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Transient conjugated heat transfer within IFMIF high flux test module
Nuclear Engineering and Design 249 (2012) 172–179
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Transient conjugated heat transfer within IFMIF high flux test module Y. Chen ∗ , F. Arbeiter, V. Heinzel, G. Schlindwein Institute for Neutron Physics and Reactor Technology, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
a r t i c l e
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Article history: Received 22 March 2011 Received in revised form 27 July 2011 Accepted 27 July 2011
a b s t r a c t Transient numerical simulations were carried out for the helium cooled high flux test module (HFTM) during start-up, shut-down, loss-of-coolant and temporary beam-off periods on a quarter-rig model. The transient responses of the specimen temperature with the changing operation conditions are the main outcome of the simulations. The results serve as reference for the design of HFTM and remote handling strategy. The commercial numerical codes CFX 12.0 and Star-CD 4.10 were used. Several turbulence models have been tested against annular channel experiments (ITHEX), including the k–ε, SST and Baseline Reynolds stress models of CFX and high and low Reynolds number k–ε models and k–ω SST model of Star-CD. The heat transfer characteristics for various coolant flows were discussed. © 2012 Published by Elsevier B.V.
1. Introduction The International Fusion Materials Irradiation Facility (IFMIF) (Martone, 1996; IFMIF International Team, 2003) is designated to generate a materials irradiation database for the future fusion reactors. The high flux test module (HFTM) is located next to the lithium target inside the test cell where a damage rate of 20–50 dpa/fpy (displacement per atom per full power year) will be achieved in a volume of about 0.5 l. Fig. 1 shows the current design of the HFTM and inside details. The HFTM container is connected to the mechanical fix point by a rigid adapter. The adapter also serves as a return duct of the cooling gas and contains the measurement and control cables. The eight independent helium cooling feed pipes and the rigid adapter are mounted on an interface head, and connected to the helium loop outside of the test module. A total of 24 irradiation rigs are installed within the HFTM container, which is divided by stiffening plates into eight compartments. Vertically, the compartment can be divided into coolant inlet section, bottom reflector (nozzle), center section with irradiation capsules, top reflector (diffuser) and outlet section. A single compartment houses three identical rigs with an outer cross section of 50 mm × 17 mm and a length of 350 mm. About 80 miniature specimens can be housed inside each capsule, which are located in the center section of the rigs. The specimen stack has a height of 81.5 mm and a cross section of 40 mm × 9.3 mm. To reduce the thermal resistance, liquid sodium–potassium eutectic alloy (NaK78) is filled up the space within the capsule. Three sections of electric heaters are wound around the capsules with a total heating length of 120 mm. The capsule-heater assembly is inserted inside the rig
∗ Corresponding author. Tel.: +49 721 60823942; fax: +49 721 60823718. E-mail addresses: [email protected], [email protected] (Y. Chen). 0029-5493/$ – see front matter © 2012 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.nucengdes.2011.07.051
leaving a gap in-between which is filled with stagnant helium acting as thermal insulation. To keep the insulation gap at a defined size, spacers are machined out on the capsule outer surface. On each end (below and above) of the specimen stack, there is an insulation cap also filled with stagnant helium. The helium cooling channels locate between adjacent rigs or compartment wall. The power released from nuclear reactions and the electric heaters is removed by helium flows at a low pressure (0.3 MPa at the inlet) and low temperature (323 K at the inlet). Because the temperature variation can have strong effects on the development of the radiation-induced defect structure and hence on the properties, the temperatures of the test specimens should be kept at prescribed levels (between 250 and 650 ◦ C) with acceptable temperature spreads (up to ±15 ◦ C). The cooling channels of the HFTM are complicated. The flow inlet possesses a big hydraulic diameter which converges to several parallel narrow rectangular channels at the middle section, thereafter the channels expand to a common large outlet. Thus a rather high flow velocity (up to 500 m/s) is expected inside the middle narrow channels, where the fluid is locally heated with high wall heat flux (up to 0.2 MW/m2 ). At the entrance section of the narrow channels, the flow is not fully developed both thermally and hydraulically. Due to these complex features, extensive tests of the CFD codes with various turbulence models are needed in order to obtain a reliable simulation result. A number of thermo-hydraulic simulations have been carried out so far with the commercial CFD package Star-CD (Gordeev et al., 2005; Chen et al., 2010). These simulations are part of the HFTM design process and were also intended to find out suitable numerical tools. For the purpose of CFD code verification, the ITHEX (IFMIF thermal–hydraulic experiment) experimental facility was constructed (Arbeiter, 2007). This paper concerns the thermo-hydraulic simulations on transient heat transfer processes within the HFTM during startup, shut-down, loss-of-coolant and temporary beam-off periods.
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Fig. 1. HFTM (left), container (middle) and rigs (right).
During these periods, the electrical heating power and/or the coolant flow rate need to be adjusted, in order to control the specimen temperatures at required levels within given periods of time. The transient responses of the specimen temperature with the changing operation conditions are the main outcome of the simulations. These results serve as reference for the design of HFTM and remote handling strategy. Relative few literatures concern the transient compressible flow with conjugated heat transfer (Zhou et al., 2007; Jang and Chiu, 2009). The reports on similar transient experiments are difficult to find. Thus the ITHEX annular channel experiments were taken as verification cases for both steady-state and transient simulations. Simulations were carried out with commercial CFD packages Ansys-CFX 12.0 (Ansys Inc., 2009) and Star-CD 4.10 (CD-adapco, 2009). 2. CFD tools assessments and validations 2.1. Turbulence models Both Ansys-CFX 12.0 and Star-CD 4.10 solve the Reynoldsaveraged Navier–Stokes equations on unstructured meshes using finite volume methods. Several built-in turbulence models were used in the simulations. The k–ε and k–ω two-equation models use the gradient diffusion hypothesis to relate the Reynolds stresses to the mean velocity gradients and the turbulent viscosity. The turbulent viscosity is modeled as the product of a turbulent velocity and turbulent length scale. The shear-stress-transport (SST) model combines the advantages of the k–ε and k–ω models with a blending function. The k–ω model is activated in the near-wall region and the k–ε model is used in the remaining region. The Baseline Reynolds stress (BSL-RS) model belongs to the second-order closure in which transport equations for the individual Reynolds stresses are solved. Likewise to the SST model there is a blending between the Omega Reynolds stress model and a transformed epsilon-based model. The V2F approach was designed to handle wall effects in turbulent boundary layers and to accommodate non-local effects. In this model, three transport equations for turbulence quantities, k, ε and v2 are solved. In addition, an elliptic equation for f22 , the redistribution term in the equation, is needed to account for near-wall and non-local effects. In CFX, the k–ε model was applied with scalable wall function, which uses the friction velocity calculated from the logarithmic law-of-the-wall and an alternative velocity scale in determination of the wall shear stress. If the non-dimensional wall distance y+
