Validation of the COTENP Code: A Steady-State Thermal-Hydraulic Analysis Code for Nuclear Reactors with Plate Type Fuel Assemblies.
Plate type fuel assemblies have been used in research and test due to improved heat transfer surface area. Currently they are considered for small and medium reactors for process heat generation, water desalination applications, and multipurpose reactors [1-4]. Plate type fuels usually consist of a central fuel meat of uranium alloys or uranium composites dispersed in metals and enveloped in a metallic cladding. The fabrication process is usually the picture frame technique with hot rolling in multiple passes and a cold rolling for defining the plate dimensions and surface characteristics. The fuel assembly consists of a set of such plates regularly spaced to form coolant channels [5, 6]. These are rectangular and closed in the sides so that no cross flow between neighboring channels can occur. The plate geometry allows a greater ratio of heat transfer area to fuel volume allowing reactor core designs with higher power densities which are beneficial for providing high flux levels for irradiation purposes. The condition of closed coolant channels suggests that simpler physical models to describe the conservation of mass and momentum phenomena may suffice since no mass transfer occurs from one channel to others in its vicinity [7-9].
Subchannel thermal-hydraulic codes that handle rectangular channels can be used to verify thermal-hydraulic design limits of plate type fuel reactors. Some of the design parameters include fuel centerline temperatures, flow rate conditions, and local heat transfer conditions based on the estimation of onset of nucleate boiling and departure from nucleate boiling limits . Most subchannel analysis codes were developed for rod type fuels and fewer are dedicated to plate type geometry. Many belong to the COBRA family evolving from the first ones developed in the 1970s [11-19]. The COBRA-3C/RERTR code is an example of such developments applied for plate type fuel research and test reactors with low pressure . The literature reports other plate type thermal-hydraulic subchannel codes [18, 19] as well as the use of thermal-hydraulic system codes to perform plate type fuel subchannel analysis [20-23]. Most of the subchannel computer codes for plate type reactors reported in the literature are not for general use but dedicated for specific parameter verifications of new research, test, or multipurpose reactors [17-19, 24].
In this work we present the validation of the COTENP code (Code for Thermal-hydraulic Evaluation of Nuclear Reactors with Plate Type Fuels) developed for steady-state thermal-hydraulic design evaluation of research and test reactors with plate type fuels and low pressure. The motivation for developing such a computer code was to provide the design team with a tool that allows investigating thermal-hydraulic design limits for the reactor named Reator Multiproposito Brasileiro (RMB), a multipurpose reactor with thermal power of 30 MW aimed at producing radioisotopes for medical and industrial applications and material studies with neutrons . The code is based on current literature of subchannel analysis models and its accuracy is validated against experimental and calculated data reported for two reactors with plate type fuels. The first set of data belongs to the Research Reactor Benchmark Database from the International Atomic Energy Agency, more specifically, data from an Instrumented Fuel Assembly (IFA) of the 5 MW IEAR1 research reactor [21, 22, 26]. The second set of data comes from calculation results for the 50 MW CARR multipurpose reactor .
In Section 2 we present the COTENP code methods furnishing details about the conservation equations for mass, momentum, and energy, the flow rate and pressure drop approach, and the numerical approach adopted to solve the equations. In Section 3 we present the data utilized for verifying the accuracy of the COTENP code and the methodology to conduct the validation. In Section 4 we present the comparison results, discussions, and some of the COTENP code capabilities regarding thermal-hydraulic design limits such as the onset of nucleate boiling and departure from nucleate boiling. Finally, in Section 5 we present the concluding remarks.
2. Methods for the COTENP Code
In this section work we describe the COTENP code to calculate the thermal-hydraulic parameters of nuclear reactors with plate type fuel elements. To represent the tridimensional behavior of the core we combine the subchannel approach and the cascade method in a two stage scheme as shown in Figure 1 [2, 5, 13, 27]. In the first stage the core is divided into subchannels with size equivalent to a fuel assembly. From the analysis of all core fuel assemblies, the subchannel with the largest enthalpy rise is identified as the hot assembly. In the second stage the hot fuel assembly is divided into subchannels with size equivalent to the actual coolant channel. As in the previous stage, the subchannel with largest enthalpy rise is identified as the hot subchannel. For this subchannel, a detailed thermal-hydraulic analysis is undertaken so that design limits such as maximum temperatures, onset of nucleate boiling, and critical heat flux conditions can be verified.
The conservation equations are solved simultaneously taking into account operational and boundary conditions. The following assumptions were adopted in the code:
(i) Steady-state power and coolant flow
(ii) Uniform inlet and outlet pressure distribution
(iii) Homogeneous equilibrium model for two-phase flow
(iv) One-dimensional heat transfer with uniform transversal heat generation
Each subchannel is divided axially in control volumes. We use mass, momentum, and energy conservation equations for each control volume to obtain along each channel the temperature distribution for the fuel, cladding, and coolant, pressure drop, enthalpy rise, and coolant thermodynamic quality.
Below we describe the conservation equations, the flow rate model, the correlations utilized for determining the onset of nucleate boiling and critical heat flux conditions, and the numerical approach considered in the COTENP code. In Section 3 we present the data and approach considered for verifying the accuracy of the COTENP code.
2.1. Conservation Equations for Mass, Momentum, and Energy. Figure 2 shows schematically the subchannel approach used to represent the coolant behavior and the variables pertaining to the three conservation equations. The [k.sub.th] subchannel is divided into axial control volumes allowing the simultaneous solution of the conservation equations for mass, energy, and momentum.
The steady-state conservation equations for the [k.sub.th] subchannel and [i.sub.th] control volume are described below. The mass conservation sketched in Figure 2a is
[[??].sub.k,i] - [[??].sub.k,i+1] = 0 (1)
[[??].sub.k,i] = [[rho].sub.k,i][[bar.u].sub.k,i][A.sub.k] (2)
where [[??].sub.k,i] is the coolant mass flow rate (kg/s), [rho] is the coolant specific mass (kg/[m.sup.3]), [[bar.u].sub.k,i] is the coolant speed (m/s), and [A.sub.k] is the cross section area of the subchannel ([m.sup.2]).
