 m was mounted on a plate and the whole plate was subjected to oscillations in the vertical plane using a mechanical simulator capable of providing low frequency oscillations in the range of 8–30 cycles/min at an amplitude of 0.125 m. The effect of the oscillations on the flow rate and the pressure drop has been measured systematically in the Reynolds number range 500–6500. The induced flow rate fluctuations were found to be dependent on the Reynolds number with stronger fluctuations at lower Reynolds numbers. The effective friction factor, based on the mean pressure drop and the mean flow rate, was also found to be higher than expected. Correlations have been developed to quantify this Reynolds number dependence.     

Two-phase flow and boiling heat transfer in two vertical narrow annuli

Experimental study associated with two-phase flow and heat transfer during flow boiling in two vertical narrow annuli has been conducted. The parameters examined were: mass flux from 38.8 to 163.1 kg/m² s; heat flux from 4.9 to 50.7 kW/m² for inside tube and from 4.2 to 78.8 kW/m² for outside tube; equilibrium mass quality from 0.02 to 0.88; system pressure from 1.5 to 6.0 MPa. It was found that the boiling heat transfer was strongly influenced by heat flux, while the effect of mass velocity and mass quality were not very significant. This suggested that the boiling heat transfer was mainly via nucleate boiling. The data were used to develop a new correlation for boiling heat transfer in the narrow annuli. In the two-phase flow study, the comparison with the correlation of Chisholm [Chisholm, D., 1967. A theoretical basis for the Lockhart–Martinelli correlation for two-phase flow. Int. J. Heat Mass Transfer 10, 1767–1778] and Mishima and Hibiki [Mishima, K., Hibiki, T., 1996. Some characteristics of air–water two-phase flow in small diameter vertical tubes. Int. J. Multiphase Flow 22, 703–712] indicated that the existing correlations could not predict the two-phase multiplier in the narrow annuli well. Based on the experimental data, a new correlation was developed.     

Experimental investigation on heat transfer from a heated rod with a helically wrapped wire inside a square vertical channel to water at supercritical pressures

A supercritical water heat transfer test section has been built at Xi’an Jiaotong University to study the heat transfer from a 10 mm rod inside a square vertical channel with a wire-wrapped helically around it as a spacer. The test section is 1.5 m long and the wire pitch 200 mm. Experimental conditions included pressures of 23–25 MPa, mass fluxes of 500–1200 kg/m² s, heat fluxes of 200–800 kW/m², and inlet temperatures of 300–400 °C. Wall temperatures were measured with thermocouples at various positions near the rod surface. The experimental Nusselt numbers were compared with those calculated by empirical correlations for smooth tubes. The Jackson correlation showed better agreement with the test data compared with the Dittus-Boelter correlation but overpredicted the Nusselt numbers almost within the whole range of experimental conditions. Both correlations cannot predict the heat transfer accurately when deterioration occurred at low mass flux and relatively high heat flux in the pseudocritical region. Comparison of experimental data at two different supercritical pressures showed that the heat transfer was more enhanced at the lower supercritical pressure but the deterioration was more likely to occur at the higher pressure, meaning increased safety. Based on a comparison with an identical channel without the helical wrapped wire, it was found that the wire spacer does not enhance the heat transfer significantly under normal heat transfer conditions, but it contributes to the improvement of the heat transfer in the pseudocritical region and to a downstream shift of the onset of the deterioration. The Jackson buoyancy criterion is found to be valid and works well in predicting the onset of heat transfer deterioration occurring in the experiments without wire.     

Numerical study on flow field in inlet plenum of a pebble-bed modular reactor

Flow distribution and pressure drop analysis in the inlet plenum of a pebble-bed modular reactor (PBMR) have been performed numerically. Three-dimensional Navier–Stokes equations have been solved in conjunction with the k– model as a turbulence closure. Non-uniformity in the flow distribution is assessed for the reference case, and parametric studies have been performed for rising channels diameter, Reynolds number, angle between the rising channels, angle between the inlet ports, and aspect ratio of the plenum cross-section. Also, two different shapes of the inlet plenum, namely, rectangular and oval shapes, have been analyzed. The relative flow mal-distribution parameter variation shows that the flow distribution in rising channels for the reference case is strongly non-uniform. As the rising channels diameter is decreased, the flow uniformity as well as the pressure drop is found to increase. The flow distribution in the rising channels is independent of Reynolds number. Increase in the angle between the inlet ports and aspect ratio is found to increase the uniformity in flow distribution.     

