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Numerical studies on helium cooled divertor finger mock up with sectorial extended surfaces
Fusion Engineering and Design 89 (2014) 2647–2658
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Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Numerical studies on helium cooled divertor finger mock up with sectorial extended surfaces Sandeep Rimza a,∗ , Kamalakanta Satpathy a , Samir Khirwadkar a , Karupanna Velusamy b a b
Divertor and First wall Technology Development Division, Institute for Plasma Research (IPR), Bhat 382428 Gandhinagar, Gujarat, India Mechanics and Hydraulics Division, Reactor Design Group (RDG), Indira Gandhi Centre for Atomic Research (IGCAR), Kalpakkam 603102, Tamilnadu, India
h i g h l i g h t s • • • • •
Studies on heat transfer enhancement for divertor finger mock-up. Heat transfer characteristics of jet impingement with extended surfaces have been investigated. Effect of critical parameters that influence the thermal performance of the finger mock-up by CFD approach. Effect of extended surface in enhancing heat removal potential with pumping power assessed. Practicability of the chosen design is verified by structural analysis.
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Article history: Received 11 February 2014 Received in revised form 10 June 2014 Accepted 4 July 2014 Available online 6 August 2014 Keywords: Jet-impingement CFD Sectorial extended surfaces Tile Thimble Fusion reactor
a b s t r a c t Jet impinging technique is an advance divertor concept for the design of future fusion power plants. This technique is extensively used due to its high heat removal capability with reasonable pumping power and for safe operation. In this design, plasma-facing components are fabricated with numerous fingers cooled by helium jets to reduce the thermal stresses. The present study is focused towards finding an optimum performance of one such finger mock-up through systematic computational fluid dynamics (CFD) studies. Heat transfer characteristics of jet impingement have been numerically investigated with sectorial extended surfaces (SES). The result shows that addition of SES enhances heat removal potential with minimum pumping power. Detailed parametric studies on critical parameters that influence thermal performance of the finger mock-up have been analyzed. Thermo-mechanical analysis has been carried out through finite element based approach to know the state of stress in the assembly as a result of large temperature gradients. It is seen that the stresses are within the permissible limits for the present design. The whole numerical simulation has been carried out using general-purpose CFD software (ANSYS FLUENT, Release 14.0, User Guide, Ansys, Inc., 2011). Benchmark validation studies have been performed against high-heat flux experiments (B. Konˇcar, P. Norajitra, K. Oblak, Appl. Therm. Eng., 30, 697–705, 2010) and a good agreement is noticed between the present simulation and the reported results. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Nuclear fusion programme is one of the most promising options to meet the increasing energy demand. However, there are interesting challenges in successful design of the fusion power plants. One among them is design of the divertor which is an important
∗ Corresponding author. Tel.: +91 8141511655. E-mail addresses: [email protected], [email protected] (S. Rimza), [email protected] (K. Satpathy), [email protected] (S. Khirwadkar), [email protected] (K. Velusamy). http://dx.doi.org/10.1016/j.fusengdes.2014.07.008 0920-3796/© 2014 Elsevier B.V. All rights reserved.