The momentum conservation equation sketched in Figure 2b is
[mathematical expression not reproducible] (3)
where [DELTA][P.sub.k,i] is the total pressure drop in the [(k, i).sub.th] control volume, [f.sub.k,i] is the friction coefficient, [z.sub.k,i] is the control volume elevation in the subchannel, [D.sub.h] is the hydraulic diameter of the subchannel, and [k.sub.k,i] is the localized form loss coefficient. In the RHS of (3) the first term accounts for friction losses, the second term accounts for form losses, the third term accounts for elevation losses, and the fourth term accounts for acceleration losses. The friction coefficient is given by the Hangen-Poiseulle correlation for laminar flows and by the Blasius correlation for turbulent flows .
We can define a hydraulic resistance [R.sub.k,i] grouping the first two terms in the RHS of (3)
[R.sub.k,i] = [f.sub.k,i][([Z.sub.k,i+1] - [Z.sub.k,i])[[rho].sub.k,i]/2[D.sub.h]] + [k.sub.k,i][[[rho].sub.k,i]/2[D.sub.h]] (4)
and rewrite it as
[DELTA][P.sub.k,i] = [R.sub.k,i][[bar.u].sup.2.sub.k,i] + [[rho].sub.k,i]g([z.sub.k,i+1] - [z.sub.k,i]) + [[[??].sub.k]/2[[rho].sub.k,i]]([1/[A.sup.2.sub.i+1]][1/[A.sup.2.sub.i]]). (5)
The energy conservation equation sketched in Figure 2c is
[[??].sub.k]([[bar.h].sub.k,i+1] - [[bar.h].sub.k,i]) = [q".sub.x k,i][P.sub.a][DELTA]z (6)
where [[bar.h].sub.k,i] is the coolant enthalpy (J/kg), [q".sub.x k,i] is the heat flux across the surface area of the fuel plate (W/[m.sup.2]), and [P.sub.a] is the heated perimeter of the subchannel (m). The heat flux is given by
[q".sub.k,i] = [q".sub.max][F.sup.N.sub.k,i] (7)
where [F.sup.N.sub.k,i] is the power density distribution factor in the [k.sub.th] subchannel and [i.sub.th] control volume which accounts for the fission heat generation in the core. The [F.sup.N.sub.k,i] can be calculated as the product of axial and fuel assembly (radial) peak factors ([F.sup.N.sub.k,i] = [F.sup.A.sub.k,i][F.sup.R.sub.k,i]) [9, 29, 31].
The temperature profile across the fuel plate is determined assuming perfect contact between the fuel meat and the cladding. Thus the heat transfer process considered inside the plate is conduction whereas the one between the cladding and the coolant is convection. The resulting temperature equations for the coolant, cladding, and fuel centerline are presented elsewhere .
2.2. Homogeneous Equilibrium Model for Two-Phase Flow. The COTENP code model assumes the homogeneous equilibrium model for the two-phase flow phenomena in the reactor core. This model assumes a homogenous flow in which there is no relative velocity between vapor and liquid phases in thermodynamic equilibrium . The possible occurrence of two-phase flow is determined relating the flow enthalpy with the saturation enthalpies of vapor and liquid at local pressure and temperature conditions determined by the code. The thermodynamic quality evaluation along the subchannel is given by
[x.sub.k,i] = [[[bar.h].sub.k,i] - [[bar.h].sub.l]]/[[[bar.h].sub.v] - [[bar.h].sub.l]] (8)
where [[bar.h].sub.k,i], [[bar.h].sub.l] and [[bar.h].sub.v], are the control volume enthalpy and the corresponding liquid and vapor saturations enthalpies with respect to the control volume pressure and temperature.
For thermodynamic quality values below zero it is considered a monophasic liquid flow while for values greater than zero it is considered two-phase flow condition. At this point, the coolant behavior is represented by a fictitious flow, which obeys the conservation equation presented above and requires the coolant properties to be given by average two-phase flow parameters. The coolant specific mass ([[rho].sub.k,i]) and coolant velocity ([u.sub.k,i]) are then given by
1/[[bar.[rho]].sub.k,i] = [[x.sub.k,i]/[([[bar.[rho]].sub.k,i]).sub.v]] + [[1 - [x.sub.k,i]]/([[bar.[rho]].sub.k,i])l] (9)
and [[bar.u].sub.k,i] = [[bar.u].sub.k,i][[bar.[rho]].sub.k,i][A.sub.k,i]/[[bar.[rho]].sub.k,i][A.sub.k,i]. (10)
2.3. Flow Rate Model Based on Balance of Pressure Drop. The flow rate in each subchannel is obtained by imposing the same pressure drop for all subchannels from the inlet to the outlet. This procedure is normally utilized to determine cross flow between neighboring coolant channels in rod bundles [14, 16]. In this work we apply it to determine the channel flow rate of closed channels in plate type fuels. This is done in an iterative process in which the coolant velocity is adjusted until all subchannels present the same pressure drop within a convergence criterion. Figure 3 shows the scheme in which the velocity initial uniform produces a variable pressure drop. In the iterative process the coolant velocity is varied to equate the pressure drop of all different subchannels. The procedure is stopped when a convergence criterion is reached.
To show how the subchannel flow rate is determined consider that the initial (first iteration) total mass flow rate for the reactor core is given by
[[??].sub.TOT] = [A.sub.T][K.summation over (k=1)][[rho].sub.k][[alpha].sub.k][[bar.u].sub.k,0] (11)
where [[??].sub.TOT] the core mass flow (kg/s), [A.sub.T] is the total flow cross section area of the core, [[rho].sub.k] is the coolant density (kg/[m.sup.3]) [[bar.u].sub.k,0] is the first iterate average velocity of the coolant (m/s), [[alpha].sub.k] = [A.sub.k]/[A.sub.T], and [A.sub.k] is the cross section area of the subchannel; the subscript k refers to the subchannel number within the set of the K subchannels in the given stage.