value drops below 11.06 (which is intersection between the logarithmic and the linear near wall velocity profile), the application of the standard wall function is no longer valid. The scalable wall function basically assumes that the wall node is on the outer edge of the viscous sub-layer and has a (solver) y+ of 11.06. This could introduce some degree of error. However, it allows finer mesh in near-wall region. The omega equation based models (e.g. SST, BSLRS) were applied with automatic wall treatment which allows for a smooth shift from a low-Reynolds number form to a wall function formulation based on the near wall mesh spacing. This shifting permits the use of coarser mesh next to the wall in contrast to a low-Reynolds formulation. In Star-CD, the k–ε and k–ω based models are categorized by “high Reynolds number” (high-Re) or “low Reynolds number” (lowRe) models. For the former, the high Reynolds number forms of (k, ε, ω) transport equations are used in conjunction with algebraic law-of-the-wall representations of flow, heat and mass transfer. For the low Reynolds number models, the transport equations are solved everywhere, including the near-wall regions. Compared to CFX, Star-CD has a stricter requirement on the near-wall mesh spacing. For the low Reynolds number models including V2F, the mesh spacing in the wall-normal direction should be chosen such that y+ of the near-wall cell centroid is about 1. For the high Reynolds number models, this y+ should be about 30–100. If the node is placed too close, the utility of the wall functions is lost; if it is placed too far away, then the profiles are more likely to depart from their assumed shape. Thus, the high Reynolds number models are inappropriate to be employed for the HFTM simulations, where the channel width (maximum 1 mm) corresponds to a y+ of about 60–200. In general, the V2F and low Reynolds number k–( models were recommended (Gordeev et al., 2005; Arbeiter, 2007). 2.2. ITHEX annular channel experiments The ITHEX facility provides a coolant gas circulating loop built from helium-tight components, into which different test-sections can be integrated (Arbeiter, 2007). The current facility has four side-channel compressors in a series (Fig. 2 left). Five plate heat exchangers are used to remove the heat generation. The mass flow is measured by a coriolis flow meter. The gas pressure and temperature were also measured. The axial cut-view of the annular test section is shown in the r.h.s. of Fig. 2. The annulus is formed by two concentric cylindrical bodies fabricated from stainless steel. The main annular channel section has a length of about 95 mm
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Fig. 2. ITHEX experimental facility (left) and annular test section (right).
with a gap size of 0.61 mm (Dh = 1.22 mm), formed by two wall surfaces with a radius of 15.39 mm and 16.00 mm, respectively. Electrical heater wires are embedded in both channel walls. The heated length for the inner cylinder wall is 51.8 mm and 48.4 mm for the outer wall. Between the channel surfaces and the heater layers, 18 thermocouples are mounted on 6 axial positions, each has 3 thermocouples evenly distributed along the circumference. Both steady-state and transient experiments were carried out with helium as working fluid. The experimental conditions for the case taken for CFD code validations are: inlet pressure 4 bar, inlet temperature 292.6 K, heat flux at inner-wall 245.2 kW/m2 , heat flux at outer-wall 248.5 kW/m2 , Reynolds number 9015.
Torii and Yang, 2000) does not occur under the current experimental conditions. The maximum non-dimensional heat flux q+ is about 0.0011 corresponding to a acceleration parameter Kv of about 4.9 × 10−7 which is smaller than the criteria for the laminarization 2–4 × 10−6 (refer McEligot and Jackson, 2004 for the definitions). In fact, the radial velocity profiles on various cross-sections of the channel are almost identical, showing a typical turbulence velocity profile. The correlations from McEligot (1986) and Colburn (1933) are also plotted in the figure for comparison. The two correlations are given by Nu = 0.021 Pr0.55 Re0.8
2.3. Comparison of simulations and ITHEX experiments Three dimensional simulations were performed with CFX and Star-CD. Fig. 3 shows the axial cut-views of model geometry. For the meshing, 42 nodes are placed inside the annular gap (radial direction, y) with the near-wall cell spacing of 2 m. The y+ at the axial middle of the channel is about 0.8. In the azimuthal direction, 4 cell layers are placed for a domain azimuthal angle of 2◦ . It has been tested that the increase of the azimuthal angle does not change the simulation results. Helium is assumed to be ideal gas with constant specific heat, while the thermal conductivity and dynamic viscosity vary with temperature. No attempt was made to optimize the mesh for individual turbulence model. Comparisons of simulations using various turbulence models with the measured inner cylinder wall temperatures are shown in Fig. 4a for the steady-state operation. Overall the Star-CD low-Re SST gives the best predictions. The CFX k–ε model slightly overpredicts the wall temperatures; while the CFX SST and BSL-RS models under-predict the wall temperature. Less good agreements are shown by the Star-CD low-Re k–ε and V2F models. The Star-CD high-Re k–ε model significantly under-predicts the wall temperatures. It should be noted that the mesh used here is not suitable for the Star-CD high Reynolds number models. The laminar model results in too high wall temperatures for this Reynolds number. Fig. 4b shows the local Nusselt number and the local Reynolds number along the flow direction calculated with CFX k–ε and SST models. In these calculations, the local bulk temperature is mass flux averaged at a given flow cross section. The lower Nusselt number at the begin and the end of the channel could be due to the inaccurate temperature samplings, since the temperature differences between the wall and the bulk are small outside the heating section. It is seen that the SST model predicts a higher Nusselt number than the k–ε model. The Nusselt number decreases along the channel. This is mainly attributed to the variation of thermophysical properties due to the heating which results in a decrease of the Reynolds number along the channel (Fig. 4b). The laminarization (or relaminarization, means a transition from turbulent to laminar flows, see Perkins et al., 1973; McEligot and Jackson, 2004;
Nu = 0.023 Pr1/3 Re0.8
−0.4 T w
Tb
+ 0.85
D h
x
(McEligot)
(Colburn)
The McEligot’s correlation accounts for effects of changing thermo-physical properties with the temperature and the entrance effects. The correlation from Colburn is quite similar to an earlier correlation developed by Dittus and Beulter in 1930. The McEligot’s correlation agrees quite well with the results using k–ε model (except at the both ends of the channel), while the Colburn’s correlation is more close to the results using SST model. Fig. 5 shows the comparison of the calculated and measured inner wall temperature at 6 thermocouple positions along the axial direction for transient flow. The simulations were carried out by using CFX k–ε model. Each measured data is the mean value of three thermocouple readings at the same axial position. The lower part of the figure shows the real-time experimental conditions which are the inputs to the simulations. Overall, the simulated temperature transients agree relatively well with the experiments. Particularly, the simulated time periods for heating-up and cooled-down agree quite well with the experiments; it is about 50 s in this case. Fig. 6 shows the comparison of the outlet fluid temperature and the pressure drop along the channel. The simulated pressure drop agrees very well with the measured data. During the heatingup period the simulated outlet temperature agrees well with the experiments, however, it is up to 10 ◦ C lower than the measurement thereafter. It should be mentioned that the simulated outlet temperature was taken at the outlet of annular gap (at x = 110 mm, see Fig. 3), however the measurement point was located inside the 40 mm diameter adiabatic outlet tube, at about 20 cm downstream from the annular channel outlet (refer Fig. 2 right). Along the mini-annular gap the flow is accelerated due to the friction and the heating, which results in a lower gas temperature at outlet of the annular gap (Chen et al., 2010) compared to the downstream gas temperature inside the adiabatic outlet tube. Therefore, the actual difference between the simulated and measured outlet temperature would be smaller for t > 320 s (Fig. 6).
