Influence of multiple jet cooling on the heat transfer and thermal stresses in DEMO divertor cooling finger
Boštjan Končar*1, Igor Simonovski1, Martin Draksler1
1
Jožef Stefan Institute, Reactor Engineering Division Jamova cesta 39, SI-1000 Ljubljana *
[email protected]
*Corresponding Author: Boštjan Končar Adress: Jožef Stefan Institute, Reactor Engineering Division, Jamova 39, SI- 1000 Ljubljana Tel: +386 1 5885 260 Fax: +386 1 5885 377 E-mail:
[email protected]
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ABSTRACT The divertor concept for DEMO fusion reactor is based on modular design cooled by multiple impinging jets. Such divertor should be able to withstand a surface heat flux of at least 10 MW/m2 at an acceptable pumping power. To reduce the thermal loads the plasmafacing side of the divertor is build up of numerous small cooling fingers. Each cooling finger is cooled by an array of jets blowing through the holes on the steel cartridge. The size, number and arrangement of jets on the cartridge influences the heat transfer and pressure drop characteristics of the divertor. Five different cartridge designs are analysed in the paper. The most critical parameters, such as structure temperature, heat removal ability, pressure drop, cooling efficiency and thermal stress loadings in the cooling finger are predicted for each cartridge design. A combined computational fluid dynamics and structural model was used to perform the necessary numerical analyses. The results have shown that the cartridge design with the best heat transfer and pressure drop characteristics is not also the most favorable choice from the point of view of minimum stress peaks.
KEYWORDS helium-cooled divertor, jet impingement, cartridge design, cooling efficiency, stress loading
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1
Introduction The use of impinging jets for divertor cooling in the conceptual fusion power plant is
attracting much attention due to its very high heat removal capability and moderate pumping power requirement. The design goal is to withstand a surface heat flux of at least 10 MW/m2 at an acceptable pumping power. One of the most promising divertor concepts, developed at the Forschungszentrum Karlsruhe (FZK) is based on the modular design [1]. To reduce the thermal loads the plasma-facing side of the divertor consists of small tungsten cooling fingers, cooled by high pressure helium impinging jets (Figure 1) [2]. The size, number and arrangement of the jets in the cooling finger certainly affects the heat transfer, pressure drop characteristics, as well as thermal and stress loadings of the divertor plasma facing structures. Five cartridge designs with different size and number of the cooling nozzles are analyzed in the paper. The structure temperature, heat removal ability, pressure drop, cooling efficiency and thermal stresses are predicted for each cartridge design. The main objective of this study is to compare the cooling solutions from the point of view of highest heat removal ability, lowest pressure drop and minimum stress loading. These criteria do not lead to the unique selection of the most favorable design. A combined computational fluid dynamics and structural model was used to perform numerical analyses.
2
Cooling finger design The divertor target plate is constructed of numerous small cooling fingers. The plasma
facing part of the cooling finger (tile) is made of tungsten that is brazed on the thimble, made of tungsten alloy W-1%La2O3 (WL10). The inner part of the thimble is cooled by the high pressure helium jets blowing out of a steel cartridge accommodated with 25 jet holes on the top of it. The reference cooling finger design, denoted as HEMJ-1c, is shown in Figure 1. It was developed at FZK [2] and should withstand the heat fluxes of at least 10 MW/m2.
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FIGURE 1
2.1
Cartridge design variants The main goal of optimization studies is to cool down the divertor structures as much as
possible and at the same time limit the pressure drop to reasonable values to save the pumping power. Various experimental and numerical investigations have shown that changed size and arrangement of jet holes on the cartridge may improve the heat transfer and flow characteristics of impinging jets [3-5]. In this study five different cartridge designs were analyzed. The reference design HEMJ-1Jc (see Figure 1) was used as a basis to perform parametric analysis. Main dimensions of tile, thimble and cartridge remained unchanged, only diameters and the number of jet nozzles on the cartridge were varied. Different cartridge designs are described below and shown in Figure 2: (1) reference HEMJ-1Jc design; central hole 1.04 mm + 24 holes (0.6 mm) in 4 rows, (2) 25 equal holes, central + 4 rows (0.6 mm), (3) central hole 1.04 mm + 18 holes (0.6 mm) in 3 rows, (4) constant jet cross-section area, 25 equal holes, central + 4 rows (0.6236 mm), (5) constant jet cross-section area, central 1.04 mm + 18 holes (0.6928 mm) in 3 rows.