In the iterative process the coolant velocity is changed from one step to the next to find the velocity distribution that adjusts the pressure drop of all subchannels, i.e.,
[[bar.u].sub.k] = [[bar.u].sub.k,0] + [DELTA][[bar.u].sub.k] (12)
where [DELTA][[bar.u].sub.k] is the velocity change. Equation (11) then turns to
[[??].sub.TOT] = [A.sub.T]([K.summation over (k=1)][[rho].sub.k][[alpha].sub.k][[bar.u].sub.k,0] + [K.summation over (k=1)][[rho].sub.k][[alpha].sub.k][DELTA][[bar.u].sub.k]). (13)
Since the first term equals [[??].sub.TOT], the second term of (13) must be zero, i.e.,
[K.summation over (k=1)][[rho].sub.k][[alpha].sub.k][DELTA][[bar.u].sub.k] = 0 (14)
The pressure drop for the [(k, i).sub.th] control volume is calculated using (5) of momentum conservation neglecting the less influential terms and keeping the friction and form losses as follows:
[DELTA][P.sub.k,i] = [R.sub.k,i][[bar.u].sup.2.sub.k,i]. (15)
The pressure drop across the subchannel is given by
[DELTA][P.sub.k] = [N.summation over (i=1)][DELTA][P.sub.k,i] = [R.sub.k][[bar.u].sup.2.sub.k]. (16)
Substituting (12) in (16) and neglecting the second order term in [DELTA][[bar.u].sub.k] we obtain
[DELTA][P.sub.k] = [DELTA][P.sub.k,0] + 2([DELTA][P.sub.k,0]/[[bar.u].sub.k,0])[DELTA][[bar.u].sub.k] (17)
From the condition of balanced pressure drop for all subchannels, i.e., [DELTA][p.sub.k] = [DELTA][p.sub.j], we obtain the coolant velocities that meet these requirements. This is a under determined problem for the case of two subchannels or over determined for 3 or more subchannels. Therefore [DELTA][[bar.u].sub.k] is obtained iteratively as presented in Section 2.5.
2.4. Onset of Nuclear Boiling and Departure from Nuclear Boiling Correlations. The heat transfer design limits are related to inadequate heat transfer to the coolant in core regions with high peak power densities. The limiting conditions depend on peak power density in the fuel meat and local coolant conditions such as pressure, quality, and temperature and are related to the nucleate boiling heat transfer condition. The parameters used to verify design limits are the onset of nucleate boiling (ONB) and departure from nucleate boiling (DNB) [2, 9,10].
To predict the ONB the code furnishes three different correlations: Bergles and Rohsenow (1964), Jens and Lottes (1951), and one developed for narrow rectangular channels proposed by Al-Yahia and Jo (2017) .
The departure from nucleate boiling ratio is defined as
DNBR = [q".sub.DNB]/[q".sub.Local] (18)
where [q".sub.DNB] is the critical heat flux furnished by the EPRI correlation  and [q".sub.Local] is the local heat flux calculated by the COTENP code.
2.5. Numerical Solution Approach. The main program controls 5 modules: (I) input parameters; (II) geometrical parameter calculations; (III) thermal-hydraulic calculations (coolant velocity estimation, conservation equations, and temperature distribution estimation); (IV) estimation of critical heat flux and onset of nucleate boiling conditions; and (V) output results. The code was developed using FORTRAN language.
Figure 4 shows the flow chart of the thermal-hydraulic calculation scheme, module (III). The code conducts the first and second stage calculations according to the size of the subchannels under study. Before starting the second stage, the code estimates the intra-assembly radial power factor for each subchannel through values of average power factors from neighboring assemblies using the Thomas algorithm .
The scheme for determining the flow rate through pressure drop balance requires varying the coolant velocity to equate all subchannels pressure drops. We start considering (17) and equating the [DELTA]P for subchannels k+1 and k, i.e.,
[DELTA][P.sub.k+1] = [DELTA][P.sub.k]. (19)
From (19) we obtain the initial coolant velocity for subchannel k+1
[mathematical expression not reproducible]. (20)
Then, to make sure that the total flow rate does not change we adjust the coolant velocity in each channel to obey (14), i.e.,
[mathematical expression not reproducible]. (21)
where [DELTA][[bar.u].sup.0.sub.j] is given by (20). The process to calculate the redistribution of the coolant velocity is iterative using Equations (19) through (21) until the convergence criterion [epsilon] is reached.
3. Validation Approach and Data
The validation of the COTENP code is conducted using experimental data from the IEA-R1 research reactor and calculated results reported for CARR multipurpose reactor. The thermal-hydraulic variables of subchannel analyses of plate type fuel reactors found in the literature are coolant, cladding, and fuel axial temperature distributions, fuel assembly flow rate distribution, pressure drops across the reactor core, mean coolant velocity in subchannels, and departure from nucleate boiling results. Below we describe the IEA-R1 research reactor and the CARR multipurpose reactor and their reported subchannel analysis data [7, 22, 26, 28, 34] and the approach taken in this work to carry out the COTENP code validation.
3.1. The IEA-R1 Research Reactor. The validation of the COTENP code is based on the experimental data presented in the Benchmark Database of the International Atomic Energy Agency from the IEA-R1 research reactor . The IEA-R1 is an open pool type research reactor with 5 MW maximum thermal power using low enrichment MTR [U.sub.3][Si.sub.2]-Al and [U.sub.3][O.sub.8]-Al dispersed fuel assemblies. The reactor heat removal occurs through a downward coolant flow. The core comprises 20 regular fuel assemblies each one with 18 fuel plates assembled in two lateral support plates conforming 17 closed flow channels heated on two sides, and 4 control fuel assemblies. The irradiation positions are located in the center of the core and in the reflector region. Figure 6 shows the top view of configuration 247 and more information about the IEA-R1 reactor can be found in Appendix A.
