Numerical Investigation of Multiple-Jet Cooling Concept for Helium Cooled Divertor B. Končar, M. Draksler, K. Oblak Jožef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia
[email protected],
[email protected],
[email protected] P. Norajitra, V. Widak Forschungszentrum Karlsruhe, P.O. Box 3640, D 76021 Karlsruhe, Germany
[email protected],
[email protected] ABSTRACT Numerical simulations presented in this paper were performed as a part of heliumcooled divertor studies for post-ITER generation of fusion reactors. The cooling ability of divertor cooled by multiple helium jets was analysed. Thermal-hydraulic characteristics and temperature distributions in the solid structures were predicted for the reference geometry of one finger module. To assess numerical errors, different meshes (hexagonal, tetra, tetra-prism) and discretisation schemes were used. The temperatures in the solid structures decrease with finer mesh and higher order discretisation and converge towards finite values. The numerical simulations are validated against high heat flux experiments, performed at Efremov Institute, St. Petersburg. The predicted design parameters show reasonable agreement with measured data. The calculated maximum thimble temperature was below the tile-thimble brazing temperature, indicating good heat removal capability of reference divertor design. 1
INTRODUCTION
The divertor is one of the most important high-heat-flux components in a fusion reactor. About 15 % of the total thermal power gained from the fusion reaction need to be removed by divertor, which results in an extremely high heat flux applied on a relatively small divertor target plate. Since several years a helium-cooled divertor for post-ITER generation of fusion reactors is being developed at Furschungszentrum Karlsruhe (FZK) [1]. Its main design requirement is to remove extremely high heat flux loads of 10 – 15 MW/m2. Usage of helium as a coolant simplifies the balance of the power plant since the same coolant can be used for all internal components. Due to its chemical and neutronic inertness helium loop may be operated at higher temperatures and lower pressures than water. Its comparatively low heat removal capability can be improved by increasing the solid/helium interface area or by turbulence enhancement by single or multiple jets [2]. The reference helium-divertor design uses small tungsten finger modules, cooled by high pressure helium jets (Figure 1). To demonstrate the performance of the reference modular design, data from numerical simulations and experiments are necessary. The focus of this paper is on numerical analyses of one finger module cooled by multiple jets. Thermalhydraulic behaviour of helium flow and temperature distributions in the solid structures are predicted. To assess and minimize numerical errors, different meshes and discretization 813.1
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schemes are used. The mesh refinement is applied especially at the helium-thimble interface, where the temperature gradients are the highest. To have confidence in CFD simulations, the numerical results are validated on experiments, performed at the Efremov Institute, St. Petersburg [3]. 2
DIVERTOR COOLING FINGER - REFERENCE DESIGN
The plasma-facing side of the divertor (target plate) is constructed of small hexagonal tungsten tiles. Each tile is brazed on the thimble, made of tungsten alloy (WL10). A steel cartridge with 25 holes on the top of it is inserted in thimble. The helium jets under high pressure blow through these holes and cool the hot inner surface of the thimble. The jetimpingement cooling method has also been applied on other engineering fields (gas-turbines, aerospace industry, computer chips cooling, etc.). The geometry of the reference design is shown in Figure 1. The tile width is 17.8 mm, the thimble thickness is 1 mm, the outer diameter of the cartridge is 11.2 mm. The holes on the top of the cartridge have the diameter of 0.6 mm, except for the central hole with the diameter of 1 mm. The gap between the thimble and cartridge is 0.9 mm. He out
He in
Cartridge (Steel) Hole Tile (W)
Thimble (WL10)
Figure 1 Divertor cooling finger 3
EXPERIMENTAL DATA