The design (2) with equal jet-hole diameters was selected, since our previous analyses [6] demonstrated that such cartridge provides a very good cooling efficiency. In the design (3), six nozzles in the last row were eliminated trying to reduce the high temperature gradients and stresses that were predicted as the highest in our earlier study [7]. The main parameters of jet arrangement at designs (4) and (5) are similar as at variants (2) and (3), respectively. The only difference between the cases is that the total jet cross-section area for designs (4) and (5) 4
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remained the same as for the reference case. For all cases the minimum nozzle diameter was limited to 0.6 mm to avoid potential danger of a blockage.
FIGURE 2
3
Modeling approach A Computational Fluid Dynamics (CFD) analysis was performed to predict the heat
transfer and flow characteristics of the cooling finger. The calculated local distribution of the heat transfer coefficient at the fluid-thimble interface was then used as a boundary condition for thermo-mechanical analysis to calculate stresses in the tile-thimble assembly.
3.1
CFD model CFD analyses were performed at the steady-state conditions using the code ANSYS-CFX
11.0 [8]. Taking into account the symmetry of the cooling finger, a 60o periodic segment of the finger was simulated. Numerical domain consisted of 3 solid domains (tile, thimble and cartridge) and of one fluid domain. Heat transfer equations in fluid and solid domains were solved simultaneously. In the fluid domain, the helium is modeled as an ideal gas. Shear stress transport (SST) two-equation turbulence model [9] has been used to resolve turbulence and heat transfer scales in the helium flow. In the solid domain the heat conduction equation was solved. 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. The flow field and the structures are meshed by hexagonal mesh with about 2 million cells. The mesh refinement is applied especially in the fluid region near the helium-thimble interface, where the highest velocity and temperature gradients occur. The maximum non5
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dimensional distance of the wall-adjacent cells (y+) is lower than 4. As reported in [10], such mesh refinement is sufficient obtain mesh independent results. Calculations were performed for the DEMO reference scenario with internal heating due to neutrons. The boundary conditions are the following:
3.2
•
He mass flow rate: 6.8 g/s
•
He inlet temperature: 634 °C
•
He inlet pressure: 10 MPa
•
Heat flux: 10 MW/m2
•
Internal heat generation: 17 MW/m3
Thermo-mechanical model The stress analyses of the tile and thimble assembly, subjected to a combined thermo-
mechanical loading were performed by the Finite Element Method (FEM) program package ABAQUS [11]. The brazing layer between the tile and the thimble was not modelled. Hexagonal finite elements with 20 nodes and quadratic interpolation function were used to create the computational mesh. A fully coupled thermo-mechanical simulation of the tilethimble assembly was carried out at steady-state conditions to predict the resulting stresses. Boundary conditions of the DEMO reference scenario were applied (see previous section). The local heat transfer coefficients (HTC), calculated by the CFD code, were applied to the inner surface of the thimble using a film condition. To enable accurate transfer of HTC values from ANSYS-CFX to the ABAQUS mesh an interpolation function in Matlab was developed. Helium inlet temperature was defined as a sink temperature for the film condition at the thimble’s inner surface. The upper surface of the tile was subjected to the constant surface heat flux. The influence of neutron heating was accounted for by adding a homogeneous body heat flux condition for the tile and the thimble. Pressure of 10 MPa was 6
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applied to the thimble’s inner surface. Constraints were applied to the bottom surface of the thimble to prevent movement in the vertical direction. Symmetry boundary conditions were prescribed on the tile and thimble to account for the 1/6th symmetry. Temperature dependent density, conductivity, thermal capacity, coefficient of thermal expansion, modulus of elasticity and Poisson ratio material data for the tungsten tile (W) and tungsten lanthanum oxide thimble (WL10) were taken from ITER material handbook [12]. Isotropic elastic material response constitutive law was used for both, the tile and the thimble.
4 4.1
Results and discussion Heat transfer and flow analysis The results of the CFD analysis for five different design variants are presented in Table 1.
The cases can be compared with each other with regard to different criteria: i.e. equal total jet cross-section ((1), (4), (5)) or equal aspect ratio H/D of the central jet. Here H denotes nozzle-to-plate distance (H= 0.9 mm) and D denotes the diameter of the central nozzle. Designs with the diameter of the central nozzle equal to 1.04 mm ((1), (3) and (5)) have the aspect ratio 0.86, while the aspect ratio of the narrow jets (designs (2) and (4); diameter of central nozzle 0.6 mm) is around 1.5.