The reactor is equipped with an Instrumented Fuel Assembly (IFA) allowing measurements of coolant and cladding temperatures, flow rate and fuel assembly power, and with a dummy fuel assembly (AP) without fuel utilized for measuring flow rate, pressure drop and other variables. Figure 5 shows the top of view of configuration 243, the IFA positioned in location (6,8), and the dummy assembly positioned in location (0,0) .
The IFA temperature experimental data comprise 14 measurement locations of coolant and cladding temperatures distributed as shown in Figure 7. There are two thermocouples to measure coolant inlet and outlet temperatures and 12 thermocouples distributed in three channels. The coolant flow rate and pressure drop experimental data were measured using the dummy fuel assembly. The coolant velocity was obtained from the coolant flow rate measurements. Figure 6 shows thermocouples positions in the IFA and Table 1 shows the measured variables and their respective locations.
Reference  does not present the experimental error for the temperature data but furnishes data plots from which they extracted their average values. Observing maximum variations in the data plot intervals we can infer that they are below 0.25[degrees]C or about 0.5% of the mean temperatures reported . We take this variation as the experimental error for all temperature data.
Reference  reports total core pressure drop measured with the dummy but does not present details such as exact location of the measurements and their experimental error.
3.2. The CARR Multipurpose Reactor. The second set of data used to verify the COTENP code came from the CARR multipurpose reactor, a 56 MW reactor with slightly pressurized light water as the primary coolant and moderator and heavy water as reflector [28, 34]. The reactor core contains 21 plate type fuel assemblies of which 17 are standard assemblies and 4 are open assemblies for different purposes. The heat removal is conducted through downward coolant flow. Each standard fuel assembly has 20 fuel plates conforming 19 closed flow channels and other experimental channels [7, 28, 34]. Figure 7 displays a top view of the CARR reactor and detailed information about its geometry and operational conditions is found in Appendix A.
Thermal-hydraulic analyses for the CARR reactor under steady and transient conditions were carried out by Lei and Zhang . They report a steady-state multichannel analysis furnishing calculated results for each fuel assembly of assembly flow rate and temperature distribution along the hot coolant channel (axial direction). They also provide information about DNBR .
3.3. Validation Approach. The goal of this validation of the COTENP code is determining discrepancies of its calculated subchannel results compared to experimental data from the IEA-R1 research reactor and calculated results from the CARR multipurpose reactor. The discrepancy is defined here as the relative difference taking the reported results as the reference ones, i.e.,
discrepancy = [[v.sub.COTENP] - [v.sub.Ref]]/[v.sub.Ref] (22)
where [v.sub.COTENP] is the COTENP code result and [v.sub.Ref] is the IEA-R1 experimental results or  results. The mean discrepancy presented is the square root of the mean of the squared discrepancies or
mean discrepancy = [square root of [1/I][I.summation over (i=1)][([[v.sub.COTENP,i] - [v.sub.Ref,i]]/[v.sub.Ref,i]).sup.2]] (23)
3.3.1. The IEA-R1 Model with the COTENP Code. The IEAR1 reactor analyses performed with the COTENP code considered the core configuration 243 in three different states: power levels at 5 MW, 4.5 MW, and 4 MW. It considers results from Instrumented Fuel Assembly positioned at locations (6,8) for temperature comparisons. The core pressure drop measurement is located at positions (0, 0) as shown in Figure 5.
The IFA is divided in three regions with 6 fuel plates each identified as fuel assembly side, central plate, and reflector side. The IFA model comprises 17 subchannels and 30 control volumes in the axial direction to represent the fuel assembly. The IFA power level [P.sub.IFA] is obtained from
[P.sub.IFA] = [[??].sub.IFA][c.sub.p]([T.sub.out] - [T.sub.in]) (24)
where [[??].sub.IFA] is the coolant flow rate in the IFA, cp is the coolant specific heat, and [T.sub.in] and [T.sub.out] are the inlet (TF1) and outlet (TF14) coolant temperatures for the IFA. The reactor operational conditions for the three states considered including the power density distribution are presented in Appendix A .
The pressure drop for the IFA model takes into account the friction losses along the coolant channel and elevation acceleration since it is a downward flow. We consider no form losses along the channel, even considering that they may be significant, because of lack of information in the experimental data . The acceleration losses and gains in the inlet and outlet are also neglected for similar reasons .
3.3.2. The CARR Model with the COTENP Code. The CARR reactor analysis includes the evaluation and comparison of the mass flow rate distribution among the fuel assemblies, coolant, cladding, and fuel centerline temperature distribution along the subchannels on the hot fuel assembly, and results for the departure from nucleate boiling ratio for the hot channel.
In addition, we present for this reactor some capabilities of the COTENP code such as identification of hot assembly based on enthalpy rise, pressure drop, thermodynamic quality, detailed temperature distribution, and results for the onset from nucleate boiling (ONB).
The CARR reactor simulation comprises the active zone with height of 850 mm where each fuel assembly is considered as a subchannel divided into 17 control volumes. In Appendix A we present the reactor operation data and the power density distribution as power factors for each fuel assembly and as axial distribution for both types of fuel assemblies .
The pressure drop model for the CARR reactor considered similar assumptions as those for the IFA in Section 3.3.1 since no information was reported .
4. Results and Discussions
4.1. Validation of the COTENP Code against Experimental Results from the IEA-R1 Research Reactor. Calculated thermal-hydraulic results obtained with the COTENP code for configuration 243 from the IEA-R1 reactor are compared in this section with experimental results [22, 26]. The thermal-hydraulic variables at 3 different power levels are temperature (10 different IFA locations), coolant velocity, and pressure drop ([DELTA]P dummy assembly location) as described in Sections 3.1 and 3.3 with locations presented in Figure 5 and Table 1.