The cooling ability of the reference cooling finger mock-ups was tested experimentally at the combined experimental facility located at the Efremov Institute, St. Petersburg, Russia. The facility consists of the TSEFEY electron beam facility (60 kW at 27 keV beam energy) and the helium loop (see Figure 2). Powerful electron beam gun enables testing of mock-ups at high heat fluxes up to 15 MW/m2. The data for validation of numerical results were extracted from the first test series, performed in 2006 [4]. During the tests thermo-cyclic loading was applied to the tile upper surface to test the integrity of divertor materials. Thermo-cycles were simulated by switching the beam on and off. For the selected test the thermo-cyclic loading was applied at five heat flux levels. At each heat flux level, 10 cycles were performed. The helium mass flow rate was kept approximately constant at about 13.5 g/s. To validate steady-state CFD simulations, the data were extracted at different heat flux levels, during the time intervals, when the laser beam was switched on. The measured parameters are presented in Table 1. Tile surface temperatures were measured by infrared (IR) camera. Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, Sept. 8-11, 2008
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Figure 2 Testing facility at Efremov Institute [3] Table 1 Measured parameters during thermo-mechanical tests of HEMJ#J1-C [4] m& He ∆p p(He inlet) q(dT He) T(He inlet) ∆THe TTile-surf. max 2 o o [MW/m ] [g/s] [MPa] [kPa] [ C] [ C] [oC] 4.01 13.06 9.61 326.74 523.56 15.26 941 6.28 13.7 9.79 321.23 536.88 22.78 1153 9.69 13.73 9.69 326.62 555.36 35.09 1424 11.63 13.7 9.84 327.37 558.84 42.19 1597 12.62 13.28 9.72 313.29 567.8 47.24 1788 4 4.1
CFD MODEL Transport equations
Conjugate heat transfer in one-finger module was simulated by the computer code ANSYS-CFX-11.0 [5]. Heat transfer equations were solved simultaneously in fluid and solid domain. The transport processes are assumed to be at steady-state. In the fluid domain, the helium is modelled as an ideal gas. The following transport equations were solved in the fluid domain: continuity equation r ∇ ⋅ ( ρv ) = 0 , momentum equation v v v v (v ⋅ ∇)v = −∇p + g + ( µ + µ t )∇ 2 v , and energy equation v v ρ ( v ⋅ ∇ U ) − ∇ ⋅ ( λ ∇ T ) + p∇ ⋅ v = 0 ,
(1) (2) (3)
v v where ρ , v , U, p, µ , µt , g , λ ,T are helium density, velocity, internal energy, pressure, dynamic viscosity, turbulent viscosity, gravity force density, thermal heat conductivity of the helium and temperature, respectively. The shear stress transport (SST) turbulence model [6]was used to resolve turbulence and heat transfer scales in the helium flow. The SST Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, Sept. 8-11, 2008
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formulation combines k-ω model to resolve near-wall turbulence and k-ε model for the bulk flow. K-ω model is used for inner parts of the boundary layer and makes the model directly usable all the way down to the wall through the viscous sub-layer. The k-ω model can be used as a Low-Re turbulence model without any extra damping functions and switches to a k-ε behaviour in the free-stream flow. In the solid domain the heat conduction equation for steady-state conditions was solved: ∇ ⋅ (λ s ∇Ts ) = − S E , (4) where ρs, cs, Ts and λs are the density, specific heat capacity and thermal conductivity of the solid, respectively. The SE denotes the internal heat generation, which is set to zero for the considered case. 4.2
Numerical model and boundary conditions
Several different meshes (tetra, hybrid, hexa) have been used to obtain mesh-invariant solution (Table 2). The mesh refinement was applied especially in the jet-impingement region at the helium-thimble interface, where the highest temperature gradients are expected. Mesh refinement analyses have been performed for the pre-test case (Table 3) on a 30o periodic segment of the one finger module. The material properties of the tile and the thimble were modeled as temperaturedependent according to ITER Material Properties Handbook [7]. Due to low temperature gradients in the steel cartridge, its material properties were taken at constant temperature. Constant heat flux is applied at the upper surface of the tile and adiabatic boundary conditions are assumed at the outer walls. Helium flow enters the cartridge at the constant mass flow rate. Boundary conditions of pre-test case are listed in Table 3. In the pre-test case numerical errors due to mesh refinement and discretisation scheme have been analysed. Table 2 Numerical meshes Name Num. of cells