part of the fusion power plant that handles extremely high heat flux generated in interior of the core. The function of the divertor is to remove fusion ash, plasma impurities and unburned fuel from the reactor first wall which affects the quality of the plasma. Due to its location in the reactor, it must survive massive volumetric heating by neutron and surface heating results from radiation and all plasma exhaust. Usage of helium as coolant has favourable safety characteristics, and it is capable of efficient heat transfer. Different type of helium-cooled divertor concepts has already been proposed by Raffray et al. [3] for a fusion power plant application. One of the designs uses small tungsten fingers, cooled by high pressure helium jets. The challenges and the design issues
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Nomenclatures A Ac Ap Ae Ace heff hact Ke k ˙ m P Re q t T Tb Ti To Tc WHe
area of top surface wall, m2 area of cooled inner surface wall, m2 area of bare plate between the sectorial extended surface, m2 surface area of the sectorial extended surface, m2 cross section area of the sectorial extended surface, m2 effective heat transfer coefficient, W/(m2 K) actual heat transfer coefficient, W/(m2 K) thermal conductivity of the sectorial extended surface, W/(m K) turbulent kinetic energy, m2 /s2 mass flow rate, kg/s perimeter of the sectorial extended surface, m reynolds number heat flux incident on the cooled surface, W/m2 thickness of thimble, m temperature, K bulk temperature of the fluid, (Ti + To )/2, K inlet temperature of fluid, K outlet temperature of fluid, K average temperature of cooled surface, K pumping power for helium, W
Greek symbols ε rate of dissipation, m2 /s3 efficiency sectorial extended surface density of fluid, kg/m3 effectiveness of the sectorial extended surface Subscripts act actual b bulk cooled c ce cross section of extended surface e extended surface eff effective helium He i inlet o outlet p plate
associated with the helium cooling viz., manifold sizes, pumping power, and leak prevention are studied by Baxi [4]. It was demonstrated that, the manifold sizes and the pumping power can be reduced to acceptable levels as per the design criteria. Baxi and Wong [5] reviewed various heat transfer enhancement techniques (viz., swirl tape, roughening, porous media etc.) to reduce the flow, pumping power and pressure requirements in helium cooling for fusion reactor applications. A modular helium cooled divertor for power plant application was studied by Diegele et al. [6] with an improved heat transfer technique. The result showed that the design has the potential of removing high heat flux (∼15 MW/m2 ). High Efficiency Thermal Shield (HETS) concept that relies on an abrupt change of momentum of the fluid was proposed by Pizzuto et al. [7]. The numerical studies along with experiments indicate that HETS solution is viable in order to attain a good heat transfer with limited pumping power. An advanced He-cooled divertor concept (DEMO) was studied by Ihli et al. [8] with modular target plate design through CFD simulations and achieved best cooling performance with jet impingement technique. Various cooling technologies for future fusion power plants were studied by
Ihli and Ilic´ [9]. Among different cooling technologies, V-rib based surface roughness approach for the first wall, the multiple impingement cooling techniques were identified as a suitable advantageous method. A comprehensive review of varying helium cooled divertor concepts for fusion power plant applications was reported by Tillack et al. [10]. In their review, they summarized recent US efforts on fusion power plants through analytical and experimental studies. Key issues were identified and future R&D (viz., fabrication, joining, material behaviour and reliability) has been widely discussed. Thermal hydraulic characteristics of fusion reactor components were analyzed by Arbeiter et al. [11] through various turbulence models using CFD code STAR–CD, and the results were validated against experiments. It is seen that, k–ε turbulence model with damping functions gives more accurate results for high heat flux test module. In order to increase the turbulence in the gas, thermal performance of the divertor design was experimentally studied by Mills et al. [12]. The objective of their studies is to assess the effect of fin’s addition on the thermal performance. Effect of fins on the heat transfer coefficient of plate-type divertor was investigated by Hageman et al. [13]. The results suggested that, adding fins nearly double the effective heat transfer coefficient. Thermal stress is regarded as an important limit for performance of the fusion power plants. Towards this, Widak and Norajitra [14] numerically investigated the thermo-mechanical aspect through finite element (FE) approach. Experimental study of DEMO helium cooled divertor target mock-ups has been done by Ovchinnikov et al. [15]. The objective of their study is to estimate thermal and pumping efficiencies of the divertor and concluded that, helium distributed cartridge options have high heat flux removing capability within mass flow ranges of 5–15 g/s. From the above literatures, it is observed that various designs for helium cooled divertor have been discussed but limited heat transfer enhancement techniques have been addressed. It is evident that manufacturing difficulties and high pressure drop associated with divertor design is of main concern. Towards this, a new type of sectorial extended surface (SES) has been proposed. This particular design is easy to manufacture and cost effective. The main objective of this paper is to numerically evaluate how addition of SES affects the thermal hydraulics performance of finger type divertor. In this regard, solution methodologies along with governing equations are presented in Section 2. As a precursor, benchmark validation studies have been performed for cooling finger against high heat flux experiments [2]. Effective heat transfer coefficients and pressure losses related to different heat fluxes, flow rates are numerically studied and are presented in Section 3. Enhancement of heat transfer is analyzed by introducing SES. Comparative studies for fluid flow features viz., turbulence kinetic energy, temperature and heat flux distributions are presented in Section 4. Finally, major conclusions have been arrived and are presented in Section 6.
