To achieve longer-life liquid-metal fast reactor cores, designers are considering to increase the wall gap of the wire-wrapped hexagonal fuel bundles to account for volumetric void swelling and radiation creep. A new wire-wrapped hexagonal test bundle has been constructed, with a wall gap larger than prior experiments, and experimental pressure drop data have been generated under laminar, transition, and turbulent flow regimes (corresponding to Re of 250–19,000), to complement the existing database of small wall gap experimental bundles. The comparison of the experimental data set with the predictions of four existing correlations (Baxi and Dalle Donne, Cheng and Todreas detailed (CTD), Kirillov, and Rehme) showed general agreement between data and the selected correlations. However, the CTD correlation most accurately predicted the experimental trend and the transition between flow regimes. The analysis of the experimental data also revealed that the larger wall gap size caused a lower bundle pressure drop due to the increased bypass flow area.
The thermal-hydraulic behavior of the flow in rod bundles has been the subject of extensive investigations in the past decades, due to their importance in different industrial applications. Rod bundles are employed in heat exchangers for air conditioning and other cooling and heating applications, used as fuel elements of commercial nuclear power plants, or as core support structures in prismatic gas-cooled reactors. The pressure drop is without any doubts one of the most important hydrodynamic parameters taken under consideration during the design and optimization of all the applications previously mentioned. This has motivated numerous experimental activities aimed to study the effects of the bundle geometry on the pressure drop and to develop and validate correlations as more convenient tools for assessing and predicting pressure losses.
Wilson et al.  have conducted experiments in near-compact heat exchangers to measure the pressure drop under different flow conditions (Reynolds number), bundle geometry, and rod number, and compared the results with the prediction of existing pressure drop evaluation approaches. Friction factor measurements in triangular arrays of tubes have been generated by Vassallo and Symolon , to assess exiting correlations, and propose a new correlation to better fit the experimental data within the extended Reynolds number range investigated. Variation of the pressure drop as function of the Reynolds number has been investigated for a confined row of cylinders by Smith et al.  to simulate some aspects of the flow in the lower plenum of a typical gas-cooled reactor.
Effects of the presence of spacers and axial or helical fins have been studied by Yang et al.  as an effective way to reduce flow-induced vibrations and to reduce the drag coefficient by promoting an early transition to turbulent regime.
Spacer grids are placed at regular intervals along fuel bundles of pressurized water reactors to held the rods in a fixed array, maintaining the lateral spacing, and promoting flow and thermal mixing . Numerous experimental activities have been carried out to study the pressure drop along these types of bundles and the effects of the spacer grids, such as the ones conducted by Rehme  and by Yang and Chung .
Commercial [8,9] and governmental [10–13] interest in the sodium-cooled fast nuclear reactor has generated a large demand for producing and validating correlations to estimate the friction factor though rod bundles with helically wrapped wire spacers, employed in this reactor design to avoid pin-to-pin contact and to guard the pin bundle against flow induced vibrations. The helical wire spacers also promote mixing of coolant among various subchannels. In view of the thermal-hydraulic design of liquid metal fast reactor cores, it is of paramount importance to investigate the coolant flow characteristics in wire-wrapped hexagonal fuel bundles and understand the effects of the bundle geometry on the pressure distributions, which need to be accurately quantified. Important geometrical parameters for a wire-wrapped hexagonal fuel bundle include the number of pins, the pin and wire diameters, pin pitch to diameter ratio (P/D), helical wire pitch, helical wire pitch to pin diameter ratio (H/D), and duct wall gap size. Of interest to current nuclear fuel designers, are hexagonal fuel bundles with relatively large wall gaps, allowing a longer life of the bundles so that higher burnups can be achieved by anticipating neutron-induced void swelling and irradiation creep.
