Thermal Analysis for an Ultra High Temperature Gas-Cooled Reactor with Pebble Type Fuels
Motoo Fumizawa, Naoya Uchiyama, Takahiro Nakayama
Department of Mechanical Engineering, Shonan Institute of Technology, Fujisawa, Kanagawa, Japan
To cite this article:
Motoo Fumizawa, Naoya Uchiyama, Takahiro Nakayama. Thermal Analysis for an Ultra High Temperature Gas-Cooled Reactor with Pebble Type Fuels. International Journal of Energy and Power Engineering. Vol. 4, No. 4, 2015, pp. 189-196. doi: 10.11648/j.ijepe.20150404.11
Abstract:This study presents a predictive thermal-hydraulic analysis with packed spheres in a nuclear gas-cooled reactor core. The predictive analysis considering the effects of high power density and the some porosity value were applied as a design condition for an Ultra High Temperature Reactor (UHTR). The thermal-hydraulic computer code was developed and identified as PEBTEMP. The highest outlet coolant temperature of 1316 oC was achieved in the case of an UHTREX at LASL, which was a small scale UHTR using hollow-rod as a fuel element. In the present study, the fuel was changed to a pebble type, a porous media. Several calculation based on HTGR-GT300 through GT600 were 4.8 w/cm3through 9.6 w/cm3, respectively. As a result, the relation between the fuel temperature and the power density was obtained under the different system pressure and coolant outlet temperature. Finally, available design conditions are selected.
Very high temperature gas-cooled reactor project is energetically developing the design study to establish 1,000 oC as a coolant outlet temperature and to realize the hydrogen production [1-2], where GIF is the Generation IV International Forum. For a long time, a fundamental design study has been carried out in the field of the high temperature gas-cooled reactor i.e. HTGR [3-8], which showed that a coolant outlet temperature was around 900 oC. The interest of HTGR is increasing in many countries as a promising energy future option. There are currently two research reactors of THGR type that are being operated in Japan and China. The inherent safety of HTGR is due to the large heat capacity and negative temperature reactivity coefficient. The high temperature heat supply can achieve more effective utilization of nuclear energy. For example, high temperature heat supply can provide for hydrogen production, which is expected as an alternative energy source for oil. Also, outstanding thermal efficiency will be achieved at about 900 oC with a Brayton-cycle gas turbine plant.
However, the highest outlet coolant temperature of 1316 oC had been achieved by UHTREX as shown in Figure 1, in Los Alamos Scientific Laboratory at the end of 1960’s [3-4]. It was a small scale Ultra High Temperature Nuclear Reactor (UHTR). The coolant outlet temperature would be higher than 1000oC in the UHTR. The UHTREX adopted the hollow rod type fuel; the highest fuel temperature was 1,582 oC, which indicated that the value was over the current design limit. According to the handy calculation, it was derived that the pebble type fuel was superior to the hollow type in the field of fuel surface heat transfer condition .
In the present study, the fuels have changed to the pebble type so called the porous media. In order to compare the present pebble bed reactor and UHTREX, a calculation based on HTGR-GT300 was carried out in the similar conditions with UHTREX i.e. the inlet coolant temperature of 871oC, system pressure of 3.45 MPa and power density of 1.3 w/cm3. The main advantage of the pebble bed reactor (PBR) is that high outlet coolant temperature can be achieved due to its large cooling surface and high heat transfer coefficient that have the possibility to get high thermal efficiency. Besides, the fuel loading and discharging procedures are simplified; the PBR system makes it possible that the frequent load and discharge are easier than the other reactor system loaded block type fuel without reactor shutdown. This report presents thermal-hydraulic calculated results for a concept design PBR system of 300MWth of the modular HTGR-GT300 with the pebble types of fuel element as shown in Figure 2. A calculation for comparison with UHTREX have been carried out and presented as well.
2. Reactor Description
2.1. Concept of Modular HTGR-GT300, GT600 and GT600
A concept of pebble-bed type HTGR are shown in Figures 2 and 3 with the main nuclear and thermal-hydraulic specifications presented in Table 1. In the case that the thermal power is 300MW (GT-300), the average power density changes to 4.8 MW/m3. The coolant gas enters from the outer shell of the primary coolant coaxial tube to the pressure vessel at temperature of 550oC and pressure of 6 MPa, follows the peripheral region of side reflectors up to the top and goes downward through the reactor active core. The outlet coolant goes out through the inner shell of primary coolant tube at temperature of 900oC. The cylindrical core is formed by the blocks of graphite reflector with the height of 9.4m and the diameter of 2.91m. There exist holes in the reflector that some of them used for control rod channels and the others used for boron ball insertion in case of an accident. In the case that the thermal powers are 450MW (GT450) and 600MW (GT600), the average power densities change to 7.2 MW/m3 and 9.6 MW/m3, respectively.