2. Solution Methodology 2.1. Design description The whole divertor is divided into a number of small volumes known as cassettes, which are independently cooled. The plasma facing components of the divertor are splitted into a number of finger mock-ups in order to reduce the thermal stress, as presented in Fig. 1. Each mock-up consists of small hexagonal tile made up of tungsten (W) with sacrificial layers used as the thermal shield. Tiles are brazed to another material of tungsten alloy (WL-10) known as the thimble. A steel cartridge carrying the nozzle is placed concentrically inside the thimble. Fluid enters through the nozzle and
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Fig. 1. (a) Schematic of test section and (b) cross sectional view (all dimensions are in mm).
flows radially outwards through the space between cartridge and the thimble. Thermo-hydraulic performance of the mock up has been studied with addition of extended surfaces which is placed between cartridge and the thimble with a supporting plate of 1 mm thickness, as depicted in Fig. 2. The circumferential pitch was varied from first row to last row that leads to reduce the expense of machining to cover the top cooled surface. Extended surfaces are angularly constructed at every 30◦ sector, resulting 36 numbers of extended surface with 1 mm thickness, 0.8 mm pitch and 2 mm height. Circumferential gap between the extended surfaces are maintained at 0.4 mm. WL-10 is used as the material for SES due to its favourable machining property. The most important design criterion is to keep thimble temperature above ductile brittle transition
temperature (DBTT, ∼600 ◦ C) and below re-crystallization temperature (RCT, ∼1300 ◦ C). The brazing filler temperature of tiles and thimble should not exceed 1050 ◦ C [2] and pumping power should be ∼10% of incident power. The aim of this design is to reduce the temperature of the thimble as low as possible below brazing melting point at the expense of small pressure drop. 2.2. Governing equations The steady state forms of continuity, momentum and energy equations for an incompressible fluid used for the present numerical simulation are described in [16]. To resolve the Reynolds stresses, realizable k–ε turbulence model is employed with buoyancy, because it accurately predicts the performance for separation,
Fig. 2. (a) Bottom and (b) 3D view of SES (all dimensions are in mm).
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Fig. 3. (a) Geometry of cooling finger mock-up for validation (b) global grid pattern and (c) close-up view of CFD mesh. Table 1 Grid sensitivity analysis. Mesh
Control volume
Minimum grid spacing (mm)
Maximum tile temperature (◦ C)
Maximum thimble temperature (◦ C)
CPU time per iterations (s)
M1 M2 M3 M4
2.5 × 105 3.5 × 105 5 × 105 6 × 105
0.2 0.15 0.1 0.08
1687 1675 1651 1649
1087 1064 1004 1003
3 5 8 12
Maximum tile and thimble temperature reported [2] = 1660.3 ◦ C, 1010.73 ◦ C
recirculation, and flows involving boundary layers under pressure gradients [1] and also used to simulate flow and heat transfer in pin fin channel [17]. Pressure-velocity coupling between the incompressible Navier–Stokes and continuity equations is resolved using the Semi Implicit Pressure Linked Equations (SIMPLE) algorithm. To declare convergence at any iteration, the absolute errors in the discretized momentum and continuity equations are set to be 10−4 where as for energy, it is set to be 10−6 .
2.3. Boundary condition Due to exist of symmetry, a 30◦ sector model is considered for the present numerical simulation. Temperature dependent material properties are taken into consideration for the tile, thimble, and supporting plate with extended surfaces [18] whereas constant material properties are considered for cartridge. Carrier fluid (helium) is considered to be steady incompressible. Initial
Fig. 4. (a) Comparison between Helium pressure drop & temperature difference with heat flux. (b) Comparison maximum tile and thimble temperature against different heat flux.
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Fig. 5. Temperature distribution for mass flow rate of 6.8 g/s with a heat flux of 10 MW/m2 (a) reported results [2] and (b) present simulation.
temperature and pressure of the fluid are 600 ◦ C and 10 MPa, respectively [2]. The boundary conditions for the present 3D numerical simulations are as follows:
• No-slip conditions are imposed on the walls and at the extended surfaces. 3. Benchmark Validation
• Symmetry boundary conditions are imposed on the 30◦ cut sections. • Adiabatic boundary conditions are imposed on outer sides of the domain. • Top surface of the domain is imposed with constant heat flux. • Specified mass flow rate and temperature are considered at the inlet where as the outlet is specified with constant pressure.
Benchmarking the numerical calculation against suitable experimental data is of vital importance in CFD studies. To this end, the reference finger geometry of [2] is considered for the validation where high heat flux experiments [15] have been reported. The computational domain with the global grid patterns considered in the validation studies are depicted in Fig. 3.