Element type
Mesh2 Mesh4 Mesh5 Hexa_B Hexa_C Hexa_D Hexa_D (whole finger)
tetra tetra/prism tetra/prism hexahedral hexahedral hexahedral hexahedral
1,027,722 996,589 1,244,049 322,415 371,643 1,370,720 16,448,640
Mesh refinement at thimble-fluid interface No Yes (7 prism layers) Yes (12 prism layers) No Yes Yes + entire fluid domain Yes + entire fluid domain
Table 3 Boundary conditions of the pre-test case Pre-test case He mass flow rate [g/s] 13.5 He inlet temperature [°C] 540 He inlet pressure [MPa] 10.0 Heat flux [MW/m2] 11.6 5 5.1
RESULTS Pre-test case
For the pre-test case simulations different numerical meshes and two different discretisation schemes (Upwind with blended factor 0.75 (0.75) and High resolution scheme Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, Sept. 8-11, 2008
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(HR)) have been used (see Table 4). The boundary conditions are similar to Efremov tests, but were pre-selected before knowing exact experimental values. Simulations were running in a steady-state mode. The solution was considered to converge, when the maximum values of normalized residuals were bellow 10-4. The integral mass imbalance was below 0.03 % for all simulations. The results are presented in Table 4. Hybrid tetra-prism meshes predict significantly higher solid temperatures as hexagonal meshes. To achieve the same accuracy as equivalent hexagonal mesh, the tetra mesh needs to be several times denser. Temperatures also decrease with mesh refinement at the fluid-thimble interface and higher order discretisation of advection term. Table 4 Influence of mesh refinement on the results TTile-surf. max TThimble max o Name [ C] [oC] Mesh2 1893 1253 Mesh4 1774 1129 HexaB 1738 1096 1671 1017 HexaC (0.75/HR) / 1660.6 / 1008.5 1655 1003 HexaD (0.75/HR) / 1646 / 995 HexaD_WholeFinger (HR only) 1650 997
THe_outlet [oC] 585 585 584.5 585 / 585 585 / 585
∆p [kPa] 383 406 411 432 / 443 445 / 450
585
442
To investigate the high temperature discrepancy between the meshes, the local temperature profile at the helium-fluid interface (central line of the finger module, above the central hole) is presented in Figure 3. As shown, the temperature boundary layer is very thin, in the range of 10 micro-meters. Medium-size Hexa C mesh is able to resolve it, while the hybrid Mesh 4 is still to coarse to capture the gradients in the thermal boundary layer. Temperature profile 1200 1100
Temp (C)
1000 900 800
Helium - gap
Mesh4 HexaC
Thimble
700 600 500 400
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Distance (mm)
Figure 3 Temperature profile at the helium-thimble interface To analyze mesh dependency on the results, the fluid temperature distributions over the thimble-fluid polyline are presented for three different hexagonal meshes (see Figure 4). The local fluid temperatures increase with mesh refinement, whereas temperatures in the solid decrease. It can be seen that the temperature values approach towards asymptotic values with finer mesh. Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, Sept. 8-11, 2008
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850
Temperature [C]
800 750
hexaC
700
hexaD 650
hexaB
600 550 500 0
1
2
3
4
5
6
7
Distance [mm]
Figure 4 Fluid temperature distribution over the polyline (left); Fluid-thimble polyline (right) The simulation results for the whole finger geometry (the finest HexaD mesh was used) are shown in Figure 5. Local temperature distributions at the thimble inner surface and at the tile upper surface are presented on Figure 5, left. The highest temperatures appear at the corners of the tile upper surface. The non-uniformity of the tile temperature distribution is less than 40 oC indicating relatively homogeneous cooling of structures by helium jets. The heat is efficiently removed in perpendicular direction to the heated surface – temperature decrease between the tile and the thimble is about 800 oC in the finger central axis. The effect of cooling jets can be seen on temperature distribution on the thimble inner wall. It is interesting to note that the highest temperature appears just above the central hole, which has larger diameter than the other holes. The velocity distribution in the jet region is shown on the right side of Figure 5. The highest velocities through the jet holes reach maximum values of about 440 m/s.
