Corresponding author: Sergey K. Podgorny ( serkonpod@gmail.com ) Academic editor: Boris Balakin
© 2019 Vyacheslav S. Kuzevanov, Sergey K. Podgorny.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Kuzevanov VS, Podgorny SK (2019) Gascooled nuclear reactor core shaping using heat exchange intensifiers. Nuclear Energy and Technology 5(1): 7580. https://doi.org/10.3897/nucet.5.34294

The need to shape reactor cores in terms of coolant flow distributions arises due to the requirements for temperature fields in the core elements (
The result of shaping a nuclear reactor core with identical cooling channels can be predicted at a quality level without detailed calculations. Therefore, it is not normally difficult to select a shaping principle in this case, and detailed calculations are required only where local heat exchange intensifiers are installed.
The situation is different if a core has cooling channels of different geometries. In this case, it will be unavoidable to make a detailed calculation of the effects of shaping and heat transfer intensifiers on changes in temperature fields.
The aim of this paper is to determine changes in the maximum wall temperatures in cooling channels of hightemperature gascooled reactors using the combined effects of shaped coolant mass flows and heat exchange intensifiers installed into the channels. Various shaping conditions have been considered. The authors present the calculated dependences and the procedure for determining the thermal coolant parameters and maximum temperatures of heat exchange surface walls in a system of parallel cooling channels.
Variant calculations of the GTMHR core (
The calculation procedure was verified by direct comparison of the results calculated by the proposed algorithm with the CFD simulation results (
Core shaping, heat exchange intensification, mass flow distribution, maximum channel wall temperature
One of the major problems in implementing gascooled nuclear reactors is the high core thermal intensity due to the need to achieve a high coolant gas temperature, which, respectively, results in high cooling channel wall temperatures. Because of the uneven heat generation in the core, the maximum wall temperatures in different channels may vary. At given total coolant flow and average core outlet temperature, the maximum wall temperature in the most heatstressed channel group can be decreased if the coolant flow through the channels of this group is increased by shaping the mass flows. The other option is to install heat exchange intensifiers into the channels of this group while maintaining the coolant flow. It is obvious that, in any option of changing the core hydraulic (aerodynamic) characteristics, the total core pressure drop increases. When implementing measures to reduce the maximum wall temperature in the cooling channels, the best option would be when an acceptable wall temperature in all the channels is achieved with a minimum core pressure drop.
The influence of the coolant mass flow shaping in a gascooled reactor on the main gas/temperature parameters of the cooling channel walls was studied in (
The paper focuses on the effect of changes in the maximum wall temperatures from the core coolant mass flow shaping using heat exchange intensifiers. Various shaping conditions were considered with equal (1) heating or increments of enthalpies in the cooling channels, (2) coolant mass flows in the channels, and (3) maximum wall temperatures in the cooling channels.
As in (
The equations for calculating the coolant mass flow distribution by groups of identical cooling channels were obtained in (
The relation between the total coolant pressure loss ΔP (a component of the pressure difference resulting from a temperature change can be neglected due to its insignificance), when passing from the core inlet to its outlet, and the total coolant mass flow G_{0} looks like this:
where n_{i} is the number of identical channels in the igroup, 1 ≤ i ≤ m; ξ_{i} and ξ_{l.}_{i} are the friction coefficients and local resistance coefficients reduced to the average coolant thermal parameters, respectively; l is the core height, m; d_{i} are the diameters of round channels, m; ρ_{i} is the average coolant density, kg/m^{3}.
The k_{p} coefficients for an arbitrary pgroup of channels are defined by the dependence
and the friction coefficients for technically smooth round channels are determined by the Blasius dependence
ξ_{p} = 0.316 / Re_{p}^{0.25}. (3)
The coolant mass flow G_{p} in a single channel of an arbitrary group is calculated by the equation
With a known flow G_{p} under the conditions of constant specific isobaric heat capacity of helium c_{p} = const, it is easy to obtain a ratio for calculating the coolant temperature at the outlet (the «out» superscript) of a pgroup channel:
where ν_{p} is the heat load deviation of the pchannel group from the average load.