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Fig. 3. Axial cut-view model geometry.
Fig. 4. Comparisons of turbulence models.
Fig. 5. Transient inner wall temperature and inlet and heating conditions.
Fig. 6. Transient pressure drop and outlet fluid temperature.
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Fig. 7. Geometry model and simulation domain.
3. HFTM transient operations Simulations were carried out on a quarter-rig without the top reflector, which is located just in front of beam center as shown in Fig. 7. The transient simulations with Star-CD were unsuccessful; the required time-step size is very small (∼1 s) due to the employed segregated solver which requires several weeks to finish one simulation. Therefore, CFX with k–ε turbulence model was used for the transient simulations. The insulation gap size is 1 mm on the long-side and 0.75 mm on the short-side. The cooling channel width is 1 mm on the long-side and 0.6 mm on the short-side. The thermal conductivity of solid materials varies with temperature. The viscosity and thermal conductivity of helium are also taken as a function of temperature. The inlet helium pressure is 3 bar with a temperature of 50 ◦ C. The mass flow rate is 1.418 g/s which corresponds to about 60% of the designed maximum helium supply capacity, i.e. 21 g/s per central compartment. The hydraulic diameter of the cooling channel is estimated to be 1.9 mm, thus the Reynolds number is about 4200 in this case. For the steady-state simulations, in order to maintain a mean specimen temperature of about 600 ◦ C, the total electrical power needed is about 300 W. The total nuclear heat generation in this quarter-rig is about 434 W. The nuclear heating data were taken from Simakov et al. (2002) by 3-D interpolation. 3.1. Grid sensitivity study The grid dependence study was done for the steady-state simulations on three mesh resolutions as summarized in Table 1. These three meshes are only different in the mesh density across the fluid channel. The mesh termed as “fine” has a near-wall cell spacing of 7.5 m, which results in a y+ less than 1.5 in the main channel. The near-wall cell spacings for the mesh “reference” and “coarse”
are 15 and 60 m, respectively. Fig. 8a and b compares the simulated temperature, relative pressure and velocity magnitude in the axial direction along the specimen center line (i.e. coordinate axis x shown in Fig. 7) and the long-side channel center line. The zero point (x = 0) is the beginning of the heater section. These parameters reveal the effects of non-uniform channel cross-section area and non-uniform heating. Overall, the results from three meshes show rather small deviations. Compared to the reference mesh, the maximum deviation of temperature is about 5 ◦ C for the coarse mesh. The deviations in the relative pressure and velocity amplitude are less than ±6%. In the following simulations coarse mesh is used. 3.2. HFTM transient results 3.2.1. Start-up It is assumed here that during the start-up, the electrical heaters, beam and helium coolant flow are switched on simultaneously. The initial temperature is 20 ◦ C. Fig. 9 shows the temperatures on several sampling points. The temperatures inside the insulation gaps (e.g. specimen, thermocouples) increase much faster than those outside the insulations gaps (e.g. rig, compartment walls, bottom reflector). Close to the electrical heaters, the temperature in the specimen corners is higher than that in the center during heatingup, while it is lower when the steady-state sets in. The center thermocouple can represent the specimen center temperature well. However, the temperatures in the specimen corners are always different from the thermocouple readings, since the thermocouples are located near the center line of the specimen stack. It takes about 300 s (5 min) to reach the steady-state. 3.2.2. Beam interruption Assuming that during the steady-state operation, the beam is interrupted for 300 s, thus the nuclear heat intensity reduces to
Table 1 Summary of three mesh resolutions. Mesh
Near wall cell width (mm)
Increase ratio
Max. cell width long/short-side (mm)
y+ main channel
Node no. across channel
Coarse Reference Fine
0.0600 0.0150 0.0075
1.2 1.2 1.2
0.0588/0.0353 0.047/0.023 0.0407/0.0196
3–12 0.8–3 0.5–1.5
18 28 36
Total cell no. 2,80,081 3,71,931 4,45,411
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Fig. 8. Comparison of simulation results with three mesh resolutions.
Fig. 11. Decay heat generation. Fig. 9. Start-up T-transients.
about 0.5% of the original value (decay heat). In this case, the temperature of each HFTM component decreases as shown in Fig. 10. Within this time period, the temperature of the specimen center decreases quickly for about 300 ◦ C, at a rate of about 1 ◦ C/s. With the beam being switched on again, within about 200–300 s, the system comes back to steady-state with all the temperatures return to the original values. 3.2.3. Decay heating without cooling and loss-of-coolant After the beam-off, there is still heat generated by radioactive atoms called decay heat. The calculated intensity of the decay heat
Fig. 10. T-transients during beam interruption.
generation for the HFTM is shown in Fig. 11 for Eurofer material (internal data from Dr. S. Simakov). The decay heat is about 0.5% of the beam-on level within the first hour after shut-down; it reduces to about 0.1% within 24 h. To simulate the effects of decay heat after beam being shut-down, we assume that the decay heat amounts 0.5% of the beam-on value. If there is no active and passive cooling and no additional electrical heating, the temperatures of the HFTM components will first come to a common value, viz. the hotter components being cooled and vice versa (Fig. 12). After about 2400 s (40 min) the specimen temperature reaches a minimum of about 310 ◦ C. Thereafter the HFTM temperature increases consistently to 1000 ◦ C at 18 h after beam-off. At this temperature the
Fig. 12. T-transients without cooling.
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Fig. 13. Cooled-down temperature transients and temperature fields with decay heat only.
pressure of the NaK filled capsule is about 5 bar, which is the saturation pressure of NaK. Any increase in capsule pressure above the design level is a severe safety risk, since there is small amount of tritium generated inside the capsules during irradiation. Therefore,
active cooling after beam-off is recommended based on this calculation. For the same reason, it would be even more dangerous when the coolant flow is interrupted during operation (loss-of-coolant). As also shown in Fig. 12, without cooling the specimen (capsule)
Fig. 14. Transient heat flux, heat transfer coefficient and Nusselt number and the local quantities along the channel at time point 1 s.