Thermal hydraulic performance analysis of the printed circuit heat exchanger using a helium test facility and CFD simulations

The thermal-hydraulic performance of the PCHE was investigated using the KAIST helium test loop. Experiments were performed in the helium laminar region with 350 < Re < 1200. The hot/cold side inlet conditions were 25–550 °C/25–100 °C over the operating pressure of 1.5–1.9 MPa, respectively. Mass flow rates were controlled in the range of 40–100 kg/h. Pressure drop and temperature difference were measured at the inlet and outlet of the hot and cold sides. A global Fanning factor correlation and a global Nusselt number correlation were proposed using information only at the inlet and outlet of the hot and cold sides. A three-dimensional (3-D) numerical simulation was performed using FLUENT, a commercial computational fluid dynamics (CFD) code, to compare simulation results to the KAIST helium test data and to obtain the local Nusselt number in the PCHE. CFD predictions showed good agreement with experimental data. A local pitch-averaged Nusselt number correlation was proposed using local temperature, pressure, surface heat fluxes, and properties provided by CFD simulations. The system analysis code, GAMMA, was also utilized to identify which correlation was more applicable for system analysis. It turns out that the proposed local pitch-averaged Nusselt number correlation from CFD simulations is more appropriate than the global Nusselt number correlation developed from experimental data.     

Some problems for bundle CHF prediction based on CHF measurements in simple flow geometries

A comparison of critical heat flux (CHF) fuel bundles data with CHF data obtained in simple flow geometries was made. The base for the comparison was primary experimental data obtained in annular, circular, rectangular, triangular, and dumb-bell shaped channels cooled with water and R-134a. The investigated range of flow parameters (pressure, mass flux, and critical quality) in R-134a was chosen to be equivalent to modern nuclear reactor water flow conditions (p=7 and 10 MPa, G=350–5000 kg (m² s)⁻¹, x_cr=−0.1–1). The proper scaling laws were applied to convert the data from water to R-134a equivalent conditions and vise versa. The effects of flow parameters (p, G, x_cr) and the effects of geometric parameters (D, L) were evaluated during comparison. The comparison showed that no one simple flow geometry can be used for accurate and reliable bundle CHF prediction in wide range of flow parameters based on local (critical) conditions approach. The comparison also showed that the limiting critical quality phenomenon is unique characteristic for each flow geometry which depends on many factors: flow conditions (pressure and mass flux), geometrical parameters (diameter or surface curvature, gap size, etc.), flow obstructions (spacers, appendages, turbulizers, etc.) and others.     

Computations of post-trip reactor core thermal hydraulics using a strain parameter turbulence model

Coolant flows in the cores of nuclear reactors consist of ascending vertical flows in a large number of parallel passages. Under post-trip conditions such heated turbulent flows may be modified strongly from the forced convection condition by the action of buoyancy, in particular exhibiting impaired levels of heat transfer with respect to corresponding forced convection cases. The heat transfer performance of these ‘mixed convection’ flows is investigated here using two physically distinct eddy viscosity turbulence models: the recent ‘strain parameter’ (or k––S) model of Cotton and Ismael [A strain parameter turbulence model and its application to homogeneous and thin shear flows. Int. J. Heat Fluid Flow 19 (1998) 326] is examined against the benchmark low-Reynolds-number k– model of Launder and Sharma [Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc. Lett. Heat Mass Transfer 1 (1974) 131]. Comparison is made with three sets of heat transfer data for ascending mixed convection flows, and it is demonstrated that both turbulence models are generally successful in resolving the Nusselt number distributions occurring along the lengths of mixed convection flow passages. The mechanisms by which the strain parameter model generates reduced turbulence levels, and hence impaired heat transfer rates, is explored in comparison with a fourth set of experimental data for mixed convection flow profiles.     