Fig. 6. (a) Sectional top view of turbulence kinetic energy distribution (m2 /s2 ) around SES (b) bottom view of 30◦ sector of SES (c) velocity distribution (m/s).
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Fig. 7. Temperature distribution of cooling finger design (a) without SES and (b) with SES.
3.1. Grid sensitivity analysis In a CFD simulation, establishing grid size towards independent nature of the solution is an essential first step. In this regard, an attempt is made to determine the optimum mesh for the present numerical simulations. Different mesh sizes employed for the grid sensitivity study are shown in Table 1 along with maximum tile and thimble temperature. It can be noticed that the difference between temperature distributions of tiles and thimbles obtained from mesh M3 and M4 are small. The percentage of deviation in temperature among M3 and M4 are 0.12% and 0.09%, respectively. Though the change is a small but computational effort is significantly higher for M4 as compared to M3 thus justifying the use of mesh M3 for further investigations. 3.2. Parametric studies
in details. Fig. 6 depicts distribution of turbulence kinetic energy with the presence of SES. It is seen that, maximum kinetic energy occurs at the nozzle entrance due to high velocity at the centre. The sectional top view of velocity distribution around SES is depicted in Fig. 6(c). Symmetric eddies are formed in between the extended surfaces due to flow obstruction, which is similar to flow across bluff bodies. Flow by-pass occurs through the gap between the wall of the extended surfaces and the channel wall which is clearly seen from the figure. Formations of eddies leads to increase in turbulence activity and hence increases the rate of heat transfer. Temperature distributions for without and with SES are shows in Fig. 7. It is observed that the temperature of tile and thimble are reduced for SES as compared to without extended surface. It is due to enhance the rate of heat transport by SES as a result of increasing in surface area. The total surface heat flux across the supporting plate and SES for the above cases is depicted in Fig. 8. It is seen that the inclusion of
Systematic studies for various mass flow rates with different heat flux have been performed using mesh M3. This particular grid is chosen after performing a detailed grid sensitivity study as discussed in Section 3.1. The outcomes of the parametric studies are depicted in Fig. 4(a) and (b). It has been observed that tile, thimble and helium temperature difference continuously increases with heat fluxes whereas the pressure drop remains almost constant as expected. Temperature distributions across tile, thimble and the helium temperature difference of the present simulation at varying heat fluxes is in good agreement with the reported results [2]. Analysis has been performed for nominal mass flow rate and is validated against the reported result. The temperature distributions in the solid and fluid regions are presented in Fig. 5. The maximum tile temperature occurs at the outer corner of the surface, and the maximum thimble temperature is noticed just above the central jet. 4. Results and Discussions 4.1. Comparative studies for flow & heat transfer analysis Comparative analysis for without and with SES have been carried out and presented for mass flow rate of 5 g/s with heat flux value of 10 MW/m2 . Flow and heat transfer features are described
Fig. 8. Total heat flux (W/m2 ) at solid-fluid interface (a) without SES and (b) with SES.
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Fig. 9. Maximum temperature as function of mass flow rate at different heat loads (a) tile and (b) thimble.
Fig. 10. Effect of Reynolds number on (a) heat transfer coefficient and (b) pressure drop at different heat loads.
extended surface increases heat flux distribution and heat transfer rate as compared to without extended surface as more surface area available for fluid to interact with the solid.
be corrected for the non homogeneous temperatures above the SES by average fin efficiency () as:
4.2. Extraction of thermal parameters
heff Ac = hact Ap + Ae
The effective heat transfer coefficient (heff ) for the case without SES is determined based on the temperature difference between the cooled surface wall and the bulk fluid as: heff =
q A (Tc − Tb ) Ac q
(4.2.1)
where represents an upper bound of average heat flux incident on the cooled surface. In order to determine heff , with SES, it must
(4.2.2)
where ‘hact ’ actual heat transfer coefficient. For the finger mockup without SES, hact = heff . Assuming no gap between inner steel cartridge and extended surfaces, an adiabatic boundary condition was assumed over the tip of the extended surfaces to determine ‘’ [19] from:
= tanh ml/ml
where m =
hact P Ke Ace
(4.2.3)
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Fig. 11. (a) Comparisons of tiles and (b) thimble maximum temperature for with and without SES at different heat loads.