TABLE 1
The effect of the cartridge geometry (central nozzle diameter) on the local heat transfer capability can be explained by observing the maximum thimble temperature. The lowest thimble temperature peak is obtained for the design (3). Since it has the smallest total jet cross-section, the highest pressure drop is predicted for this design. Decreasing the total jet cross-section for 22% increases the pressure drop for almost 70%. On the other hand the 7
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pressure drop for design variants (4) and (5) is very similar to the reference case due to the same jets cross-section area (∆p/p less than 5 %). Comparison of cases (2) and (4) shows that even a very small change of the nozzle diameter from 0.6 to 0.623 mm (in the range of manufacturing accuracy) causes an increase of the maximum thimble temperature for approximately 15 °C and decreases the pressure drop for about 15 %. The finger unit is cooled on the inner surface of the thimble by the helium impinging jets. The measure for the local cooling capability is the local heat transfer coefficient (HTC), which is defined at the fluid thimble interface, relatively to the helium inlet temperature:
HTC =
q w ,i (Tw,i − T f ,inlet )
,
(1)
where q w,i , Tw,i and T f ,inlet are the local wall heat flux, the local wall temperature at the fluidthimble interface and the inlet temperature of the helium, respectively. The contour of the local heat transfer coefficient for the reference design is shown in Figure 3a. Since the local heat transfer is strongly influenced by the helium flow field, the location of the heat transfer enhancement coincides with the jets position (higher velocities in the impingement region). The velocity magnitude distribution in the vicinity of the thimble inner surface is plotted in Figure 3b. Comparison of the figures reveals that the patterns are very similar. The highest local velocities of the impinging jets are in the regions where the jet is deflected outward.
FIGURE 3
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The influence of design variants on the local heat transfer is presented in Figure 4a. The radial distribution of the HTC is plotted along the curve through the middle of the thimble inner surface (see Figure 4b). The local heat transfer distribution in the stagnation region of the central jet resembles the single jet impingement case [13], where the heat transfer maximum is shifted away from the stagnation point for about one half of the nozzle diameter in the radial direction. The influence of the side jets on the central jet stagnation region is not significant, while in outer region the interaction of the side jets can be recognized by the local HTC peaks in Figure 4a. Smaller diameter of the central nozzle (designs 2 and 4) tends to increase the heat transfer coefficient in the stagnation region. Both designs have a better heat transfer capability in the stagnation region than other geometries. The enhancement persists up to the radial distance of approximately 0.6 to 0.8 mm while further away the heat transfer is smaller due to the smaller turbulence of the exiting jet. For the designs 3 and 5 where the fourth row is closed, the heat transfer in the stagnation region depends on the total jets cross-section area. Due to the smaller total cross section of the jets, the design 3 has a higher HTC than the design 5, where the heat transfer is almost the same as for the reference case. The HTC peaks in the second and third row are significantly higher due to the flow redistribution, while in the corner of the thimble’s inner surface there is no heat transfer enhancement due to the elimination of the jet cooling in the last row. Considering only the central HTC peak, the best results are obtained for the design with the smallest central nozzle diameter of 0.6 mm (case 2), which shows the highest HTC value.
FIGURE 4
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HTC distribution at the fluid-thimble interface is affected by the flow characteristics in the particular nozzle. Figure 5 shows the effect of design variants on the portion of the total mass flow and average jet velocity through each nozzle row. Jet velocities are averaged over the cross-section of the nozzle outlet. The maximum temperature in the thimble structure appears just above the central jet at the tile-thimble joint ([6], [14]). Mass flow and jet velocity through the central nozzle are therefore the most important for enhancement of the heat removal in the stagnation region. Distribution of the mass flow over the nozzle rows is shown in Figure 5a. The mass flow portion through the central nozzle is the highest for the designs (1), (3) and (5) with a larger central nozzle diameter (1.04 mm). Absolutely the highest mass flow portion is obtained for design (3), which has the smallest total jets cross-section area. The mass flow through the other nozzle rows is more or less evenly distributed for the same design, except for the last row, where the mass flow is somewhat higher. Average jet velocities are presented in Figure 5b. The highest velocity through the central nozzle (212 m/s) is obtained for the design (3) and the lowest (163 m/s) for design (5). Design (3) has the smallest cross-section of the jets and consequently the highest jet velocity. For all cases the highest average jet velocity is obtained in the last, most outer row.
FIGURE 5
To analyze the heat transfer in the thimble above the central jet region, the thimble temperature along the central axis (from the fluid-thimble interface towards the tile-thimble joint) is shown in Figure 6. The slopes of the temperature profile differ especially with regard to the nozzle aspect ratio H/D of the central jet.