Condensation in the presence of noncondensable gases

An experimental investigation to examine the effects of surface orientation on the condensation of steam in the presence of noncondensable gas is reported. An air-steam mixture was directed into a rectangular flow-channel over a condensing aluminum surface that has a painted surface finish. The mixture flow was concurrent in all the tests with condensate flow. In this series of experiments, the orientation of the condensing surface was varied from 0–90° (plate surface was facing downwards at 0°), with a variable air-steam mass fraction of 0–0.87, and a mixture velocity of 1–3 m/s. The heat transfer coefficient was measured in addition to making visual observations of the condensation process. It was found that the heat transfer coefficient varied from 100 to 600 W/m² K with the mass fraction of 0.87-0.24 and the maximum heat transfer coefficient of 6200 W/m² K was measured with mass fraction of 0. By tilting the condensing surface from the horizontal to vertical position, the heat transfer coefficient decreased 15 to 25% depending on the mass fraction. With a higher vapor content the effect of the orientation was smaller. This dependence was attributed to the existence of interfacial structure (droplets and ridges) that promoted heat transfer at small inclination angles, when the angle was increased the interface became smoother and heat transfer rates decreased. Heat transfer rates were also observed to increase with flow velocity, vapor content and pressure. The results are compared with some previously published data and a proposed condensation model that showed reasonable agreement with the data trends.     

A power perturbation technique for the measurement of fuel-to-coolant heat transfer coefficients in fast reactors

This technique provides a method of obtaining average fuel to coolant heat transfer coefficients for individual fuel subassemblies in fast reactors. A series of experiments on the UK prototype fast reactor (PFR) over the period 1977–1979 have demonstrated that the technique is simple, requires no special instrumentation other than thermocouples to monitor coolant outlet temperatures, and the measurement can be made during normal reactor operation. Thus it is possible to determine how heat transfer coefficients change with operating conditions and with the degree of burn-up in the fuel.The analysis of a single experiment is presented to illustrate the technique. This was conducted at a single reduced power level of 200 thermal megawatts for two different primary coolant flow rates, both steady fractions of the maximum (0.88 and 0.47). Cyclic and single-step perturbations of about 10% amplitude were impressed on the steady power and the delayed coolant temperature response at subassembly outlets was monitored. Burn-ups in the subassemblies ranged between 1.0% and 4.7%. From the measured delays at the two flows it was possible to determine the fuel time-constant and hence the fuel-to-coolant heat transfer coefficient. It was also shown that a simple, lumped-element, heat transfer model can be used to obtain sufficiently accurate estimates from measurements at just one coolant flow.Fuel surface-to-coolant thermal conductances (i.e. gap conductances) were subsequently derived from the heat transfer coefficients. These ranged between 2.4 kW m⁻² K⁻¹ and 3.3 kW m⁻² K⁻¹ with the smaller conductances being obtained for those fuel elements with the larger degree of burn-up. These values are lower than expected but consistent with a higher than expected value for the negative power coefficient of reactivity feedback which has been observed at reduced power.     

Analysis of three different types of blockage in a sodium flow path with the MATRA-LMR-FB code

A local blockage in a subassembly of an LMR is of particular importance because the local temperature of the coolant increases at the downstream of a blockage and the integrity of the fuel clad can be threatened when an obstacle or a blockage is formed in a flow path. To analyze a flow blockage in a nuclear reactor core, Korea Atomic Energy Research Institute developed a subchannel analysis computer code MATRA-LMR-FB. This code adopts several enhanced modeling features such as a distributed resistance model, state-of-the-art turbulent mixing models, a hybrid difference scheme, and a porous body pressure drop model, therefore, it is applicable to a flow path with a plate-type or a porous-type blockage. The effect of each model has been evaluated through an analysis for the THORS experiment, in which a plate-type blockage was located in a flow channel with wire-wrapped fuel rods. The overall capability of the code has also been evaluated for the KNS experiment with a plate-type blockage in a grid-spaced flow channel, and for the SCARLET-II experiments with a porous blockage in channels formed by wire-wrapped fuel rods. The code shows good predictions for the experiments with a wire-wrapped flow path with a plate-type or a porous type blockage. The analyses for the KNS experiments reveal that the code requires a precise blockage model related to a grid spacer model.     