Y. Chen et al. / Nuclear Engineering and Design 249 (2012) 172–179
temperature will reach 1000 ◦ C within 90 s with both nuclear and electrical heating, and within 150 s with nuclear heating alone. 3.2.4. Decay heating with active cooling Besides the safety reason mentioned above, active cooling is also required in order to prevent the annealing of irradiation damage on the test specimens. According to this requirement, after the beamoff, the temperature of the specimens needs to be brought down to below 200 ◦ C within 10 min. For a longer beam-off period, the specimens must be cooled down to about 50 ◦ C. Under the normal operation conditions helium will be used as coolant. Under the emergent shut-down of the facility or during the change of the test-rigs, argon will be filled inside the test-cell and will be also used as coolant for the HFTM. Fig. 13 shows the temperature transients after beam-off with helium and argon as coolants. For the helium cooling with full coolant flow rate (here it is 1.418 g/s), the specimen center temperature goes down to 200 ◦ C within 110 s. The cooled-down time increases to 130 s and 160 s for the half and quarter helium flow rate, respectively. However, for the argon cooling with full flow rate it takes 250 s to bring down the temperature to 50 ◦ C; it takes about 400 s for full helium flow, and more than 1000 s for the full argon flow. The temperature fields of the central plane are shown in the r.h.s. of Fig. 13 for the helium and argon cooling with full flow rate. Fig. 14a–c shows the transient wall heat flux, heat transfer coefficient and Nusselt number on two center points indicated by “sampling point long-side” and “sampling point short-side” on the top of the figure. The axial position of the points corresponds to the specimen axial center (x = 0.0577 m). These quantities along two sampling lines, i.e. “sampling line long-side” and “sampling line short-side” are shown in Fig. 14d and e for time point 1 s. For the transient heat transfer, the wall heat flux decreases as the wall temperature decreases. The heat transfer coefficient and the Nusselt number remain more or less constant through out the cooling period. The small increase of the Nusselt number at the end of this period is probably due to the inaccuracy of the temperature samplings. Because during this period the heat flux and temperature difference between the wall and fluid is very small. Along the axial direction (Fig. 14d and e), the local heat transfer is strongly influenced by the spacers and different heat intensities of the three heater sections. The “sampling line long-side” goes though four positions corresponding to the spacer positions where the heat flux is much higher than that nearby. The effects of three different heater sections can be seen in the heat flux curve along the “sampling line short-side”. Close to the simulated channel outlet (outside the electrical heating region, from x = 0.12–0.14 m), the local heat flux decreases quickly, even to a negative value indicating a reversed heat transfer from the fluid to the rig-wall. Overall, the heat flux is higher in the long-side channel than that in the short-side channel due to the higher coolant mass flow rate in the long-side channel. The heat transfer coefficient is higher in the short-side channel because of the higher flow velocity; however the Nusselt number is lower due to the smaller hydraulic diameter (1.11 mm for the short-side channel, 1.91 mm for the long-side channel). For helium flow, reducing the mass flux leads to a smaller local wall heat flux. Compared to helium, the cooling by argon has a much lower heat flux and heat transfer coefficient. This mainly attributed to the much lower thermal conductivity and specific heat capacity of argon; the both quantities are only about one tenth of helium. Because of the low heat capacity, the argon flow shows a rapid temperature rise due to heating (Fig. 13b); as a result the
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wall superheat is reduced. These explain the fact that the argon flow needs much longer time to cool down the HFTM than the helium flow as shown above. 4. Summaries and conclusions Transient numerical simulations were carried out on the HFTM of IFMIF on a quarter-rig model using CFX. The time for the startup is about 5 min provided that the heater, neutron beams and cooling are switched on simultaneously. The interruption of the beams will lead to a quick decrease of specimen temperature at a rate of about 1 ◦ C/s. After the shut-down of the beams, active cooling is still required due to the decay heating, in order to keep the test materials at a required temperature level. The loss-of-coolant during operation is dangerous in that the HFTM will be heated up very quickly to an unacceptable level. The shut-down of the beams and heaters or the resume of the cooling should be done within 1 min. The cooling with argon flow is ineffective because of the low thermal conductivity and heat capacity. Partial verifications of the numerical codes CFX and Star-CD employing several turbulence models have been done against ITHEX annular channel experiments. Overall, for a Reynolds number of about 9000, the low-Re k–ω SST of Star-CD and SST, Baseline Reynolds stress and k–ε models of CFX give relatively good predictions. The Star-CD high-Re k–ε model significantly over-predicts the heat transfer coefficient for the mesh used. For the transient simulations, the predictions of CFX k–ε model agree well with the experiments. Acknowledgment The financial support by BMBF (Bundesministerium für Bildung und Forschung) under the grant No. 03FUS0008 is acknowledged. References Ansys Inc., 2009. Ansys CFX-12. 0. Arbeiter, F., 2007. Experimental and numerical investigations on minichannel cooling gas thermal–hydraulics. In: Proc. of Int. Conf. on Nuclear Engr., Nagoya, Japan. CD-adapco, 2009. Star-CD 4. 10. Chen, Y., Arbeiter, F., Heinzel, V., Ihli, Th., Moeslang, A., Slobodchuk, V., Stratmanns, E., 2010. Design optimizations of IFMIF high flux test module towards uniform specimen temperature distribution. Fusion Eng. Des. 85, 1952–1956. Colburn, A.P., 1933. A method of correlating forced convection heat transfer data and a comparison with fluid friction. Trans. AIChE 29, 174. Gordeev, S., Heinzel, V., Slobodtchouk, V., 2005. Features of convective heat transfer in heated helium channel flow. Int. J. Heat Mass Transfer 48, 3363–3380. IFMIF International Team, 2003. IFMIF comprehensive design report. IAEA Report. Jang, J.-Y., Chiu, Y.-W., 2009. 3-D Transient conjugated heat transfer and fluid flow analysis for the cooling process of sintered bed. Appl. Therm. Eng. 29, 2895–2903. Martone, M. (Ed.), 1996. IFMIF international fusion materials irradiation facility, conceptual design activity. Final Report, IFMIF CDA TEAM, ENEA, Frascati, Report ENEART/ERG/FUS/96.11. McEligot, D.M., 1986. Convective heat transfer in internal gas flows with temperature-dependent properties. Adv. Transp. Process. IV, 113–300. McEligot, D.M., Jackson, J.D., 2004. “Deterioration” criteria for convective heat transfer in gas flow through non-circular ducts. Nucl. Eng. Des. 232, 327–333. Perkins, K.R., Schade, K.W., McEligot, D.M., 1973. Heated laminarizing gas flow in a square duct. Int. J. Heat Mass Transfer 16, 897–916. Simakov, S.P., Fischer, U., Heinzel, V., von Möllendorff, U., 2002. International Fusion Material Irradiation Facility (IFMIF): Neutron source term simulation and neutronics, analyses of the high flux test module. Report FZKA 6743. Torii, S., Yang, W.-J., 2000. Thermal-fluid transport phenomena in strongly heated channel flows. Int. J. Numer. Methods Heat Fluid Flow 10, 802–823. Zhou, J., Zhang, Y., Chen, J.K., 2007. Numerical simulation of compressible gas flow and heat transfer in a microchannel surrounded by solid media. Int. J. Heat Fluid Flow 28, 1484–1491.