Effectiveness () of the extended surface is defined as the ratio of heat transfer rate by SES to the without extended surface is written as: =
Ae × Ac
(4.2.4)
The corresponding pumping power (W) was then determined by: WHe =
˙ × pHe m He
(4.2.5)
where the symbols have their usual meanings and are described in the nomenclature.
Fig. 12. Comparisons of (a) effective wall heat transfer coefficient and (b) pressure drop for with and without SES at optimized heat loads.
4.3. Assessment of performance for flow parameters (without SES) The prime motive of this investigation is to find optimum mass flow rate at an acceptable pressure drop for cooling of finger mock-up. Towards this, numerical studies have been performed without considering SES at different heat fluxes value, viz., 8, 10 and 12 MW/m2 over a wide range of mass flow rates (5–20 g/s). Temperature distributions on the surface of tile and thimble for various mass flow rates for given heat loads are depicted Fig. 9(a) and (b), respectively. Fig. 9 shows that, tile and thimble brazing temperature are within design limits for lower heat flux value of 8 MW/m2
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Fig. 14. Comparison of pumping power with and without SES as function of mass flow rate.
4.4. Performance analysis with extended surfaces Thermal-hydraulics performance of finger mock-up has been analyzed to find the effectiveness of SES at specified heat load conditions describe in Section. 4.3. Four cases (Flow with & without SES) are analyzed with two heat flux, viz., 8 and 10 MW/m2 . Coolant mass flow rate is varied from 5 to 20 g/s. Maximum temperature values on tiles and thimble without, and with SES at different mass flow rates are depicted in Fig. 11. It is observed that, tiles and thimble temperature reduces with an increase in flows rate. The temperature values along the tiles and thimble with SES are significantly lower than that without SES. With the presence of SES, lesser mass flow rates (5 g/s for heat flux of 8 MW/m2 and 7.3 g/s for 10 MW/m2 ) are adequate to keep thimble temperature within the desire limits. Fig. 12 represents the variation of effective heat transfer coefficient (heff ) and pressure drop for without and with SES at different
Fig. 13. (a) Comparison of efficiency () and (b) effectiveness () with SES.
with mass flow rate of ∼10 g/s, whereas for higher heat flux (10–12 MW/m2 ), flow rate in the range of 14–19 g/s is required to keep thimble temperature within the design limits (1050 ◦ C). From the above figure, it implies that without SES, cooling finger will require very high mass flow rate and hence pumping power will be high to maintain the desired constraint. Fig. 10(a) and (b) represents heat transfer coefficient and pressure drop as a function of Reynolds number (Re). With increasing Re, both heff and pHe increases, however there is no appreciable effect observed with variation in heat flux due to the temperature variation of cooled wall surface.
Fig. 15. Comparison of mass flow rate without and with SES for different heat flux values.
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Fig. 17. Comparison of effective wall heat transfer coefficient for without and with SES as a function of pumping power.
4.5. Design analysis of divertor finger mock-up The dependence of pumping power on the proposed design of finger mock-up has been investigated for various mass flow rates and is presented in Fig. 14. It is seen that, the pumping power continuously increases with mass flow rate for a constant heat flux 10 MW/m2 ). Dashed line marks the design limit on pumping power. From the figure, clearly the mass flow rate should not exceed 10 g/s for the finger mock up without SES, which contradicts our earlier statements (Fig. 9b, Section 4.3). So the reference design is unable to tolerate 10 MW/m2 unless extended surface is added to it. It is also seen that, with the addition SES, even a lower mass flow rate ∼7.3 g/s is adequate to maintain the desired pumping power and thimble temperature limit for the above heat load. The maximum heat flux to be accommodated by finger mockup at allowable tile/thimble filler temperature constraint has been estimated as:
q =
Fig. 16. Comparison of pumping power (a) without SES and (b) with SES as a function of heat flux.
Re. It is notice that ‘heff ’ for both the cases increase with the rise in Re, but the increase is much faster with the presence of SES. This is due to increasing in surface area that enhances turbulence in flow and hence improves the effective heat transfer coefficient. Similarly, the values of pressure drop increase in the presence o f SES as compared to that without extended surfaces as seen from Fig. 12(b) as expected. Variation in efficiency () and effectiveness () with mass flows rate are depicted in Fig. 13. It is seen that both and are maximum at lower mass flow rate, and they start decreasing continuously mass flow further increases. This particular behaviour expected as both these factors inherently depend on hact . From the above comparison, it is implied that extended surfaces potentially enhance the thermal performance of the finger mock-up.