In Table 2 we present results for the coolant and cladding temperature at different location of the IFA for 4 MW, 4.5 MW, and 5 MW. The calculated results at steady-state condition for the IEA-R1 reactor are compared against experimental data through relative difference between them . The experimental error for the temperature measurements, as discussed in Section 3.1, is taken as 0.25[degrees]C or about 0.5%. The comparisons yield mean discrepancies varying between 4.1% and 5%. Relative discrepancies between calculation and measurement at each location are also presented and vary between 0.1 and 11%. The maximum discrepancy for the 3 power levels occur at the same measurement location (TC3) at 252,5 mm from the top.
The results for the IFA power, coolant velocity, and pressure drop are shown in Table 3 for similar power levels. The IFA power maximum discrepancy occurs for 5 MW (13.2%) while for the other 2 power levels it is below 2.9%, the coolant velocity discrepancies are below 1.5%, and pressure drop discrepancy are all equal to 10.7%.
4.1.1. Discussion. The maximum discrepancy for the temperature was observed at the central channel of the assembly at position TC3. According to Hainoun et al.  similar evaluations of this problem conducted by other researchers using CATHARE, RELAP5, MERSAT, and PARET presented similar discrepancies at this location during the IAEA benchmark study conducted for the IEA-R1 reactor [22, 26]. On the other hand, their average discrepancy for the several temperature measurements were 8.8%, 4.8%, 4.9%, and 9.2%, respectively, which are similar to those obtained with the COTENP code presented in Table 2 (root mean square discrepancy below 5%) .
About the TC3 experimental temperature result, the researchers have concluded that the discrepancy at this location may possibly be due to the experimental data [22, 26]. Additionally one may consider that at this location the axial power factor is strongly affected by the control rods, which are inserted in the core up to this depth. A local variation in the power density distribution may influence the local temperature results [35, 36].
The coolant velocity and pressure drop for the 3 power level conditions presented similar discrepancies, below 1.5% and 10.7%, respectively. The IFA power results at 4 MW and 4.5 MW presented discrepancies below 2.9% while at 5 MW the discrepancy increased to 13.2% although all other results discrepancies remained similar. The 5 MW IFA power comparison requires further study.
The pressure drop discrepancy is important and should be discussed. The COTENP results take into account only friction losses and elevation acceleration for the downward flow. The difference may be due to neglecting the form loss and gain in the inlet and outlet of the coolant subchannel (see Section 3.3.1). Most probably the pressure drop measurement was made outside the coolant channel and would include these form effects. The 10% error indicates that the friction losses appear adequately considered. Further validation appears necessary for better assessing the accuracy of the COTENP code.
4.2. Validation of COTENP Code against Calculated Results from the CARR Research Reactor. The thermal-hydraulic variables verified in this section are the mass flow rate in each fuel assembly, axial temperature distributions, and DNBR results obtained with the COTENP code for the CARR multipurpose reactor. The COTENP code results are compared with those reported by Lei and Zhang .
The results of thermodynamic quality and pressure drop along the hot FA are presented in Table 4; it shows that during steady-state operation of the reactor core there is no occurrence of two-phase flow at respective local pressure.
Figure 8 compares the mass flow rate at each fuel assembly obtained with the COTENP code and those reported by Lei and Zhang . The flow rate distribution among the several fuel assemblies presents maximum discrepancy of about 0.51% and negligible mean average discrepancy. The pressure drop and coolant mean velocity calculated with the COTENP are 0.767 MPa and 10.28 m/s, respectively. The discrepancies when compared to reported results are 9.7% for the pressure drop and 1.8% for the mean velocity.
Figure 9 compares results of axial temperature distribution in the hot channel at the fuel centerline, cladding, and coolant region from the COTENP code and Lei and Zhang . The outlet coolant temperature calculated by the COTENP code is 70.2[degrees]C while the reported value is 68[degrees]C with 3.2% discrepancy. The mean and maximum relative discrepancies for the coolant, cladding, and fuel center line temperature distributions are presented in Figure 9.
Figure 10 compares the DNBR results near the region of heat transfer condition of minimum departure from nucleate boiling ratio. The results obtained from the COTENP code and those from  present similar trends with minimum DNBR equal to 9 and 11, respectively.
4.2.1. Discussion. Regarding the mass flow rate variable for different fuel assemblies, the COTENP code results compare well with those from  since the mean discrepancy is negligible and the maximum discrepancy is small (0.51%). Taking into account the fact that the mass flow rate distribution depends on the pressure drop, the adjusting procedure through the coolant velocity in each fuel assembly subchannel (see Section 2.3) appears as good model. The large pressure drop discrepancy (9.7%), similar to that observed in the IEA-R1 reactor analysis presented in Section 4.1, seems to emphasize that the justification for the difference lies in not accounting for form losses in the inlet and outlet of the coolant channel. As was mentioned in Section 3.3.2, the CARR model did not account for such effects due to lack of information.
The axial temperature distributions for the coolant, cladding, and fuel centerline present similar shapes to those from Lei and Zhang . The mean discrepancy below 2.6% for the coolant and cladding temperatures is not reproduced for the fuel centerline. This is due to the approximation of uniform temperature conductivity in the fuel region. The consequence is that the peak fuel temperature produced by the COTENP code is 202[degrees]C while Lei and Zhang  report 193[degrees]C.
The differences presented by the DNB ratio from the COTENP code and those from  in Figure 11 can be considered small and can be attributed to the different critical heat flux correlations utilized by the two codes and the small differences on the local temperature and pressure results produced by the two calculations (see the coolant and cladding temperature results for axial volumes 12 and 13 in Figure 9).