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It may be observed that the temperature distributions for narrow jets (H/D ~1.5) increase faster than for wider jets (H/D =0.86). Although the temperature at the thimble inner wall is lower for narrow jet (comparing the designs (1) and (4)), the maximum thimble temperature at the thimble-tile joint is not reduced. This may be attributed to the smaller influence area of the central jet on the thimble’s inner surface. Figure 7 shows HTC values for all design cases averaged over the specified area of the central jet. The diameter of this area is 4 mm. The calculated averaged heat transfer values (HTCAVG) agree with the predicted trend of the maximum thimble temperature. Namely, the highest HTCAVG corresponds to the lowest value of maximum thimble temperature (design 3), whereas the lowest HTCAVG corresponds to the highest thimble temperature peak (design 5). The HTCAVG values are listed in Table 1.
FIGURE 6
FIGURE 7
To evaluate and classify the heat removal ability versus the helium flow resistance for different designs, the percentage enhancement of the ratio between the HTCAVG and the pressure drop comparing to the reference design is defined as follows:
HTC AVG − HTC AVG ∆p ∆p ref , % enhancement = HTC AVG ∆p ref
(2)
The percentage enhancement in (HTCAVG/∆p) due to changed nozzle diameters is listed in Table 1. As can be seen, more or less all designs show some deterioration in the ratio (HTCAVG/∆p) as compared to the reference design. The design (4) with equal nozzle diameters and the same jets cross section gives practically the same ratio as the reference 11
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case. The highest reduction in the maximum thimble temperature (more than 33 oC) is achieved for the case (3) without nozzles in the fourth row. However, the pressure drop is unacceptably high (220 kPa) for this design.
4.2
Structural analysis Thermal stresses due to heat flux loading were also analyzed for different cartridge
designs. CFD analysis provides different HTC distribution for each design, which is used as a boundary condition for the structural analysis. The structural analysis revealed 3 regions of increased stresses in the tile-thimble assembly (see Figure 8). The highest Mises stresses were observed: •
on the tile’s outer edge, indicated as “Area 1” in Figure 8,
•
on the outer edge between the tile and the thimble, (Area 2 in Figure 8),
•
and on the thimble’s inner surface.
FIGURE 8
The most problematic region in terms of Mises stress distribution is the thimble’s inner surface, as shown in Figure 9. Maximum values of Mises stresses are above 500 MPa, regardless of the applied cooling configuration, see Figure 9. Different helium cooling solutions may result in up to 7% change of the maximum stress peak. Initial anticipation that the stresses would decrease by removing the last row of nozzles was not completely confirmed by simulation results. On the contrary, the highest peak stress values were obtained exactly for the design (3) with the removed nozzles. This result deserves some more discussion. Namely, the overall jet cross-section area is significantly reduced by elimination of 6 outer nozzles (for about 22% with respect to the reference design). Accordingly, at the 12
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same mass flow rate and reduced jet cross-section area, the heat removal from the thimble inner surface increased, as well as the the pressure drop (see Table 1). Hence, the temperatures over the thimble inner surface are the lowest and the temperature gradient over the thimble structure is the highest for the case (3). The highest temperature gradient in the thimble structure is closely linked with the highest stress maximum, as shown in Table 2 and Figure 9. However, if the overall jet cross-section area remains constant, as in the case of design (5), the elimination of outer nozzles indeed reduced the stress peak. As presented in Table 2, the local stress maximum is the lowest for the design (5). As may be observed in Figure 9, the highest stresses occur approximately at the same location, on the inner side of the thimble bending, regardless of the arrangement of cooling nozzles. In the case of designs without outer nozzles (3 and 5), the highest stresses in this region seem to be more smeared along the thimble circumference. On the other hand the maximum stress regions for the cases 1, 2 and 4 tend to be more localized with a distinctive stress peak. In general, the influence of different helium cooling solutions on the local stress maximum on the thimble’s inner surface can be considered as small (up to 7% with respect to the reference design, see Table 2). This result indicates that different cooling solutions may somewhat reduce the maximum stresses in the thimble bending region, but they cannot significantly affect the overall stress loading or even shift the location of local stress maxima. The concentration of the highest stresses in the thimble bending region is mainly affected by the geometry of the tile-thimble assembly itself. It is worth mentioning that the predicted maximum stresses are above the yield stress for all design cases. However when evaluating these results, one should be aware that a rigid tilethimble joint was assumed in the thermo-mechanical model.