Several experimental investigations have been conducted to study the pressure drop in wire-wrapped hexagonal test bundles of different size, geometry, and flow regimes. Recent tests have been conducted by the Korea Atomic Energy Research Institute. Chang et al.  have performed pressure drop and flow distribution measurements on a wire-wrapped 37-pin test bundle (pitch over diameter ratio, P/D = 1.13) in turbulent regime (Re = 37,100) at high pressure (0.4 MPa). The test bundle investigated has a small wall gap of 0.06 mm. Choi et al.  have conducted pressure drop measurements in a full-scale 271 pin test bundle under transition and turbulent flow regimes, to support the design of the KALIMER reactor. The test bundle was characterized by a P/D = 1.2 and a small wall gap size of less than 0.1 mm. Pressure drop experiments have been conducted by Chun and Seo  using a 19-pin wire-wrapped fuel bundles of different P/D ratios, under laminar, transition, and turbulent regimes. All test configurations explored had very small wall gaps. Among older tests conducted in wire-wrapped hexagonal bundles, the ones conducted by Reihman  and Rehme [18,19] are the most interesting, as they produced a large database of pressure drop measurements within a wide range of P/D ratios, other geometrical characteristics, and flow regimes. The combinations of geometrical parameters investigated by Rehme were all characterized by a very small gap (<0.01 mm) or no wall gap (wires in contact with the wall). Reihman was the first to investigate configurations characterized by larger gap size, up to 0.74 mm.
A comprehensive review of existing pressure drop experimental data has been conducted by Cheng et al.  with the objective of evaluate existing pressure drop correlations based on the available test data. Cheng and Todreas identified 132 experimental data sets generated from 80 test bundles, which include the experimental bundles mentioned earlier. Table 1 contains a selection of the most representative test bundles with similar geometric parameters to the bundle presented in this work. The experimental bundles were chosen based on specific characteristics such as pin and wire diameters, P/D, H/D, and wall gap size.
Table 1 clearly shows that there is little data available for bundles with large wall gaps, confirming the needs for new experimental data that can be used to validate the capability of existing correlation in predicting pressure drops through wire-wrapped hexagonal bundles with larger wall gaps.
An experimental facility containing a 61-pin hexagonal fuel bundle with helically wrapped wire spacers has been designed and constructed to conduct isothermal flow tests to produce high resolution measurements of the flow using advanced laser-based techniques. The facility is able to provide high-resolution pressure measurements at different axial and azimuthal locations in the bundle. The unique geometrical parameter of this bundle is duct wall gap, being one of the largest ever investigated, second only to the configurations investigated by Reihman. This experimental work presents the friction factor data generated for a wide range of Reynolds numbers from 250–19000. According to Cheng and Todreas , these data set contains measurements in the laminar, transition, and turbulent regimes. The experimental data produced is compared with the predictions of four existing friction factor correlations, namely Cheng and Todreas detailed (CTD) , Rehme , Baxi and Dalle Donne , and Kirillov , contributing to the validation of these correlations for bundles with larger gap size within a wide range of flow regimes.
Experimental Facility Description
The experimental facility, Fig. 1, consists of a primary loop, which provides the flow for the experiments, and a secondary loop, performing volume control, temperature control, and filtration. The primary loop includes the following components:
The hexagonal test section containing the 61-pin bundle
The primary tank, used to store the working fluid between experiments, and as an inline surge volume
The primary pump and associated variable frequency drive (VFD), which controls the flow rate in the test section
An inline turbine flow meter
A resistance temperature detector (RTD)
Nine pressure transducers and one additional differential pressure transducer which span a wire spacer pitch within the fully developed region.
The secondary loop contains the secondary tank, secondary pump and associated VFD, and the filtration system. A heat exchanger is installed and supplied with chilled water to control the primary loop temperature. During tests, the temperature control system is used to minimize the temperature change of the working fluid and, subsequently, of all components of the test section. All facility components are made of chemical-resistant materials (316 stainless steel, Viton, and cross-linked polyethylene). The test section was isolated from the primary loop utilizing support structures, flexible hoses, and rubber dampers, to reduce vibration of the test section.
The test section can be divided into three distinct sections, Fig. 2:
The inlet plenum located at the bottom of the bundle
The central section where the flow measurements are conducted
The outlet plenum located at the top of the bundle.
The test section includes the 61-pin hexagonal fuel bundle, where each pin is wrapped the same using a single wire. The direction is clockwise when looking from the bottom of the fuel bundle to the top. The pins are arranged in a triangular lattice set by machined grid plates at the bottom and top of the fuel bundle. A three-dimensional representation of the test bundle and a close-up picture of a pin are shown in Fig. 3. The flow enters the inlet plenum and exits the outlet plenum symmetrically from the sides of each plenum.
The pins, wires, and hexagonal duct enclosure are made of transparent acrylic. This material was selected to allow for flow visualization and measurements using laser diagnostic velocity measurement techniques such as particle image velocimetry and laser Doppler velocimetry. Results of the velocity measurements using particle image velocimetry have been described by Nguyen et al. .