The thermophysical properties of the coolant gas (helium) necessary for carrying out calculations – the average density ρ_{av}_{p} and dynamic viscosity coefficient μ_{av}_{p} – are found by the ideal gas low equation and Sutherland equation, respectively:
Ρ_{av}_{p} = [ρ_{0} + (P_{0} – ΔP) / (R_{He}·T_{p})] / 2, (6)
Μ_{av}_{p} = [µ_{0} + µ_{0}^{*}(T_{p} / T_{0}^{*})^{3/2} (T_{0}^{*} + S) / (T_{p} + S)] / 2, (7)
where P_{0} is the coolant pressure at the core inlet, Pa; ρ_{0} is the coolant density at the core inlet; R_{He} is the individual gas constant for helium, J/kg∙K; T_{p} is the outlet temperature of an arbitrary pchannel, K; µ_{0}^{*} is the control viscosity at temperature Τ_{0}^{*} (273 K), Pa∙s; S is Sutherland constant or effective gas temperature (reference value), K; µ_{0} is the viscosity at the core inlet temperature and pressure, Pa∙s.
The accepted shaping condition means specifying the relationship of at least two coolant parameters. For shaping under the conditions of the same mass flows in the channels and the same coolant heating in them, the functions of the relationship between the coolant flow and its heating in any channel are trivial. For shaping under the condition of the same maximum wall temperatures in the cooling channels, the following equation for the relationship between the channel coolant flow and its maximum wall temperature Θ_{wall}^{max} was obtained in (
Relation (8) is obtained using the dependence for the heat transfer coefficient proposed by B.S. Petukhov (
It is obvious that, with the same channel coolant flow and the heat load maintained, the maximum channel wall temperature depends on whether the channel is smooth or has an extended area with specific features of the heat exchange surface (i.e., heat exchange intensifier). The dependence for a gaseous coolant, reflecting the effect of a heat exchange intensifier installed into a smooth channel on changes in the maximum wall temperature, was obtained and verified in (
Θ^{*}_{wall}^{max} = Θ^{*}_{wall 0}^{max}·(1 + γ·δT_{h.c} / Θ^{*}_{wall 0}^{max}) / (1 + γ), (10)
where
Θ^{*}_{wall}^{max} = Θ_{wall}^{max} – T^{in}_{int}, Θ^{*}_{wall 0}^{max} = Θ_{wall 0}^{max} – T^{in}_{int}, K; T^{in}_{int}
is the coolant temperature at the inlet of the area of the installed extended heat exchange intensifier, K; δT_{h.c} = T_{h.c} – T^{in}_{int}; T_{h.c} is the coolant temperature in cross section with the maximum channel wall temperature, K; the “0” subscript refers to the option of a technically smooth channel.
In Dependence (10), γ reflects the intensifier’s effect:
γ = H_{0}/l_{int} ·(ΔP/ΔP_{0} – 1), (11)
where H_{0} is the core height equal to the cooling channel length, m; l_{int} is the heat exchange intensifier length, m; ΔP_{0} is the pressure difference in a technically smooth channel, Pa; ΔP is the pressure difference in a channel with a heat transfer intensifier at the same channel coolant flow, Pa.
The coolant flows are usually redistributed through the cooling channels by individual local resistances installed at the inlet to the core channels. This shaping arrangement was considered in (
The use of heat exchange intensifiers with uniquely shaped coolant mass flows in the core at given local resistances ξ_{м.}_{i} for each identical igroup channel implies implementing the following obvious relations:
ξ_{int,}_{i} + ξ^{*}_{м.}_{i} = ξ_{l.}_{i}, ξ_{int,}_{i} ≤ ξ_{l.}_{i}, (12)
where ξ_{int,}_{i} is the aerodynamic drag coefficient of a single igroup channel if a heat exchange intensifier is installed in it; ξ^{*}_{l.}_{i} are the modified local resistances for a single igroup channel with a heat exchange intensifier.