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Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Transient conjugated heat transfer within IFMIF high flux test module Y. Chen ∗ , F. Arbeiter, V. Heinzel, G. Schlindwein Institute for Neutron Physics and Reactor Technology, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
a r t i c l e
i n f o
Article history: Received 22 March 2011 Received in revised form 27 July 2011 Accepted 27 July 2011
a b s t r a c t Transient numerical simulations were carried out for the helium cooled high flux test module (HFTM) during start-up, shut-down, loss-of-coolant and temporary beam-off periods on a quarter-rig model. The transient responses of the specimen temperature with the changing operation conditions are the main outcome of the simulations. The results serve as reference for the design of HFTM and remote handling strategy. The commercial numerical codes CFX 12.0 and Star-CD 4.10 were used. Several turbulence models have been tested against annular channel experiments (ITHEX), including the k–ε, SST and Baseline Reynolds stress models of CFX and high and low Reynolds number k–ε models and k–ω SST model of Star-CD. The heat transfer characteristics for various coolant flows were discussed. © 2012 Published by Elsevier B.V.
1. Introduction The International Fusion Materials Irradiation Facility (IFMIF) (Martone, 1996; IFMIF International Team, 2003) is designated to generate a materials irradiation database for the future fusion reactors. The high flux test module (HFTM) is located next to the lithium target inside the test cell where a damage rate of 20–50 dpa/fpy (displacement per atom per full power year) will be achieved in a volume of about 0.5 l. Fig. 1 shows the current design of the HFTM and inside details. The HFTM container is connected to the mechanical fix point by a rigid adapter. The adapter also serves as a return duct of the cooling gas and contains the measurement and control cables. The eight independent helium cooling feed pipes and the rigid adapter are mounted on an interface head, and connected to the helium loop outside of the test module. A total of 24 irradiation rigs are installed within the HFTM container, which is divided by stiffening plates into eight compartments. Vertically, the compartment can be divided into coolant inlet section, bottom reflector (nozzle), center section with irradiation capsules, top reflector (diffuser) and outlet section. A single compartment houses three identical rigs with an outer cross section of 50 mm × 17 mm and a length of 350 mm. About 80 miniature specimens can be housed inside each capsule, which are located in the center section of the rigs. The specimen stack has a height of 81.5 mm and a cross section of 40 mm × 9.3 mm. To reduce the thermal resistance, liquid sodium–potassium eutectic alloy (NaK78) is filled up the space within the capsule. Three sections of electric heaters are wound around the capsules with a total heating length of 120 mm. The capsule-heater assembly is inserted inside the rig
∗ Corresponding author. Tel.: +49 721 60823942; fax: +49 721 60823718. E-mail addresses: [email protected], [email protected] (Y. Chen). 0029-5493/$ – see front matter © 2012 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.nucengdes.2011.07.051
leaving a gap in-between which is filled with stagnant helium acting as thermal insulation. To keep the insulation gap at a defined size, spacers are machined out on the capsule outer surface. On each end (below and above) of the specimen stack, there is an insulation cap also filled with stagnant helium. The helium cooling channels locate between adjacent rigs or compartment wall. The power released from nuclear reactions and the electric heaters is removed by helium flows at a low pressure (0.3 MPa at the inlet) and low temperature (323 K at the inlet). Because the temperature variation can have strong effects on the development of the radiation-induced defect structure and hence on the properties, the temperatures of the test specimens should be kept at prescribed levels (between 250 and 650 ◦ C) with acceptable temperature spreads (up to ±15 ◦ C). The cooling channels of the HFTM are complicated. The flow inlet possesses a big hydraulic diameter which converges to several parallel narrow rectangular channels at the middle section, thereafter the channels expand to a common large outlet. Thus a rather high flow velocity (up to 500 m/s) is expected inside the middle narrow channels, where the fluid is locally heated with high wall heat flux (up to 0.2 MW/m2 ). At the entrance section of the narrow channels, the flow is not fully developed both thermally and hydraulically. Due to these complex features, extensive tests of the CFD codes with various turbulence models are needed in order to obtain a reliable simulation result. A number of thermo-hydraulic simulations have been carried out so far with the commercial CFD package Star-CD (Gordeev et al., 2005; Chen et al., 2010). These simulations are part of the HFTM design process and were also intended to find out suitable numerical tools. For the purpose of CFD code verification, the ITHEX (IFMIF thermal–hydraulic experiment) experimental facility was constructed (Arbeiter, 2007). This paper concerns the thermo-hydraulic simulations on transient heat transfer processes within the HFTM during startup, shut-down, loss-of-coolant and temporary beam-off periods.
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Fig. 1. HFTM (left), container (middle) and rigs (right).
During these periods, the electrical heating power and/or the coolant flow rate need to be adjusted, in order to control the specimen temperatures at required levels within given periods of time. The transient responses of the specimen temperature with the changing operation conditions are the main outcome of the simulations. These results serve as reference for the design of HFTM and remote handling strategy. Relative few literatures concern the transient compressible flow with conjugated heat transfer (Zhou et al., 2007; Jang and Chiu, 2009). The reports on similar transient experiments are difficult to find. Thus the ITHEX annular channel experiments were taken as verification cases for both steady-state and transient simulations. Simulations were carried out with commercial CFD packages Ansys-CFX 12.0 (Ansys Inc., 2009) and Star-CD 4.10 (CD-adapco, 2009). 2. CFD tools assessments and validations 2.1. Turbulence models Both Ansys-CFX 12.0 and Star-CD 4.10 solve the Reynoldsaveraged Navier–Stokes equations on unstructured meshes using finite volume methods. Several built-in turbulence models were used in the simulations. The k–ε and k–ω two-equation models use the gradient diffusion hypothesis to relate the Reynolds stresses to the mean velocity gradients and the turbulent viscosity. The turbulent viscosity is modeled as the product of a turbulent velocity and turbulent length scale. The shear-stress-transport (SST) model combines the advantages of the k–ε and k–ω models with a blending function. The k–ω model is activated in the near-wall region and the k–ε model is used in the remaining region. The Baseline Reynolds stress (BSL-RS) model belongs to the second-order closure in which transport equations for the individual Reynolds stresses are solved. Likewise to the SST model there is a blending between the Omega Reynolds stress model and a transformed epsilon-based model. The V2F approach was designed to handle wall effects in turbulent boundary layers and to accommodate non-local effects. In this model, three transport equations for turbulence quantities, k, ε and v2 are solved. In addition, an elliptic equation for f22 , the redistribution term in the equation, is needed to account for near-wall and non-local effects. In CFX, the k–ε model was applied with scalable wall function, which uses the friction velocity calculated from the logarithmic law-of-the-wall and an alternative velocity scale in determination of the wall shear stress. If the non-dimensional wall distance y+