Laminar flow instability in multiple channels

Temperature-viscosity-induced laminar flow instability (LFI) in two gaseous heated parallel channels with interchannel heat exchange is purely excursive, rather than oscillatory. Constant total flow always leads to a stable system, while constant pressure drop could have an instability, depending on the sign of (∂ΔP/∂W)_Q. The system was studied numerically with negative heat perturbations yielding bounded excursions, and positive heat perturbations giving unbounded excursions asymptotically approaching zero. A nine-channel system was probed, giving excursive behavior with the ultimate growth rate the same for single and multichannel systems.     

Modeling and simulation of coupled nuclear heat energy deposition and transfer in the fuel assembly of the Ghana Research Reactor-1 (GHARR-1)

Monte Carlo N-Particle (MCNP) code coupled with PLTEMP/ANL code were used to model and simulate the heat transfer problems in the fuel elements assembly of the Ghana Research Reactor-1 (GHARR-1) by solving Boltzmann transport approximation to the heat conduction equation. Coupled neutron radiation-thermal codes were used to determine the spatial variations of thermal energy in the fuel channels, the heat energy distribution in the radial and axial segments of the fuel assembly and the convective heat transfer processes in the entire core of the reactor. The thermal energy at maximum reactivity load of 4 mk, reactor power of 30 kW and inlet system pressure of 101.3 kPa were found to be 8.896 × 10⁻¹⁶ J for a single fuel pin, and 1.104 × 10⁻¹⁵ J and 7.376 × 10⁻¹⁶ J, for the radial and axial sectioning of the core respectively. Using the PLTEMP/ANL V4.0 code and given that the inlet coolant temperature was 30 °C, the maximum outlet coolant temperature was 51 °C. The energy values were obtained using the following thermodynamic parameters as maximum pressure drop of 0.7 MPa and mass flow rate of 0.4 kg/s. Neutronics point kinetics model and Safety Analysis Report used to validate the results confirmed that the heat distribution in the core did not exceed 100 °C. The heat energy profiles based on the data suggested no nucleate boiling at the simulated energies, and since the melting point of U–Al alloy fuel material is 640 °C, the reactor was considered to be inherently safe during normal or steady state operations.     

Experimental investigation and CFD simulation of horizontal stratified two-phase flow phenomena

For the investigation of stratified two-phase flow, two horizontal channels with rectangular cross-section were built at Forschungszentrum Dresden-Rossendorf (FZD). The channels allow the investigation of air/water co-current flows, especially the slug behaviour, at atmospheric pressure and room temperature. The test-sections are made of acrylic glass, so that optical techniques, like high-speed video observation or particle image velocimetry (PIV), can be applied for measurements. The rectangular cross-section was chosen to provide better observation possibilities. Moreover, dynamic pressure measurements were performed and synchronised with the high-speed camera system.CFD post-test simulations of stratified flows were performed using the code ANSYS CFX. The Euler–Euler two fluid model with the free surface option was applied on grids of minimum 4 × 10⁵ control volumes. The turbulence was modelled separately for each phase using the k–ω-based shear stress transport (SST) turbulence model. The results compare very well in terms of slug formation, velocity, and breaking. The qualitative agreement between calculation and experiment is encouraging and shows that CFD can be a useful tool in studying horizontal two-phase flow.     

Experimental and analytical studies on turbulent heat transfer performance of a fuel rod with spacer ribs for high temperature gas-cooled reactors

Turbulent heat transfer performance of a fuel rod with three-dimensional trapezoidal spacer ribs for high temperature gas-cooled reactors was studied for various Reynolds numbers using an annular channel at the same coolant condition as the reactor operation, maximum outlet temperature of 1000 °C and pressure of 4 MPa, and analytically by a numerical simulation using the k- turbulence model. The turbulent heat transfer coefficients of the fuel rod were 18–80% higher than those of a concentric smooth annulus at a region of Reynolds number exceeding 2000. On the other hand, the predicted average Nusselt number of the fuel rod agreed well with the empirical correlation obtained from the experimental data within a relative error of 10% with Reynolds number of more than 5000. It was verified that the numerical analysis results had sufficient accuracy. Furthermore, the numerical prediction could clarify quantitatively the effects of the heat transfer augmentation by the spacer ribs and the axial velocity increase due to a reduction in the annular channel cross-section.     