The uniquely shaped mass flows are determined by the condition
or by the condition ΔT_{p} = ΔT_{av} = idem, when
These flows do not depend on whether there are heat exchange intensifiers in the cooling channels.
For the mass flow shaping options, it is possible to calculate a decrease in the maximum wall temperatures in different cooling channel groups using Equation (10) if the aerodynamic characteristics of heat exchange intensifiers used for shaping are known. These characteristics can be represented as the γ parameter from Equation (11).
The GTMHR core consists of fuel assemblies (FA) made of grade H451graphite (
In contrast to the shaping conditions G_{p} = idem and ΔT_{p} = idem, the local coolant mass flow distribution under the condition that Θ_{wall}_{p}^{max} = idem depends on whether or not there are heat exchange intensifiers in the channels. In this case, the basic calculational equation (8) for this condition of shaping the coolant mass flows will be
C1_{i} G_{0}/(ξ_{int,}_{i} G_{i}) = a^{1/2}·(a – C2_{i} G_{0}/G_{i})^{1/2}, (13)
where
ξ_{int,}_{i} = ξ_{i} ·(1 + l_{int,}_{i}·γ/H_{0}). (14)
Note that it does not specify the features of the heat exchange intensifier, in particular, its design. There are numerous options. We assume that the integral characteristics of the intensifier used, from which the γ parameter can be calculated, are known. We also take into account the fact that the range of γ values is limited:
0 < γ < γ^{max}. (15)
The results presented in (
The calculations of the GTMHR core took into account the following design features.
The cylindrical ringshaped core consists of perforated graphite hexagonal blocks (fuel assemblies) with cooling and fuel channels. The core thickness corresponds to the size of three rows of fuel assemblies; therefore, two peripheral (outer and inner) and central areas of the core are distinguished, each of which consists of one row of fuel assemblies located circumferentially and having their own specific heat load. The cooling channels are represented by two groups: (1) with an inner diameter of 15.88 mm and (2) with a diameter of 12.7 mm. The length of each channel is equal to the core height H_{0} = 7.93 m. The core thermal power is 600 MW. The total helium mass flow is G_{0} = 320 kg/s, its temperature at the core inlet T_{0} = 491 °C (
With the above core specification, there will be four identical channel groups in the reactor: two groups of channels in the central area with diameters of 15.88 and 12.7 mm, respectively, and two groups of analogous channels in the peripheral area.
The analysis of the influence of heat exchange intensifiers involved in shaping the coolant mass flows on changes in the maximum channel wall temperature is made by comparison with the results obtained, when the shaping conditions were implemented by installing local resistances at the inlet of channels, and presented in (
Table
Maximum cooling channel wall temperatures depending on the coolant mass flow distribution.
Core area  Channel diameter, mm  Maximum channel wall temperature, Θ_{wall}_{i} ^{max}, °C  

Without shaping  ΔT_{i} = idem  G_{i} = idem  Θ_{ст.}_{i} ^{max} = idem  
Peripheral  15.88  857.108  877.037  864.811  877.671 
12.7  896.082  865.562  717.155  877.671  
Central  15.88  910.185  878.504  915.623  877.671 
12.7  955.713  867.823  747.864  877.671 
The arrangement of shaping the coolant mass flows for any shaping condition leads to an increased core pressure drop. Table
The ΔP/ΔP_{0} value for the mass flow shaping options.
Shaping condition  Without shaping  ΔT_{i} = idem  G_{i} = idem  Θ_{walll}_{i} ^{max} = idem 

ΔP/ΔP_{0} value  1  1.4368  2.6873  1.3562 
Figures
Figure
Dependence Θ_{wall}^{max} = f (γ) for identical channels of different groups with ΔT_{i} = idem: 1 – channels with ϕ = 15.88 mm, of the peripheral core area; 2 – channels with ϕ = 12.7 mm, of the peripheral core area; 3 – channels with ϕ = 15.88 mm, of the central core area; 4 – the maximum temperature of the channel walls with ϕ = 12.7 mm, of the central core area.