Figure 5 Local temperature distributions at the thimble inner surface and at the tile upper surface (left); velocity distribution in the jet region (right) Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, Sept. 8-11, 2008
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5.2
Post-test calculations
To validate the CFD simulations, post-test calculations of Efremov experiments from Table 1 were performed on medium-size hexagonal Mesh_C. This mesh demonstrates a good compromise between the numerical accuracy and the required calculation time. The comparison of simulation results and measured data is shown in Table 5. The critical quantity of interest in this study is maximum thimble temperature. Two critical values should be considered. The first one is melting temperature of thimble material WL10 (1300 oC) and the other limitation is melting temperature of brazing filler material. Tile and thimble are brazed together with STEMET 1311®, which has a melting temperature of 1050 oC. The helium mass flow rate for Efremov experiments was raised up to approximately 13.5 g/s to keep the temperature at the tile/thimble brazing layer below 1050 oC. It should be noted that the tile size of experimental mock-up is slightly different than the tile size of reference design (pretest case). Namely, the tile width of the experimental mock-up is 17.2 mm. As shown in Table 5, a reasonable agreement between the measured and calculated tile surface temperature has been obtained. The experimental heat flux in Table 5 was recalculated from the measured helium temperature difference (the removed heat is absorbed in helium) to exclude the errors due to beam reflection and due to heat losses through the flange, where the mock-up is fixed (the real boundary condition is not adiabatic). The calculated thimble temperature exceeds the allowed brazing temperature of 1050 oC only for the highest heat flux value 12.62 MW/m2. During the experiment, overheating of the mock-up surface was observed only at the highest power level, where the testing was terminated. The post-test metallographic examination of the mock-up confirmed tile detachment, which indicates that the tile-thimble brazing temperature was exceeded also in the experiment. Table 5 Comparison of calculated and measured parameters TTile-surf. max q(dT He) TThimble max ∆p 2 o [MW/m ] [ C] [oC] [kPa] Calc Exp Calc Calc Exp 4.01 866.35 941 674.68 428.2 326.74 6.28 1090.35 1153 773.65 466.26 321.23 9.69 1447.35 1424 927.45 477.93 326.62 11.63 1648.65 1597 1009.95 477.1 327.37 12.62 1765.95 1788 1065.25 459.71 313.29 6
∆THe
[oC] Calc 14.72 22.11 34.27 41.32 46.37
Exp 15.26 22.78 35.09 42.19 47.24
CONCLUSIONS
CFD simulations were used to analyze the cooling ability of divertor cooled by multiple helium jets. Thermal-hydraulic behaviour of helium flow and temperature distributions in the solid structures were predicted for the reference geometry of one finger module. To assess and minimize numerical errors, different meshes (hexagonal, tetra, tetra-prism) and discretisation schemes were analysed. The results have shown that temperatures in the solid structures decrease with finer mesh and higher order discretisation of advection terms. Convergence of the results with mesh refinement was demonstrated on hexagonal meshes. The simulations on tetra-prism meshes are less accurate than on equivalent hexagonal meshes as they predict significantly higher temperatures in the tile and thimble structure. To validate CFD simulations, the numerical results were compared against experimental data extracted from thermo-cyclic high heat flux experiments, performed at Efremov Institute, St. Petersburg. Measurements were obtained at five different heat flux level and at approximately constant helium mass flow rate. The calculated and measured values of the tile Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, Sept. 8-11, 2008
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surface temperature show good agreement. The critical design parameter of interest at the considered Efremov experiments was the tile-thimble brazing temperature of 1050 oC. Except for the highest heat flux level (12.6 MW/m2), the predicted maximum thimble temperature was well below the critical value, indicating good heat removal capability of reference cooling finger design. ACKNOWLEDGMENTS This work, supported in part by the Slovenian Research Agency (research project J29362-0106-06) was carried out within the framework of the European Fusion Development Agreement (EFDA). REFERENCES [1] P. Norajitra et al., “He-cooled Divertor for DEMO: Experimental Verification of the Conceptual Modular Design”, Fusion Eng. Des., 81 (1-7), 2006, pp. 341-346. [2] P. Norajitra et al., Conceptual design of a He-cooled divertor with integrated flow and heat transfer promoters (PPCS subtask TW3-TRP-001-D2), Part II: Detailed Version. Forschungszentrum Karlsruhe, Scientific Report, FZKA 6975, April 2004. [3] I. Ovchinnikov et al., “Experimental study of DEMO helium cooled divertor target mockups to estimate their thermal and pumping efficiencies”, Fusion Eng. Des., 73, 2005, pp. 181–186. [4] R. Giniytulin et al., Manufacturing and testing the He-cooled target module mock-ups for DEMO fusion reactor divertor, Status report, EFREMOV Institute STC Sintez St. Peterburg, 2006. [5] ANSYS CFX, Release11.0, ANSYS CFX-Solver Theory Guide, ANSYS, 2006. [6] F.R. Menter, “Multiscale model for turbulent flows”, 24th Fluid Dynamics Conference, American institute of aeronautics and astronautics, 1986. [7] ITER Material Properties Handbook, 2001.
Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, Sept. 8-11, 2008