Post-CHF two-phase flow with low wall-superheat

Heat transfer was measured to a two-phase flow in the post-CHF region under liquid-heated conditions and low wall-superheat. The boiling fluid was water at high pressure, 7.0–15.3 MPa, and mass fluxes in the range of 720–3200 kg/m²s. Experiments were performed in a vertical tube with a 10 mm inside diameter and a 13.1 m heated length. In considering the effects of thermodynamic non-equilibrium and direct drop-wall heat transfer at the low wall-superheats of this investigation (25–100°C), 13 correlations, models and analysis were compared to the data. A review of these formulations is presented including development bases and approaches. The effects of both non-equilibrium and drop-wall heat transfer were evaluated, and recommendations are presented for post-CHF heat transfer predictions at low wall-superheat.     

SCALE calculation for evaluation of spent fuel condition during long-term storage

Experiences with an advanced spent nuclear fuel management in Slovakia are presented in this paper. The evaluation and monitoring procedures are based on practices at the Slovak wet interim spent fuel storage facility in NPP Jaslovské Bohunice. Since 1999, leak testing of WWER-440 fuel assemblies were completed using a special leak tightness detection system developed by Framatome-anp, “Sipping in Pool”. This system utilized external heating for the precise defects determination.Optimal methods for spent fuel disposal and monitoring were designed. A new conservative factor for specifying of spent fuel leak tightness is introduced in the paper. Limit values of leak tightness were established from the combination of SCALE4.4a (ORIGEN-ARP) calculations and measurements from the “Sipping in Pool” system. These limit values are: limiting fuel cladding leak tightness coefficient for tight fuel assembly – k_FCT(T) = 3 × 10⁻¹⁰, limiting fuel cladding leak tightness coefficient for fuel assembly with leakage – k_FCT(L) = 8 × 10⁻⁷.     

Gas–liquid two-phase flow in narrow horizontal annuli

Experimental data associated with the two-phase flow regimes, void fraction and pressure drop in horizontal, narrow, concentric annuli are presented. Two transparent test sections, one with inner and outer diameters of 6.6 and 8.6 mm, and an overall length of 46.0 cm; the other with 33.2 and 35.2 mm diameters and 43.0 cm length, respectively, were used. Near-atmospheric air and water constituted the gas and liquid phases, respectively. The gas and liquid superficial velocities were varied in the 0.02–57 and 0.1–6.1 m s⁻¹ ranges, respectively. The major two-phase flow patterns observed included bubbly, slug/plug, churn, stratified, and annular. Transitional regimes, where the characteristics of two distinct flow regimes could be observed in the test sections, included bubbly-plug, stratified-slug and annular-slug. The obtained flow regime maps were different than flow regime maps typical of large horizontal channels and microchannels with circular cross-sections. They were also different from the flow regimes in rectangular thin channels. The measured average void fractions for the two test sections were compared with predictions of several empirical correlations. Overall, a correlation proposed by Butterworth [Butterworth, D., 1975. A comparison of some void fraction relationships for co-current gas–liquid flow. Int. J. Multiphase Flow 1, 845–850] based on the results of Lockhart and Martinelli (1949) provided the most accurate prediction of the measured void fractions. The measured pressure drops were compared with predictions of several empirical correlations. The correlation of Friedel [Friedel, L., 1979. Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow. 3R Int. 18, 485–492] was found to provide the best overall agreement with the data.     

Effects of wire-spacer shape in LMR on thermal–hydraulic performance

In this work, analyses of three-dimensional flow and convective heat transfer in wire-wrapped fuel assemblies with different shaped wire-spacers have been carried out using Reynolds-averaged Navier–Stokes equations with shear stress transport turbulence model. Three cross-sectional shapes of wire-spacer, circle, hexagon and rhombus have been tested. All the assemblies have been analyzed for single pitch of wire-spacer with periodic boundary conditions applied at inlet and outlet of the calculation domain. It is found that the assemblies exhibit the directional periodicity in radial gradients between the adjacent subchannels due to presence of wire-spacer. The overall pressure drop is highest in case of rhombus shaped wire-spacer assembly followed by hexagonal shaped. Although circular shaped wire-spacer gives lowest peak temperature as well as lowest overall temperature difference in the assembly, the rhombus shaped wire-spacer assembly gives highest Nusselt number on fuel rod surface.