value drops below 11.06 (which is intersection between the logarithmic and the linear near wall velocity profile), the application of the standard wall function is no longer valid. The scalable wall function basically assumes that the wall node is on the outer edge of the viscous sub-layer and has a (solver) y+ of 11.06. This could introduce some degree of error. However, it allows finer mesh in near-wall region. The omega equation based models (e.g. SST, BSLRS) were applied with automatic wall treatment which allows for a smooth shift from a low-Reynolds number form to a wall function formulation based on the near wall mesh spacing. This shifting permits the use of coarser mesh next to the wall in contrast to a low-Reynolds formulation. In Star-CD, the k–ε and k–ω based models are categorized by “high Reynolds number” (high-Re) or “low Reynolds number” (lowRe) models. For the former, the high Reynolds number forms of (k, ε, ω) transport equations are used in conjunction with algebraic law-of-the-wall representations of flow, heat and mass transfer. For the low Reynolds number models, the transport equations are solved everywhere, including the near-wall regions. Compared to CFX, Star-CD has a stricter requirement on the near-wall mesh spacing. For the low Reynolds number models including V2F, the mesh spacing in the wall-normal direction should be chosen such that y+ of the near-wall cell centroid is about 1. For the high Reynolds number models, this y+ should be about 30–100. If the node is placed too close, the utility of the wall functions is lost; if it is placed too far away, then the profiles are more likely to depart from their assumed shape. Thus, the high Reynolds number models are inappropriate to be employed for the HFTM simulations, where the channel width (maximum 1 mm) corresponds to a y+ of about 60–200. In general, the V2F and low Reynolds number k–( models were recommended (Gordeev et al., 2005; Arbeiter, 2007). 2.2. ITHEX annular channel experiments The ITHEX facility provides a coolant gas circulating loop built from helium-tight components, into which different test-sections can be integrated (Arbeiter, 2007). The current facility has four side-channel compressors in a series (Fig. 2 left). Five plate heat exchangers are used to remove the heat generation. The mass flow is measured by a coriolis flow meter. The gas pressure and temperature were also measured. The axial cut-view of the annular test section is shown in the r.h.s. of Fig. 2. The annulus is formed by two concentric cylindrical bodies fabricated from stainless steel. The main annular channel section has a length of about 95 mm
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Fig. 2. ITHEX experimental facility (left) and annular test section (right).
with a gap size of 0.61 mm (Dh = 1.22 mm), formed by two wall surfaces with a radius of 15.39 mm and 16.00 mm, respectively. Electrical heater wires are embedded in both channel walls. The heated length for the inner cylinder wall is 51.8 mm and 48.4 mm for the outer wall. Between the channel surfaces and the heater layers, 18 thermocouples are mounted on 6 axial positions, each has 3 thermocouples evenly distributed along the circumference. Both steady-state and transient experiments were carried out with helium as working fluid. The experimental conditions for the case taken for CFD code validations are: inlet pressure 4 bar, inlet temperature 292.6 K, heat flux at inner-wall 245.2 kW/m2 , heat flux at outer-wall 248.5 kW/m2 , Reynolds number 9015.
Torii and Yang, 2000) does not occur under the current experimental conditions. The maximum non-dimensional heat flux q+ is about 0.0011 corresponding to a acceleration parameter Kv of about 4.9 × 10−7 which is smaller than the criteria for the laminarization 2–4 × 10−6 (refer McEligot and Jackson, 2004 for the definitions). In fact, the radial velocity profiles on various cross-sections of the channel are almost identical, showing a typical turbulence velocity profile. The correlations from McEligot (1986) and Colburn (1933) are also plotted in the figure for comparison. The two correlations are given by Nu = 0.021 Pr0.55 Re0.8
2.3. Comparison of simulations and ITHEX experiments Three dimensional simulations were performed with CFX and Star-CD. Fig. 3 shows the axial cut-views of model geometry. For the meshing, 42 nodes are placed inside the annular gap (radial direction, y) with the near-wall cell spacing of 2 m. The y+ at the axial middle of the channel is about 0.8. In the azimuthal direction, 4 cell layers are placed for a domain azimuthal angle of 2◦ . It has been tested that the increase of the azimuthal angle does not change the simulation results. Helium is assumed to be ideal gas with constant specific heat, while the thermal conductivity and dynamic viscosity vary with temperature. No attempt was made to optimize the mesh for individual turbulence model. Comparisons of simulations using various turbulence models with the measured inner cylinder wall temperatures are shown in Fig. 4a for the steady-state operation. Overall the Star-CD low-Re SST gives the best predictions. The CFX k–ε model slightly overpredicts the wall temperatures; while the CFX SST and BSL-RS models under-predict the wall temperature. Less good agreements are shown by the Star-CD low-Re k–ε and V2F models. The Star-CD high-Re k–ε model significantly under-predicts the wall temperatures. It should be noted that the mesh used here is not suitable for the Star-CD high Reynolds number models. The laminar model results in too high wall temperatures for this Reynolds number. Fig. 4b shows the local Nusselt number and the local Reynolds number along the flow direction calculated with CFX k–ε and SST models. In these calculations, the local bulk temperature is mass flux averaged at a given flow cross section. The lower Nusselt number at the begin and the end of the channel could be due to the inaccurate temperature samplings, since the temperature differences between the wall and the bulk are small outside the heating section. It is seen that the SST model predicts a higher Nusselt number than the k–ε model. The Nusselt number decreases along the channel. This is mainly attributed to the variation of thermophysical properties due to the heating which results in a decrease of the Reynolds number along the channel (Fig. 4b). The laminarization (or relaminarization, means a transition from turbulent to laminar flows, see Perkins et al., 1973; McEligot and Jackson, 2004;
Nu = 0.023 Pr1/3 Re0.8
−0.4 T w
Tb
+ 0.85
D h
x
(McEligot)
(Colburn)
The McEligot’s correlation accounts for effects of changing thermo-physical properties with the temperature and the entrance effects. The correlation from Colburn is quite similar to an earlier correlation developed by Dittus and Beulter in 1930. The McEligot’s correlation agrees quite well with the results using k–ε model (except at the both ends of the channel), while the Colburn’s correlation is more close to the results using SST model. Fig. 5 shows the comparison of the calculated and measured inner wall temperature at 6 thermocouple positions along the axial direction for transient flow. The simulations were carried out by using CFX k–ε model. Each measured data is the mean value of three thermocouple readings at the same axial position. The lower part of the figure shows the real-time experimental conditions which are the inputs to the simulations. Overall, the simulated temperature transients agree relatively well with the experiments. Particularly, the simulated time periods for heating-up and cooled-down agree quite well with the experiments; it is about 50 s in this case. Fig. 6 shows the comparison of the outlet fluid temperature and the pressure drop along the channel. The simulated pressure drop agrees very well with the measured data. During the heatingup period the simulated outlet temperature agrees well with the experiments, however, it is up to 10 ◦ C lower than the measurement thereafter. It should be mentioned that the simulated outlet temperature was taken at the outlet of annular gap (at x = 110 mm, see Fig. 3), however the measurement point was located inside the 40 mm diameter adiabatic outlet tube, at about 20 cm downstream from the annular channel outlet (refer Fig. 2 right). Along the mini-annular gap the flow is accelerated due to the friction and the heating, which results in a lower gas temperature at outlet of the annular gap (Chen et al., 2010) compared to the downstream gas temperature inside the adiabatic outlet tube. Therefore, the actual difference between the simulated and measured outlet temperature would be smaller for t > 320 s (Fig. 6).