The outlet flow quality for the hot channel is all negative as shown in Table 4 indicating that no saturated boiling had occurred. In this regard the two-phase flow model implemented in the COTENP code could not be validated with the CARR results.
4.3. Other Results Furnished by the COTENP Code. Beside the thermal-hydraulic variable shown in the previous sections, the COTENP code furnishes additional information about onset from nucleate boiling condition (ONB), which is important for typical research reactors, departure from nucleate boiling, and enthalpy rise. Such results are presented below for the CARR multipurpose reactor.
The onset of nucleate boiling can be found observing the trend of the wall superheat temperature versus heat flux as shown in Figure 11. The slope of the wall temperature reduces around the ONB location as shown by the trend lines for low and high heat fluxes for the 3 correlations considered, Al-Yahia and Jo, Bergles and Rohsenaw, and Jens and Lottes. These correlations indicate that the onset of nucleate boiling occurs for heat fluxes just below 800 kW/[m.sup.2]. The wall superheat temperature varies between 3[degrees]C and 9[degrees]C. This point occurs at control volume number 5 at 250 mm from the subchannel inlet.
The homogeneous equilibrium two-phase flow model utilized in the COTENP code accounts for saturated boiling but not for local subcooled nucleate boiling in the coolant. Thus these local effects on the pressure drop, local coolant specific mass, local wall temperature, and local heat flux are not accounted for in the results presented in Figures 10 and 11 in the current COTENP code model.
Figure 12 displays the enthalpy rise for the several fuel assemblies of the CARR multipurpose reactor. The FA with largest enthalpy rise is the number 9 with 103.76 kJ/kg.
The COTENP code was developed for thermal-hydraulic design evaluation of nuclear reactors with plate type fuel assemblies. It is a subchannel analysis code based on conservation equations for mass, momentum, and energy which calculates the flow and temperature distributions in plate type fuel assemblies for steady-state conditions. It furnishes detail information about mass flow rate distribution, core pressure drop, average coolant velocity, and temperature distributions. Regarding design parameters it identifies the hot channel, fuel, cladding and coolant maximum temperatures, and information about onset of nucleate boiling (ONB) and departure from boiling ratio (DNBR). The COTENP code accuracy was verified through comparisons with measured results from the IEA-R1 research reactor and comparisons with calculated results from the CARR multipurpose reactor.
The mean discrepancies for the coolant temperature at different power level conditions were below 5% for the Benchmark Database from the IEA-R1 research reactor of the International Atomic Energy Agency. The COTENP code presented good results. The pressure drop and coolant velocity presented discrepancies below 1.5% and 10.7%, respectively. These results indicate that the model for pressure drop and coolant velocity takes into account correctly the friction losses along the channel and that the 10.7% discrepancy should be due the disregard of form losses in the channel inlet and outlet due to lack of detailed information in the experimental data.
The validation of the COTENP code against calculated results from the CARR multipurpose reactor has evidenced good results for the flow rate distribution among the fuel assemblies and for the coolant temperature axial distribution. The former presented negligible mean discrepancy and the latter presented mean discrepancy of 2.6% which is about half of that presented in the validation against the IEA-R1 reactor experimental data. The pressure drop result presented a discrepancy of 9.7%, similar to that presented in the IEA-R1 reactor validation. This result emphasizes the need to verify results including form effects on the pressure drop in the coolant channel inlet and outlet. The COTENP code presented good estimation of the DNB ratio for the CARR multipurpose reactor.
These two verifications of the COTENP code presented good results indicating that with additional improvements it can be used for verifying thermal-hydraulic limits of the planned Brazilian multipurpose reactor. Appendix A lists the improvements planned to be implemented in the code.
A.1. Data from the IEA-R1 Reactor. Table 5 summarizes the main parameters describing the IEA-R1 reactor. The reactor holds to types of plate type of dispersion fuels: [U.sub.3][Si.sub.2]-Al and [U.sub.3][O.sub.8]-Al. The fuel is the Instrumented Fuel Assembly (IFA) which was designed and manufactured to perform measurements of different core cooling parameters in actual reactor conditions. It was used to validate computer codes used in the safety analysis of the IEA-R1 reactor . The IFA has three regions comprising 6 plates each. The transverse power factors assumed for the regions are 1.0 for the fuel assembly side, 0.89 for the central plates, and 0.96 for the reflector side. Figure 13 shows the normalized axial power distribution for the 3 regions of the IFA and Figure 14 shows the average power factors for the fuel assemblies.
A.2. Data from the CARR Research Reactor. The CARR reactor has a [U.sub.3][Si.sub.2]-Al dispersion type fuel. Table 6 presents the main parameters describing the CARR research reactor. Figure 15 shows the radial power fuel assembly and the axial power distribution for both types of fuel assemblies.
A.3. Future Improvements. The future improvements planned to be implemented in the COTENP code include an improved model for two-phase flow, for estimating the pressure drop, allow nonuniform temperature across the fuel meat, estimating the coolant critical velocity in the hot subchannel, additional means to calculate critical heat flux, for instance, look-up tables, qualifying the input, and discuss uncertain factors.
A: Cross section area of the subchannel ([m.sup.2])
AVD: Average relative derivation
c: Cladding thickness
[C.sup.*]: Heat capacity of the coolant
CHF: Critical Heat Flux
[Dh.sub.:] Hydraulic diameter
DNBR: Departure from nucleate boiling ratio
f: Friction coefficient
FA: Fuel assemblies
[F.sup.N.sub.z,i]: Axial power distribution factor in the volume control
[F.sup.N.sub.R,i]: Radial power distribution factor in the subchannel
[bar.h]: Coolant enthalpy (J/kg)
[h.sub.c]: Heat transfer coefficient of coolant
IFA: Instrumented Fuel Assembly
[k.sub.k,i]: Localized form loss coefficient
[k.sub.cool]: Thermal conductivity of the fluid
[k.sub.fuel]: Thermal conductivity of the fuel
m: Mass flow rate (kg/s)
PWR: Pressurized Water Reactors
[P.sub.a]: Heated perimeter of the subchannel (m)
[DELTA]P: Pressure drop
[q".sub.x]: Heat flux across the surface area of the fuel plate (W/[m.sup.2])
q'": Power density (W/[cm.sup.3])
S: Half thickness of fuel
Tc: Coolant temperature
[T.sub.clad]: Cladding temperature
[T.sub.f]: Fuel temperature
[bar.u]: Coolant speed (m/s)
[DELTA][[bar.u].sub.j]: Coolant speed change
Z: Node elevation in the subchannel
[[alpha].sub.i]: Area relation [A.sub.i]/[A.sub.T]
[rho]: Specific mass of the coolant (kg/[m.sup.3])
[epsilon]: Convergence criterion.