2.2. Fuel Element
The two types of pebble fuel elements, consisting of fuel and moderator, are shown in Figure 4. One is a solid type where radius of inner graphite rco=0, and the other is a shell type fuel element. The fuel compacts are a mixture of coated particles .
3. Thermlhydraulic Analysis
3.1. PEPTEMP Code
A one-dimensional thermal-hydraulic computer code was developed that was named PEPTEMP  as shown in Figure 5. The code solves for the temperature of fuel element, coolant gas and core pressure drop using assumed power, power distribution, inlet and outlet temperature, the system pressure, fuel size and fuel type as input data.
The options for fuel type are of the pebble type; the multi holes block type and the pin-in-block type. The power distribution for cases of cosine and exponential is available., The users can calculate for the other distributions by preparing the input file.
The maximum fuel temperature will be calculated in PEPTEMP as follows:
where Tmax(z): fuel temperature at the center of fuel element i.e. the maximum fuel temperature; DTcl: gas temperature increment from inlet to height z; Tin: gas inlet temperature; DTfilm(z): temperature difference between fuel element surface and coolant gas at z; DTsl(z): temperature difference between fuel matrix outer surface and fuel element surface; DTcom(z): temperature difference between fuel matrix outer surface and fuel center; : power density; Af: fuel element surface area; z: axial distance from the top of the core; Cp: coolant heat capacity.
3.2. Temperature Difference in the Spherical Fuel Element
Figure 4 shows fuel configuration of the solid type and the shell type fuel element. In the solid type, DTcom is given as follows
In the case of the shell type fuel element, DTcom can be calculated by the following expression;
3.3. Film Temperature Difference
The film temperature differences are calculated as follows;
3.4. Heat Transfer Coefficient
Heat transfer coefficient h in Equation (4) is calculated using the following correlation :
where, r: coolant density; vs.: coolant velocity; Re: Reynolds number; Pr: Prandtl number; e: Porosity; d: fuel element diameter and m: viscosity of fluid.
|Thermal power (MW)||300 / 450 / 600|
|Inlet coolant temperature (oC)||550|
|Outlet coolant temperature (oC)||900 (900 – 1650 oC )|
|Coolant Pressure (MPa)||6.0 (1 – 15 MPa)|
|Total coolant flow rate (kg/s)||172.1 / 258.2 / 344.2|
|Core coolant flow rate (kg/s)||165.2 / 247.8 / 320.8|
|Core diameter (m)||2.91|
|Core height (m)||9.4|
|Core fuel porosity (－)||0.39 (0.26 – 0.50)|
|Average power density (MW/m3)||4.8 / 7.2 / 9.6|
|Fuel type (for standard case)||6 cm diameter pebble|
3.5. Pressure Drop
Pressure drop through the core expresses by the following correlation :
where, H: core height; R: core radius and DPa: acceleration pressure drop.
3.6. Effective Flow Rate Consideration
As many blocks of graphite form the reflector, there exist gaps by which the coolant flow may pass through . Actually, only one portion of coolant passes through the reactor core from the top to the bottom. This portion is called effective flow rate and can be calculated iteratively in the code. The empirical equation used in this code is as follows :
where, Weff: effective coolant flow rate that has dimensionless value due to the normalization by the total coolant flow rate.
DP: pressure drop through the core
4. Calculation Results
4.1. Handy Calculation Results for Small Scale HTGR
Before the main calculation, we have done the prediction study of the comparison of key factors of heat transfer in the small scale HTGR with three types of different fuel elements. They are the hollow-rod , the multi-hole [1,8] and the pebble-bed . The small reactor thermal data are as follows; thermal power of 50MW, power density of 2.5 MW/m3 and inlet/ outlet coolant temperature of 395 oC/ 850 oC, respectively. Figure 6 shows the results of heat transfer area in the core and heat transfer coefficient on the fuel surface. Heat transfer area of the pebble-bed is 5 times larger than that of the hollow-rod. Heat transfer coefficient of the pebble-bed is twice larger than that of the hollow-rod. Therefore heat transfer performance of pebble-bed is superior to other types of fuel elements.
4.2. Temperature Calculation for HTGR-GT300 to GT600
Table 2 shows the 20 analysis cases and fuel maximum temperature in the 300MW of thermal power i.e.GT300. The system pressure ranges from 1 MPa through 15 MPa. The system pressure does not have any effect onthe fuel maximum temperature. Thus we focus our intension to 6 MPa of system pressure . Figure 7, 8 and 9 show the dependence of maximum fuel temperature on outlet coolant temperature for GT300, GT450 and GT-600 with different porosity and Weff=1. The maximum fuel temperature for GT600 is 168 oC higher than that for GT300 where the outlet coolant temperature is 900 oC and the porosity is 0.39.The maximum fuel temperature for GT-600 is 163 oC higher than that for GT-300, where the outlet coolant temperature is 1150 oC and the porosity is 0.39. The high porosity leads to low fuel maximum temperature.