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Fig. 3. Axial cut-view model geometry.
Fig. 4. Comparisons of turbulence models.
Fig. 5. Transient inner wall temperature and inlet and heating conditions.
Fig. 6. Transient pressure drop and outlet fluid temperature.
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Fig. 7. Geometry model and simulation domain.
3. HFTM transient operations Simulations were carried out on a quarter-rig without the top reflector, which is located just in front of beam center as shown in Fig. 7. The transient simulations with Star-CD were unsuccessful; the required time-step size is very small (∼1 s) due to the employed segregated solver which requires several weeks to finish one simulation. Therefore, CFX with k–ε turbulence model was used for the transient simulations. The insulation gap size is 1 mm on the long-side and 0.75 mm on the short-side. The cooling channel width is 1 mm on the long-side and 0.6 mm on the short-side. The thermal conductivity of solid materials varies with temperature. The viscosity and thermal conductivity of helium are also taken as a function of temperature. The inlet helium pressure is 3 bar with a temperature of 50 ◦ C. The mass flow rate is 1.418 g/s which corresponds to about 60% of the designed maximum helium supply capacity, i.e. 21 g/s per central compartment. The hydraulic diameter of the cooling channel is estimated to be 1.9 mm, thus the Reynolds number is about 4200 in this case. For the steady-state simulations, in order to maintain a mean specimen temperature of about 600 ◦ C, the total electrical power needed is about 300 W. The total nuclear heat generation in this quarter-rig is about 434 W. The nuclear heating data were taken from Simakov et al. (2002) by 3-D interpolation. 3.1. Grid sensitivity study The grid dependence study was done for the steady-state simulations on three mesh resolutions as summarized in Table 1. These three meshes are only different in the mesh density across the fluid channel. The mesh termed as “fine” has a near-wall cell spacing of 7.5 m, which results in a y+ less than 1.5 in the main channel. The near-wall cell spacings for the mesh “reference” and “coarse”
are 15 and 60 m, respectively. Fig. 8a and b compares the simulated temperature, relative pressure and velocity magnitude in the axial direction along the specimen center line (i.e. coordinate axis x shown in Fig. 7) and the long-side channel center line. The zero point (x = 0) is the beginning of the heater section. These parameters reveal the effects of non-uniform channel cross-section area and non-uniform heating. Overall, the results from three meshes show rather small deviations. Compared to the reference mesh, the maximum deviation of temperature is about 5 ◦ C for the coarse mesh. The deviations in the relative pressure and velocity amplitude are less than ±6%. In the following simulations coarse mesh is used. 3.2. HFTM transient results 3.2.1. Start-up It is assumed here that during the start-up, the electrical heaters, beam and helium coolant flow are switched on simultaneously. The initial temperature is 20 ◦ C. Fig. 9 shows the temperatures on several sampling points. The temperatures inside the insulation gaps (e.g. specimen, thermocouples) increase much faster than those outside the insulations gaps (e.g. rig, compartment walls, bottom reflector). Close to the electrical heaters, the temperature in the specimen corners is higher than that in the center during heatingup, while it is lower when the steady-state sets in. The center thermocouple can represent the specimen center temperature well. However, the temperatures in the specimen corners are always different from the thermocouple readings, since the thermocouples are located near the center line of the specimen stack. It takes about 300 s (5 min) to reach the steady-state. 3.2.2. Beam interruption Assuming that during the steady-state operation, the beam is interrupted for 300 s, thus the nuclear heat intensity reduces to
Table 1 Summary of three mesh resolutions. Mesh
Near wall cell width (mm)
Increase ratio
Max. cell width long/short-side (mm)
y+ main channel
Node no. across channel
Coarse Reference Fine
0.0600 0.0150 0.0075
1.2 1.2 1.2
0.0588/0.0353 0.047/0.023 0.0407/0.0196
3–12 0.8–3 0.5–1.5
18 28 36
Total cell no. 2,80,081 3,71,931 4,45,411
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Fig. 8. Comparison of simulation results with three mesh resolutions.
Fig. 11. Decay heat generation. Fig. 9. Start-up T-transients.
about 0.5% of the original value (decay heat). In this case, the temperature of each HFTM component decreases as shown in Fig. 10. Within this time period, the temperature of the specimen center decreases quickly for about 300 ◦ C, at a rate of about 1 ◦ C/s. With the beam being switched on again, within about 200–300 s, the system comes back to steady-state with all the temperatures return to the original values. 3.2.3. Decay heating without cooling and loss-of-coolant After the beam-off, there is still heat generated by radioactive atoms called decay heat. The calculated intensity of the decay heat
Fig. 10. T-transients during beam interruption.
generation for the HFTM is shown in Fig. 11 for Eurofer material (internal data from Dr. S. Simakov). The decay heat is about 0.5% of the beam-on level within the first hour after shut-down; it reduces to about 0.1% within 24 h. To simulate the effects of decay heat after beam being shut-down, we assume that the decay heat amounts 0.5% of the beam-on value. If there is no active and passive cooling and no additional electrical heating, the temperatures of the HFTM components will first come to a common value, viz. the hotter components being cooled and vice versa (Fig. 12). After about 2400 s (40 min) the specimen temperature reaches a minimum of about 310 ◦ C. Thereafter the HFTM temperature increases consistently to 1000 ◦ C at 18 h after beam-off. At this temperature the
Fig. 12. T-transients without cooling.
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Fig. 13. Cooled-down temperature transients and temperature fields with decay heat only.
pressure of the NaK filled capsule is about 5 bar, which is the saturation pressure of NaK. Any increase in capsule pressure above the design level is a severe safety risk, since there is small amount of tritium generated inside the capsules during irradiation. Therefore,
active cooling after beam-off is recommended based on this calculation. For the same reason, it would be even more dangerous when the coolant flow is interrupted during operation (loss-of-coolant). As also shown in Fig. 12, without cooling the specimen (capsule)
Fig. 14. Transient heat flux, heat transfer coefficient and Nusselt number and the local quantities along the channel at time point 1 s.