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TABLE 2
FIGURE 9
In this study a non-homogeneous HTC distribution obtained directly from CFD calculation was used. However, some authors [15] used averaged HTC values for the thimble’s inner surface to calculate the structural response. To evaluate the error due to averaging, the design (1) was re-calculated using the HTC values, averaged over the three zones of the thimble inner surface: •
HTC1 =34107 W/m2K
•
HTC2 =27631 W/m2K
•
HTC3 =5402 W/m2K
The resulting Mises stress distribution is presented in Figure 10. The zones where the average HTC values were used are indicated in the figure and are consistent with [15]. The simulations with averaged HTC values result in the reduction of maximum Mises stresses for about 40 MPa (~7%) comparing to the original design (1) with non-homogeneous HTC distribution. FIGURE 10
5
Conclusions The influence of different cartridge designs on the cooling efficiency and stress loading
of the cooling finger was investigated. The diameter and the number of nozzles on the cartridge were varied at mass flow and heat flux conditions characteristic for DEMO fusion
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reactor. The most relevant parameters that determine the divertor design limits are maximum thimble temperature, pressure drop and maximum stress. The heat transfer coefficient averaged over the central jet region (HTCAVG) appears to be the most appropriate parameter to evaluate the heat removal ability of the specific cartridge design. The hydrodynamic efficiency of different cartridge designs was evaluated by comparing the ratios of heat transfer coefficient in the central jet region and overall pressure drop over the cooling finger (HTCAVG/∆p). More or less all designs show some deterioration in the ratio (HTCAVG/∆p) with regard to the reference design. The design (4) with equal nozzle diameters and the same jets cross section gives practically the same ratio as the reference one. The highest reduction in the maximum thimble temperature (for more than 33 o
C) is achieved for the design (3) with no nozzles in the fourth row. However, the pressure
drop is unacceptably high (220 kPa) for this design. Different cooling solutions have a relatively small effect on the maximum values of Mises stress (up to 7%). For all analyzed cases, the maximum stresses appear on the thimble’s inner surface and exceeded 515 MPa. The lowest stress peak is predicted for the design (5) with no jets in the last row and equal jets cross-section as the reference design. Comparison between the non-homogeneous and averaged HTC boundary conditions indicated that the peak stresses are underestimated by about 40 MPa when averaged HTC values are used.
ACKNOWLWDGEMENTS This work, supported by the European Commission and the Slovenian Research Agency was carried out within the framework of European Fusion Development Agreement (EFDA). The authors also gratefully acknowledge the financial support from the Slovenian Research Agency through the research programme P2-0026.
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REFERENCES
[1] P. Norajitra et al., He-cooled Divertor for DEMO: Experimental Verification of the Conceptual Modular Design, Fusion Engineering Design 81 (2006), 341-346. [2] P. Norajitra, et al., He-cooled divertor development for DEMO, Fusion Engineering Design 82 (2007) 2740–2744. [3] E. Baydar, Y. Ozmen, An experimental and numerical investigation on a confined impinging air jet at high Reynolds numbers, Applied Thermal Engineering, 25 (2008) 409-421. [4] B.P. Whelan, A.J. Robinson, Nozzle geometry effects in liquid jet array impingement, Applied Thermal Engineering 29 (2009) 2211-2221. [5] Z.Q. Luo, A.S. Mujumdar, C. Yap, Effects of geometric parameters on confined impinging jet heat transfer, Applied Thermal Engineering, 25 (2008) 2687-2697. [6] B. Končar, P. Norajitra, K. Oblak, Effect of nozzle sizes on jet impingement heat transfer in He-cooled divertor, Applied Thermal Engineering, 30 (2010) 697-705. [7] I. Simonovski, B. Končar, L. Cizelj, Thermo-mechanical analysis of a DEMO divertor cooling finger under the EFREMOV test conditions, Fusion Engineering Design 85 (2010) 130–137. [8] ANSYS CFX, Release11.0, ANSYS CFX-Solver Theory Guide, ANSYS, 2006. [9] F.R Menter., Multiscale model for turbulent flows, 24th Fluid Dynamics Conference, 1986, American institute of aeronautics and astronautics. [10]
B. Končar, M. Draksler, P. Norajitra, V. Widak, Numerical investigation of
multiple-jet cooling concept for helium cooled divertor, in: Proceedings of the
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International Conference Nuclear Energy for New Europe 2008, Portorož, Slovenia, September 8–11, 2008, 2008. [11]
Simulia, ABAQUS/Standard, Version 6.8-1 (2008).