Test Section Dimensions
Figure 4 presents a horizontal cross section of the test bundle and identifies the main geometrical dimensions. These dimensions are listed in Table 2. The faces of the hexagonal duct are identified with letters A to F (flow inlet and outlet occur through faces B and E).
The total length of the bundle, L, includes the length of the inlet plenum, central section (test section), and outlet plenum. The length of the central section, Lc, was designed to:
Allow full development of the flow
Perform the flow visualization measurements
Minimize the exit effects
Nine pressure transducers are installed at different axial locations (denoted as pressure taps PT#0–8). The axial location of the pressure taps is listed in Table 3 3. All pressure taps are located at the center of face F, with pressure transducers directly installed at the duct’s wall. PT#0 is located at the inlet plenum to monitor and control pressure of the test section inlet (maximum operating pressure). The total pressure drop through the entire test section is measured by the difference in pressure measured by PT#0 (inlet tap) and PT#8 (outlet tap). Pressure transducers PT#1–7 are used to record the pressure at seven axial locations along the test section, including the development region. One high-accuracy differential transducer (full scale (FS) = ±6894.76 Pa, accuracy < 0.05% of FS) is connected between PT#5 and PT#7 to measure the axial pressure drop within one wire pitch in the fully developed region. The pressure drop across PT#5 and PT#7 is the one selected to calculate the bundle averaged friction factor presented in this paper. These pressure taps are located in the fully developed region of the test section. The effect on the pressure from the wire clocking angle is the same at the selected locations, being one full wire pitch apart.
An RDF Corporation, Hudson, NH, RTD is utilized to measure and record the temperature of the fluid during the experiments. The accuracy of the device is ±0.3 °C at 0 °C with an operating range of −196 °C to 480 °C. The RTD is located near the primary pump outlet.
Flow Rate Hardware.
A Sponsler (Westminster, SC) in-line precision turbine flowmeter (SP3-MB-PHL-D-4X) is installed near the test section inlet and utilized to measure the volumetric flow rate of the working fluid. The uncertainty of the flow meter analog output is 0.025% of full scale at 20 °C. The full-scale reading is 2271 l/min. A Sponsler IT400 totalizer records the analog output from the flow meter with a digital uncertainty of ±3.8 l/min.
Data Acquisition System.
Pressure transducers, RTD, and flow meter are connected to a National Instruments (Austin, TX) data acquisition (DAQ) system and interfaced to a laptop computer using LabVIEW. Pressure, temperature, and flow rate data are continuously recorded during the tests.
Experimental tests are conducted to analyze the bundle averaged friction factor over a range of Reynolds numbers within the laminar, laminar-to-transition, transition-to-turbulent, and turbulent flow regimes. During test preparation, written procedures are followed to verify the correct functionality of the test equipment and instrumentation. The following steps are applied to execute each experimental run:
The pump speed was adjusted using the primary VFD until the desired volumetric flow rate is achieved. This pump speed is maintained for period of time sufficiently long to guarantee that steady flow conditions are achieved in the loop and test section, before executing the required measurements;
While the flow is maintained constant, three consecutive sets of 10 s pressure measurements are recorded through the DAQ system. Flow rate is continuously recorded during this step; and
The procedure is repeated from step 1 to investigate the flow rates of interest.
The working fluid used to conduct the experiments is p-cymene4 . This fluid was primarily selected to allow the use of the matched index of refraction technique when performing velocity measurements.
During the entire duration of the tests, the temperature of the fluid is constantly monitored and recorded through the DAQ system, and maintained at ambient conditions using the secondary loop heat exchanger. Ambient temperature is recorded at the beginning of each run. Table 4 summarized the main test conditions, including sampling frequency and duration.
Reynolds Number Estimation
The bundle flow area, A, and wetted perimeter, Pwet, are calculated accounting for the interior, wall, and corner subchannels using the methodology proposed by Cheng et al. . Temperature-dependent density and viscosity of p-Cymene were linearly interpolated  based on the temperature at the beginning of each pressure measurement.