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temperature will reach 1000 ◦ C within 90 s with both nuclear and electrical heating, and within 150 s with nuclear heating alone. 3.2.4. Decay heating with active cooling Besides the safety reason mentioned above, active cooling is also required in order to prevent the annealing of irradiation damage on the test specimens. According to this requirement, after the beamoff, the temperature of the specimens needs to be brought down to below 200 ◦ C within 10 min. For a longer beam-off period, the specimens must be cooled down to about 50 ◦ C. Under the normal operation conditions helium will be used as coolant. Under the emergent shut-down of the facility or during the change of the test-rigs, argon will be filled inside the test-cell and will be also used as coolant for the HFTM. Fig. 13 shows the temperature transients after beam-off with helium and argon as coolants. For the helium cooling with full coolant flow rate (here it is 1.418 g/s), the specimen center temperature goes down to 200 ◦ C within 110 s. The cooled-down time increases to 130 s and 160 s for the half and quarter helium flow rate, respectively. However, for the argon cooling with full flow rate it takes 250 s to bring down the temperature to 50 ◦ C; it takes about 400 s for full helium flow, and more than 1000 s for the full argon flow. The temperature fields of the central plane are shown in the r.h.s. of Fig. 13 for the helium and argon cooling with full flow rate. Fig. 14a–c shows the transient wall heat flux, heat transfer coefficient and Nusselt number on two center points indicated by “sampling point long-side” and “sampling point short-side” on the top of the figure. The axial position of the points corresponds to the specimen axial center (x = 0.0577 m). These quantities along two sampling lines, i.e. “sampling line long-side” and “sampling line short-side” are shown in Fig. 14d and e for time point 1 s. For the transient heat transfer, the wall heat flux decreases as the wall temperature decreases. The heat transfer coefficient and the Nusselt number remain more or less constant through out the cooling period. The small increase of the Nusselt number at the end of this period is probably due to the inaccuracy of the temperature samplings. Because during this period the heat flux and temperature difference between the wall and fluid is very small. Along the axial direction (Fig. 14d and e), the local heat transfer is strongly influenced by the spacers and different heat intensities of the three heater sections. The “sampling line long-side” goes though four positions corresponding to the spacer positions where the heat flux is much higher than that nearby. The effects of three different heater sections can be seen in the heat flux curve along the “sampling line short-side”. Close to the simulated channel outlet (outside the electrical heating region, from x = 0.12–0.14 m), the local heat flux decreases quickly, even to a negative value indicating a reversed heat transfer from the fluid to the rig-wall. Overall, the heat flux is higher in the long-side channel than that in the short-side channel due to the higher coolant mass flow rate in the long-side channel. The heat transfer coefficient is higher in the short-side channel because of the higher flow velocity; however the Nusselt number is lower due to the smaller hydraulic diameter (1.11 mm for the short-side channel, 1.91 mm for the long-side channel). For helium flow, reducing the mass flux leads to a smaller local wall heat flux. Compared to helium, the cooling by argon has a much lower heat flux and heat transfer coefficient. This mainly attributed to the much lower thermal conductivity and specific heat capacity of argon; the both quantities are only about one tenth of helium. Because of the low heat capacity, the argon flow shows a rapid temperature rise due to heating (Fig. 13b); as a result the
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wall superheat is reduced. These explain the fact that the argon flow needs much longer time to cool down the HFTM than the helium flow as shown above. 4. Summaries and conclusions Transient numerical simulations were carried out on the HFTM of IFMIF on a quarter-rig model using CFX. The time for the startup is about 5 min provided that the heater, neutron beams and cooling are switched on simultaneously. The interruption of the beams will lead to a quick decrease of specimen temperature at a rate of about 1 ◦ C/s. After the shut-down of the beams, active cooling is still required due to the decay heating, in order to keep the test materials at a required temperature level. The loss-of-coolant during operation is dangerous in that the HFTM will be heated up very quickly to an unacceptable level. The shut-down of the beams and heaters or the resume of the cooling should be done within 1 min. The cooling with argon flow is ineffective because of the low thermal conductivity and heat capacity. Partial verifications of the numerical codes CFX and Star-CD employing several turbulence models have been done against ITHEX annular channel experiments. Overall, for a Reynolds number of about 9000, the low-Re k–ω SST of Star-CD and SST, Baseline Reynolds stress and k–ε models of CFX give relatively good predictions. The Star-CD high-Re k–ε model significantly over-predicts the heat transfer coefficient for the mesh used. For the transient simulations, the predictions of CFX k–ε model agree well with the experiments. Acknowledgment The financial support by BMBF (Bundesministerium für Bildung und Forschung) under the grant No. 03FUS0008 is acknowledged. References Ansys Inc., 2009. Ansys CFX-12. 0. Arbeiter, F., 2007. Experimental and numerical investigations on minichannel cooling gas thermal–hydraulics. In: Proc. of Int. Conf. on Nuclear Engr., Nagoya, Japan. CD-adapco, 2009. Star-CD 4. 10. Chen, Y., Arbeiter, F., Heinzel, V., Ihli, Th., Moeslang, A., Slobodchuk, V., Stratmanns, E., 2010. Design optimizations of IFMIF high flux test module towards uniform specimen temperature distribution. Fusion Eng. Des. 85, 1952–1956. Colburn, A.P., 1933. A method of correlating forced convection heat transfer data and a comparison with fluid friction. Trans. AIChE 29, 174. Gordeev, S., Heinzel, V., Slobodtchouk, V., 2005. Features of convective heat transfer in heated helium channel flow. Int. J. Heat Mass Transfer 48, 3363–3380. IFMIF International Team, 2003. IFMIF comprehensive design report. IAEA Report. Jang, J.-Y., Chiu, Y.-W., 2009. 3-D Transient conjugated heat transfer and fluid flow analysis for the cooling process of sintered bed. Appl. Therm. Eng. 29, 2895–2903. Martone, M. (Ed.), 1996. IFMIF international fusion materials irradiation facility, conceptual design activity. Final Report, IFMIF CDA TEAM, ENEA, Frascati, Report ENEART/ERG/FUS/96.11. McEligot, D.M., 1986. Convective heat transfer in internal gas flows with temperature-dependent properties. Adv. Transp. Process. IV, 113–300. McEligot, D.M., Jackson, J.D., 2004. “Deterioration” criteria for convective heat transfer in gas flow through non-circular ducts. Nucl. Eng. Des. 232, 327–333. Perkins, K.R., Schade, K.W., McEligot, D.M., 1973. Heated laminarizing gas flow in a square duct. Int. J. Heat Mass Transfer 16, 897–916. Simakov, S.P., Fischer, U., Heinzel, V., von Möllendorff, U., 2002. International Fusion Material Irradiation Facility (IFMIF): Neutron source term simulation and neutronics, analyses of the high flux test module. Report FZKA 6743. Torii, S., Yang, W.-J., 2000. Thermal-fluid transport phenomena in strongly heated channel flows. Int. J. Numer. Methods Heat Fluid Flow 10, 802–823. Zhou, J., Zhang, Y., Chen, J.K., 2007. Numerical simulation of compressible gas flow and heat transfer in a microchannel surrounded by solid media. Int. J. Heat Fluid Flow 28, 1484–1491.