[12]
ITER Material Properties Handbook, 2001.
[13]
M. Draksler, B. Končar, Analysis of heat transfer and flow characteristics in
turbulent impinging jet, Nuclear Engineering and Design (2010) In Press. [14]
R. Kruessmann, G. Messemer, P. Norajitra, J. Weggen, K. Zinn, Validation of
computational fluid dynamics (CFD) tools for the development of a helium-cooled divertor, Fusion Engineering Design 82 (2007) 2812-2816. [15]
Widak, V., Norajitra, P., Optimization of He-cooled divertor cooling fingers
using a CAD-FEM method, Fusion Engineering and Design 84 (2010), 1973-1978.
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TABLES
Table 1: Effect of design variations on cooling efficiency, maximum temperatures and pressure drop (1)
(2)
(3)
(4)
(5)
Tmax, Tile [oC]
1,779.30
1,764.11
1,778.81
1,778.78
1,813.14
Tmax, Thimble. [oC]
1,203.21
1,186.39
1,169.55
1,202.53
1,220.36
THe,out [oC]
714.07
713.56
713.51
714.05
713.13
∆p [kPa]
131.35
152.37
220.71
130.58
133.53
d∆p [kPa]
-
21.03
89.37
-0.76
2.19
HTCAVG/∆p
233.53
213.09
170.05
233.29
223.99
HTCAVG [W/m2K]
30,673
32,468
37,533
30,463
29,910
dTmax,Thimble [oC]
-
-16.82
-33.66
-0.68
17.15
% enhancement in
-
-8.75
-27.18
-0.1
-4.08
(HTCAVG/∆p)
Table 2: Effect of design variations on maximum and minimum values of stress load Mises stress
(1)
(2)
(3)
(4)
(5)
Max [MPa]
533.91
543.93
567.99
531.14
515.38
Min [MPa]
36.30
32.06
35.20
36.68
39.59
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FIGURE CAPTIONS
Figure 1: Divertor cooling finger Figure 2: Examples of different cartridge designs; (1), (2) and (3) Figure 3: Heat transfer coefficient distribution on the inner surface of the thimble (a) and helium velocity distribution at the normal distance 0.1 mm from the thimble-fluid interface (b). Figure 4: Local HTC values along the curve at the fluid-thimble interface (a); sketch of the polyline (b) Figure 5: Portion of the total mass flow rate (a) and averaged jet outlet velocity (b) at each hole for different design variants Figure 6: The thimble structure temperature along the symmetry line Figure 7: HTC averaged over the stagnation region of the central jet Figure 8: Mises stress distribution for the reference case (1) Figure 9: Mises stress distribution for different design variants Figure 10: Mises stress calculation for design (1) with averaged HTC values
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FIGURES
Figure 1: Divertor cooling finger
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Figure 2: Examples of different cartridge designs; (1), (2) and (3)
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(a)
(b)
Figure 3: Heat transfer coefficient distribution on the inner surface of the thimble (a) and helium velocity distribution at the normal distance 0.1 mm from the thimble-fluid interface (b).
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(a)
(b)
Figure 4: Local HTC values along the curve at the fluid-thimble interface (a); sketch of the polyline (b)
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Mass Flow Portion [%]
45 40 35 30 25 20 15 10 5 0 central
row1
row2
row3
row4
1 2 3 4 5
Average Jet Velocity [m/s]
Case Case Case Case Case
50
case1
250 240 230 220 210 200 190 180 170 160 150
case2 case3 case4 case5
central
row1
(a)
row2
row3
row4
(b)
Figure 5: Portion of the total mass flow rate (a) and averaged jet outlet velocity (b) at each hole for different design variants
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Thimble temperature [°C
thimble-tile joint 1250
Case 1 Case 2 Case 3
1150
Case 4 Case 5
1050
fluid-thimble interface 950 -0.1
0.4
0.9
z [mm]
Figure 6: The thimble structure temperature along the symmetry line
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Averaged HTC
case1 case2
2
HTCAVG [W/m K]
40,000
case3 case4
35,000
case5
30,000 25,000 20,000 central
Figure 7: HTC averaged over the stagnation region of the central jet
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Figure 8: Mises stress distribution for the reference case (1)
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(1)
(2)
(3)
(4)
(5)
Figure 9: Mises stress distribution for different design variants
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Figure 10: Mises stress calculation for design (1) with averaged HTC values
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