All data underlying this research are available upon request to the corresponding author.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
The authors want to acknowledge the financial support provided by Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES) (a scholarship for Duvan A. Castellanos-Gonzalez), Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq), and Universidade Federal do ABC (UFABC).
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Duvan A. Castellanos-Gonzalez (ID), Joao Manoel Losada Moreira (ID), Jose Rubens Maiorino (ID), and Pedro Carajilescov
Centro de Engenharia, Modelagem e Ciencias Sociais Aplicadas, Universidade Federal do ABC, Av. dos Estados 5001, Santo Andre-SP 09210-508, Brazil
Correspondence should be addressed to Duvan A. Castellanos-Gonzalez; firstname.lastname@example.org
Received 1 September 2018; Accepted 28 October 2018; Published 2 December 2018
Academic Editor: Arkady Serikov
Caption: Figure 1: The chain method for the two stage approach of the COTENP code.
Caption: Figure 2: Representation of the conservation equations in the [i.sub.th] control volume of the [k.sub.th] subchannel. H is the subchannel length, L is the plate side length, and d is the distance between plates or coolant channel width.
Caption: Figure 3: Model of mass flow rate distribution used in COTENP code.
Caption: Figure 4: Calculation procedure for stages 1 and 2 in Module (III).
Caption: Figure 5: Top view of configuration 243 of the IEA-R1 nuclear core. Adapted from .
Caption: Figure 6: Thermocouples positions in the Instrumental Fuel Assembly (side view). Adapted from .
Caption: Figure 7: Top view of the CARR multipurpose reactor.
Caption: Figure 8: Mass flow rate fraction for the several fuel assemblies of the CARR reactor. Comparison between the COTENP code and .
Caption: Figure 9: Comparison of the temperature distribution in the hot channel of the CARR reactor between the COTENP code and reported results . TF is the centerline temperature, Tclad is the cladding temperature, and TC is the coolant temperature.
Caption: Figure 10: Comparison of DNBR results in the hottest fuel assembly for the CARR reactor between the COTENP code and reported results .
Caption: Figure 11: Variation in the wall superheat temperature with heat flux for the proposed correlations.
Caption: Figure 12: Enthalpy rise for the several fuel assemblies of the CARR reactor obtained with the COTENP code.
Caption: Figure 13: Axial power distribution in the Instrumented Fuel Assembly .
Caption: Figure 14: Average fuel assembly power factors from the CARR reactor .
Caption: Figure 15: Axial power factors for the standard and open fuel assemblies from the CARR reactor .
Table 1: Measurement variables from the IEA-R1 reactor utilized in the COTENP code validation. Temperature variables are measured in the IFA and flow rate and pressure drop are measured in the dummy fuel assembly ([DELTA]P) . Label Location Measurement variable TC2 cladding lateral Temperature (IFA) plate (side reflector) TC3 cladding central Temperature (IFA) plate TC4 cladding lateral Temperature (IFA) plate (side fuel assembly) TC5 cladding lateral Temperature (IFA) plate (side reflector) TC6 cladding central Temperature (IFA) plate TC7 cladding lateral Temperature (IFA) plate (side fuel) assembly TC8 cladding lateral Temperature (IFA) plate (side reflector) TC10 cladding central Temperature (IFA) plate TC12 cladding lateral Temperature (IFA) plate (side fuel assembly TF14 fluid outlet (bottom Temperature (IFA) of the core) [DELTA]P in dummy assembly Pressure ([DELTA]P assembly) [bar.u] in dummy assembly Coolant velocity ([DELTA]P assembly) IFA location (see Position (6,8) Figure 7) DFA location (see Position (0,0) Figure 7) Table 2: Temperature results obtained with the COTENP code for the IEA-R1 reactor at different power levels. Temperature results simulate measurement results at different locations of the IFA. The IFA is located at the (6,8) position. Inferred error from experimental results is [+ or -]0.25[degrees]C or [+ or -]0.5%. Temperature ([degrees]C) Power level = 4 MW Experimental COTENP Discrepancy (%) TC2 44.41 43.60 1.8 TC3 37.28 41.20 10 TC4 45.27 42.70 5.7 TC5 49.25 49.35 0.2 TC6 42.95 45.85 6.7 TC7 50.51 48.05 4.9 TC8 45.99 46.45 1.0 TC10 42.02 43.55 3.6 TC12 47.64 45.30 4.9 TF14 37.28 36.71 1.5 Root Mean Square Discrepancy 4.1 (%) Temperature ([degrees]C) Power level = 4.5 MW Experimental COTENP Discrepancy (%) TC2 46.47 45.50 2.1 TC3 38.68 42.90 11 TC4 47.29 44.35 6.2 TC5 51.78 51.80 0.1 