Figure
Dependence Θ_{wall}^{max} = f (γ) for identical channels of different groups with G_{i} = idem: 1 channels with ϕ = 15.88 mm, of the peripheral core area; 2 –channels with ϕ = 12.7 mm, of the peripheral core area; 3 –channels with ϕ = 15.88 mm, of the central core area; 4 – the maximum temperature of the channel walls with ϕ = 12.7 mm, of the central core area.
Figure
Dependence Θ_{wall}^{max} = f (γ) for the core channel with the maximum Θ_{wall}_{i}^{max} : 1 – the maximum wall temperature of identical channels with ϕ = 15.88 mm, of the central core area, when shaped under the condition that ΔT_{i} = idem; 2 – the maximum wall temperature for any channel when shaped under the condition that Θ_{wall}_{i}^{max} = idem; 3, 4 – efficient shaping condition boundaries.
Curves 1 and 2 in Fig.
Note that the coolant mass flow shaping option under the condition that G_{i}_{°}=°idem is not shown in Figs
In order to verify the adequacy of the method for analyzing changes in the temperature regime of the reactor core with the combined use of local resistances and heat exchange intensifiers to ensure shaping the coolant mass flow through the core cooling channels, the calculation results were compared with the CFD simulation results (Fig.
Comparison of Q_{wall}_{i}^{maxс}, values obtained by direct calculation of the coolant mass flow distribution (Р) and the CFDsimulation results (М): 1 – М, channels with ϕ = 15.88 mm, the central core area, shaping at ΔT_{i} = idem; 2 – Р, channels with ϕ = 15.88 mm, the central core area, shaping at ΔT_{i} = idem; 3 – М, channels with ϕ = 15.88 mm, the peripheral core area, shaping at ΔT_{i} = idem; 4 – Р, channels with ϕ = 15.88 mm, the peripheral core area, shaping at ΔT_{i} = idem; 5 – М, channels with ϕ = 12.7 mm, the peripheral core area, shaping at ΔT_{i} = idem; 6 – Р, channels with ϕ = 12.7 mm, the peripheral core area, shaping at ΔT_{i} = idem; 7 – М, channels with ϕ = 15.88 mm, the central core area, shaping at Q_{wall}_{i}^{max} = idem; 8 – Р, channels with ϕ = 15.88 mm, the central core area, shaping at Q_{wall}_{i}^{max} = idem; 9 – М, channels with ϕ = 15.88 mm, the peripheral core area, shaping at Q_{wall}_{i}^{max} = idem; 10 – Р, channels with ϕ = 15.88 mm. the peripheral core area, shaping at Q_{wall}_{i}^{max} = idem; 11 – М, channels with ϕ = 12.7 mm, the peripheral core area, shaping at Q_{wall}_{i}^{max} = idem; 12 – Р, channels with ϕ = 12.7 mm, the peripheral core area, shaping at Q_{wall}_{i}^{max} = idem.
Simulations were made for single cooling channels of all the groups with given (calculated) coolant flow/heat load values. The intensifier used corresponded to the design presented in (
The paper has demonstrated the capabilities of the method for calculating temperature changes in the coolant and cooling channel walls during the channelbychannel coolant mass flow shaping using heat exchange intensifiers in the reactor core. For the investigated GTMHR core, there are two options that can reduce the maximum cooling channel wall temperature. The first option, when there is a strict limitation on the core pressure drop, is to shape the coolant mass flows under the condition that Θ_{wall}_{i}^{max} = idem. In this case, the use of heat exchange intensifiers slightly changes the maximum channel wall temperature and is impractical at γ ≥ 2.247. The second option, when there are no principal obstacles to increasing the core pressure drop, is shaping under the condition that ΔT_{i} = idem with the combined use of local resistances and heat exchange intensifiers. Moreover, the second option is definitely preferable for the integral characteristic of heat exchange intensifiers (γ°>°2.247).
The calculation procedure was verified by direct comparison of the results calculated by the proposed algorithm with the results of a detailed gas flow simulation in heated channels with a specific heat exchange intensifier design.