Several pressure drop correlations have been developed based on existing experimental data to estimate the friction factor. The complexity of developing said correlations is primarily due to the wide range of bundle geometric parameters and Reynolds numbers used in various experiments. Cheng et al. evaluated a large number of correlations and ranked them according to two figures of merit, the agreement index and credit score . From that evaluation, the four most relevant pressure drop correlations for the experimental bundle of this paper are the CTD, Rehme, Baxi and Dalle Donne (BDD), and Kirillov (KIR). The correlations selected for comparison with the experimental data are presented in Table 5. The formulation of the CTD correlation used in this paper accounts for the improvement in the transition flow regime described in Ref. . The correlation proposed by Rehme has shown good agreement with experimental data in the turbulent regime, but its applicability cannot be extended to the laminar regime. The correlations proposed by BDD and Kirillov (KIR) are applicable to a wide range of Re number but the transition from laminar regime and to turbulent regime are fixed (Re = 5000 and Re = 400, respectively) and independent of the bundle geometry. Since the BDD correlation is a combination of the Novendstern  and Engel et al.  correlations in the turbulent and transition and laminar regimes, respectively, a direct comparison of the experimental data with these correlations is not performed.
Experimental Data Uncertainty
Results and Comparison
For the laminar flow regime, m = 1. The application of the CTD correlation with the geometrical parameters of the experimental bundle yielded the predicted laminar constant, Cfl = 81.45. A least squares regression of the experimental points in the laminar region, in the form of Eq. (11), yielded the experimental laminar constant, Cfl = 75.48. The difference between the experimental and predicted laminar constants appears similar when compared to different H/D presented in Ref. .
An inflection in the CTD predicted friction factor is observed at Re = 629 (Fig. 6), corresponding to the transition from the laminar regime. The transition from laminar regime can be seen as a change of the experimental data trend for both sets near the experimental point at Re = 627.
For turbulent regime, the CTD correlation utilizes a value of m = 0.18, derived from aggregating other bundle data sets. The application of the CTD correlation with the geometrical parameters of the experimental bundle yielded the predicted turbulent constant, Cft = 0.16. The experimental results presented in this paper yielded a value of m = 0.1945, and an experimental turbulent constant, Cft = 0.165 (using the least mean square method), as shown in Fig. 7. The correlation predicts the transition to turbulent regime to occur at Re 13,500, corresponding to the inflection visible in Fig. 7. This inflection is not physical and is the result of the numerical process the CTD correlation employs to predict the behavior in the transition regime. The experimental data points in Fig. 7, laying on the line defined by Eq. (11), may indicate that the transition to turbulent regime for the current configuration occurs at a lower Reynolds number than the one predicted by the CTD correlation.
There appears to be an inflection point in the experimental trend of both data sets at approximately Re = 3400. As stated before, the experimental friction factor is estimated from Eq. (3) based exclusively on edge subchannel pressure drop and the bundle-averaged Reynolds number. Cheng and Todreas  showed that for low Reynolds numbers (between 200–3000), the pressure drop in the edge subchannel is greater than the bundle-averaged pressure drop, and that for Re ≳ 3000, the bundle-averaged pressure drop is greater than the edge subchannel pressure drop. Subsequently, using the edge subchannel pressure drop to calculate the friction factor of the bundle would result in an experimental friction factor that is overvalued at Re ≲ 3000 and undervalued at Re ≳ 3000.
Experimental pressure data in a 61-pin wire-wrapped test bundle has been produced within a wide range of Reynolds numbers. Laminar, transition, and turbulent flow regimes were investigated. The data have been compared with existing pressure drop correlations, selected based on their applicability range. The comparison showed that the experimental data are in general agreement with all selected correlations. However, there was excellent agreement with the CTD correlation where it more accurately predicted the experimental trend and the transitions between flow regimes. As previously noted, the current experimental bundle has a much larger wall gap size than prior experimental bundles. The larger wall gap size causes a lower bundle pressure drop because of the increased bypass flow. Therefore, the experimental friction factor is lower than CTD because of the larger wall gap of this bundle. This confirms the importance of investigating bundle designs with larger wall gaps to account for their unique geometrical parameters when predicting hexagonal wire-wrapped bundle friction factors and the need of new experimental data.
The origin of the axial reference system is assumed to be at the entrance of the central section (test section).
Density = 855.23 kg/m3; viscosity = 8.18 × 10−4 Pa·s (at 22.5 °C).
All tests performed with water except the current bundle (p-cymene), and Esthair (air).
Corresponding to 3.5 wire pitches.
This experimental facility described in this paper was designed and constructed under a project sponsored by the Department of Energy (Award No. DE-NE0008321).
U.S. Department of Energy (Grant No. DE-NE0008321).