TC6 44.87 48.00 7 TC7 53.02 50.25 5.2 TC8 48.22 48.75 1.1 TC10 42.81 45.45 6.2 TC12 43.92 47.40 8 TF14 38.70 38.10 1.6 Root Mean Square Discrepancy 4.8 (%) Temperature ([degrees]C) Power level = 5 MW Experimental COTENP Discrepancy (%) TC2 48.72 47.60 2.3 TC3 40.30 44.80 11 TC4 49.57 46.50 6.2 TC5 54.56 54.30 0.5 TC6 47.01 50.25 6.9 TC7 55.85 52.75 5.5 TC8 50.69 50.95 0.5 TC10 44.90 47.60 6.1 TC12 46.08 49.65 7.7 TF14 40.34 39.15 2.9 Root Mean Square Discrepancy 5.0 (%) Table 3: IFA power, coolant velocity, and IFA pressure drop at different power levels of the IEA-R1 reactor *. The IFA is located at the (6,8) position. Power level = 4 MW Experimental COTENP Discrepancy (%) IFA Power (kW) 147.61 143.40 2.9 Coolant velocity (m/s) 1.920 1.946 1.4 Pressure drop (kPa) 7.835 7.00 10.7 Power level = 4.5 MW Experimental COTENP Discrepancy (%) IFA Power (kW) 162.39 158.26 2.6 Coolant velocity (m/s) 1.920 1.948 1.5 Pressure drop (kPa) 7.835 7.0 10.7 Power level = 5 MW Experimental COTENP Discrepancy (%) IFA Power (kW) 177.53 154.29 13.2 Coolant velocity (m/s) 1.920 1.949 1.5 Pressure drop (kPa) 7.835 7.0 10.7 * The experimental errors were not reported. Table 4: Thermodynamic quality and pressure drop in the hot fuel assembly from the CARR reactor. Control Core height Thermodynamic Pressure volume (mm) quality (kPa) 1 50 -1.14E-03 628.255 2 100 -1.13E-03 636.55 3 150 -1.10E-03 644.89 4 200 -1.06E-03 653.282 5 250 -9.90E-04 661.732 6 300 -9.01E-04 670.245 7 350 -7.94E-04 678.823 8 400 -6.78E-04 687.463 9 450 -5.63E-04 696.161 10 500 -4.60E-04 704.908 11 550 -3.70E-04 713.696 12 600 -2.86E-04 722.521 13 650 -2.13E-04 731.378 14 700 -1.54E-04 740.261 15 750 -1.04E-04 749.165 16 800 -5.86E-05 758.088 17 850 -1.86E-05 767.029 Table 5: Main description parameters of IEA-R1 research reactor [22, 26]. Reactor parameter Data Thermal power reactor [MW] 2-5 Number of Fuel assembly 24 (i) Standard FA 20 (ii) Control FA 4 Total coolant flow rate 772 [[m.sup.3]/h] Bypass flow rate [[m.sup.3]/h] 547.2 Coolant flow rate of FA 22.8 [[m.sup.3]/h] Inlet Pressure [Mpa] 0.17 Inlet temperature [[degrees]C] 31.67/32.50/32.53 Power Density [W/c[m.sup.3]] 143/158/172 Number of fuel plates: (i) Standard FA 18 (ii) Control FA 12 Fuel meat dimensions ([U.sub.3] 0.76 x 62.6 x 600 [Si.sub.2]-Al or [U.sub.3] [O.sub.8]-Al) [mm] Thickness of coolant channel [mm] 2.89 Clad thickness [mm] 0.38 Reactor parameter Note Thermal power reactor [MW] Depends on irradiation program Number of Fuel assembly (i) Standard FA (ii) Control FA Total coolant flow rate [[m.sup.3]/h] Bypass flow rate [[m.sup.3]/h] Coolant flow rate of FA [[m.sup.3]/h] Inlet Pressure [Mpa] Inlet temperature [[degrees]C] For 4.0 / 4.5 /5.0 [MW] respectively Power Density [W/c[m.sup.3]] For 4.0 / 4.5 /5.0 [MW] respectively Number of fuel plates: (i) Standard FA (ii) Control FA Fuel meat dimensions ([U.sub.3] [Si.sub.2]-Al or [U.sub.3] [O.sub.8]-Al) [mm] Thickness of coolant channel [mm] Clad thickness [mm] * FA, Fuel assembly. Table 6: Main operational and geometric parameters of CARR research reactor [7, 28]. Reactor parameter Data Thermal power reactor [[MW.sub.th]] 56 Number of Fuel assembly 21 (i) Standard FA 17 (ii) Open FA 4 Total coolant flow rate [[m.sup.3]/h] 2650 Outlet Pressure [Mpa] 0.62 Inlet temperature [[degrees]C] 45 Power Density [W/[cm.sup.3]] 568 Core radius [m] 0.4 Height of active area [m] 0.85 Number of fuel plates: (i) Standard FA 21 Fuel meat dimensions [mm] 0.76 x 77.2 x 850 Thickness of coolant channel [mm] 2.59 Clad thickness[mm] 0.38 Thermal conductivity of [U.sub.3] 50.03 [Si.sub.2]-Al [W/m K] Clad thermal conductivity [W/m K] 176.01 Reactor parameter Note Thermal power reactor [[MW.sub.th]] Depends on irradiation necessity Number of Fuel assembly (i) Standard FA (ii) Open FA Total coolant flow rate [[m.sup.3]/h] Outlet Pressure [Mpa] Inlet temperature [[degrees]C] Power Density [W/[cm.sup.3]] Core radius [m] Height of active area [m] Number of fuel plates: (i) Standard FA Fuel meat dimensions [mm] Data taken from [28, 29] Thickness of coolant channel [mm]  Clad thickness[mm]  Thermal conductivity of [U.sub.3]  [Si.sub.2]-Al [W/m K] Clad thermal conductivity [W/m K]  * FA, Fuel assembly.
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|Title Annotation:||Research Article|
|Author:||Castellanos-Gonzalez, Duvan A.; Moreira, Joao Manoel Losada; Maiorino, Jose Rubens; Carajilescov, Pe|
|Publication:||Science and Technology of Nuclear Installations|
|Date:||Jan 1, 2018|
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