4.3. Pressure Drop Calculation for HTGR-GT300 to GT600
Table 3 shows the 20 analysis cases and pressure drop (DP) in the core of 300MW of thermal power. The system pressure ranges from 1 MPa through 15 MPa. The high system pressure leads to low-pressure drop in the core. In the case of 6 MPa of system pressure, the DP changes from 40.2 kPa to 16.7 kPa, where the Tout increases from 900oC to 1150oC. The DP changes from 16.7 kPa to 6.3 kPa, where the porosity increases from 0.39 to 0.50 with 1150oC of Tout. The high porosity leads to low-pressure drop. In the case of 15 MPa of system pressure, the DP changes from 16.7 kPa to 6.7 kPa, where the Tout increases from 900oC to 1150oC. The DP changes from 6.7 kPa to 2.6 kPa, where the porosity increases from 0.39 to 0.50 with 1150oC of Tout.
Table 4 shows the 20 analysis cases and pressure drop (DP) in the core of 450MW of thermal power. The system pressure ranges from 1 MPa through 15 MPa. The high system pressure leads to low-pressure drop in the core. In the case of 6 MPa of system pressure, the DP changes from 86.2 kPa to 35.3 kPa, where the Tout increases from 900oC to 1150oC. The DP changes from 35.3 kPa to 13.7 kPa, where the porosity increases from 0.39 to 0.50 with 1150oC of Tout. The high porosity leads to low-pressure drop. In the case of 15 MPa of system pressure, the DP changes from 35.3 kPa to 14.7 kPa, where the Tout increases from 900oC to 1150oC. The DP changes from 14.7 kPa to 5.5 kPa, where the porosity increases from 0.39 to 0.50 with 1150oC of Tout.
Table 5 shows the 20 analysis cases and pressure drop (DP) in the core of 600MW of thermal power. The system pressure ranges from 1 MPa through 15 MPa. The high system pressure leads to low-pressure drop in the core. In the case of 6 MPa of system pressure, the DP changes from 147 kPa to 60.8 kPa, where the Tout increases from 900oC to 1150oC. The DP changes from 60.8 kPa to 23.5 kPa, where the porosity increases from 0.39 to 0.50 with 1150oC of Tout. The high porosity leads to low-pressure drop. In the case of 15 MPa of system pressure, the DP changes from 59.8 kPa to 24.5 kPa, where the Tout increases from 900oC to 1150oC. The DP changes from 124.5 kPa to 9.4 kPa, where the porosity increases from 0.39 to 0.50 with 1150oC of Tout.
Design Limit of maximum fuel temperature(℃) and pressure drop (kPa) in 300MW thermal power
Design Limit of maximum fuel temperature(℃) and pressure drop (kPa) in 600MW thermal power
4.4. Consideration of Available Reactor Core Design
The traditional design limits in Japan suggested that the maximum fuel temperature should be lower than 1300 oC. From the engineering judgments, the effective coolant flow rate should be higher than 70 %. Thus the design limit of the pressure drop in the core is 23.3 kPa, according to the eq. (11) as shown in Figure 10. Table 6 and 7 show the available analysis cases of GT300 and GT600. The available analysis cases in GT300 are case A05, A06, A09, A10, A13, A14, A17, and A18. It means that 1150oC of the outlet coolant temperature is available. On the contrary, the available analysis case in GT600 is the case A17. It means that 900oC of the outlet coolant temperature is available.
The followings can be concluded:
1. High porosity leads to low fuel maximum temperature.
2. High system pressure leads to low-pressure drop in the core.
3. High porosity leads to low-pressure drop.
4. The available analysis cases in 300MW of thermal power are 8 cases, which indicates that the outlet coolant temperature is lower than 1150oC.
5. On the contrary, the available analysis case in 600MW of thermal power is only 1 case, which indicate that the outlet coolant temperature is up to 900oC.
Af: fuel element surface area; (m2)
Cp: coolant heat capacity; (J/kgK)
H: core height; (m)
h : heat transfer coefficient; (W/m2K)
q’’’: power density; (W/m3)
R: core radius; (m)
Re: Reynolds number
Tf(z): fuel temperature at the center of fuel element, i.e., the maximum fuel temperature; (oC)
Tin: gas inlet temperature; (oC)
Tout: gas outlet temperature; (oC)
Weff: effective coolant flow rate, dimensionless value due to the normalization
z: axial distance from the top of the core; (m)
DP: pressure drop through the core (kPa)
DPa: acceleration pressure drop; ((kPa)
DTcl: gas temperature increment from inlet to height z; (oC)
DTcom(z): temperature difference between fuel matrix outer surface and fuel center; (oC)
DTfilm(z): temperature difference between fuel element surface and coolant gas at z; (oC)
DTsl(z): temperature difference between fuel matrix outer surface and fuel element surface; (oC)