(Tc − Ti )
A/heff Ac + t/K
(4.5.1)
where t and K denote the thickness and thermal conductivity of the thimble, respectively. Fig. 15 depicts the variation of heat flux with mass flow rate for the cases with and without SES at 10 MW/m2 . It is observed that prototypical flow rates conditions for fusion power plant (∼7.3 g/s) with SES can accommodate a heat flux of 10 MW/m2 whereas it is only ∼4.5 MW/m2 without SES. In order to accommodate high heat flux exceeding 10 MW/m2 with the present design, melting limits of the tile/thimble brazing filler material should be increased. Parametric studies on pumping power without and with SES are analyzed for two different pumping power limits, viz., 10–15% of the total power removed from the tile and thimble. The corresponding results are depicted in Fig. 16. It is observed that with extended surface, finger mock-up can tolerate up to a maximum heat load of 10–11.2 MW/m2 at the expense of pumping powers 10% and 15% of the incident power. However, without the extended surfaces, it can abide by a highest load of only 5 MW/m2 . Fig. 17 compare the effective heat transfer coefficient obtained for heat flux 10 MW/m2 with pumping power for with and without extended surface. From the figure, it is found that at identical
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Fig. 18. 30◦ sector cooling finger mock-up (a) temperature distribution (b) Von-Mises stress distribution.
required pumping power, the mock-up with extended surface offer a higher heat transfer coefficient and thereby higher heat transfer enhancement. From all these parametric studies, it is evident that the use of extended surface in the finger mock up significantly increase the thermal performance associated with low additional pressure drop. To respect pumping power and thimble temperature limit, low mass flow rates (∼7.3 g/s) is adequate for the present design. It can also accommodate higher heat flux, if melting temperature limit of the tile and thimble brazing filler material further increased. 5. Thermo-Mechanical Analysis In order to verify the practicability of design, thermomechanical investigations are carried out using finite element based tools [1]. Towards this, nodal temperatures and pressure obtained from the CFD optimization studies are imported to the FEM software for structural analysis. For the entire solid domain, temperature dependent material properties [18] are considered, and frictionless boundary condition is considered at the bottom. Fig. 18 represented temperature distribution around the extended surface as well as the Von-Mises stress for the optimized geometry. Fig. 18(a) illustrate the maximum temperature occur at top of the mock up and also the temperature distribution around the extended surface is non homogeneous. It is seen that the maximum stress develops at the tile-thimble interface. However, the stresses developed in present design are within the permissible limit (Fig. 18b). 6. Conclusions The fluid flow and heat transfer characteristics of divertor cooling finger mock-up are investigated through jet impinging technique with sectorial extended surfaces (SES). The main objective of the present study is to numerically evaluate how addition of SES affects the thermal hydraulics performance of finger type divertor. Towards this, systematic studies by modelling of one such cooling finger have been carried out. As a first precursor, grid sensitivity analyses have been performed through a 30◦ sector model,
and the optimized grid has been arrived. In the second stage, flow and heat transfer features have been investigated and are compared with the published experimental and computational data. The calculated and measured values of the tile and thimble surface temperatures show good agreement with the reported results. Numerical investigations showed that addition of SES greatly increases thermal-hydraulic performance of the finger mock-up. Performance analysis indicates that present mock-up design should be acceptable for mass flow rate less than 7.3 g/s (Rejet ∼ 1,11,000) to ensure desired pumping power and thimble temperature limits. Adding the array of extended surface, double the maximum heat flux that can accommodated by the finger mock-up. This design can also accommodate high heat flux, if melting temperature limit of the tile and thimble brazing temperature are increased further. Thermo-mechanical analysis has been carried out for the finger mock-up through finite element based approach. It is seen that, all the stresses are within the permissible limit.
References [1] ANSYS FLUENT, Release 14.0, User Guide, Ansys, Inc., Lebanon, US, 2011. [2] B. Konˇcar, P. Norajitra, K. Oblak, Effect of nozzle sizes on jet impingement heat transfer in He-cooled divertor, Appl. Therm. Eng. 30 (2010) 697–705. [3] A.R. Raffray, S. Malang, X. Wang, Optimizing the overall configuration of He cooled W-alloy divertor for a power plant, Fusion Eng. Des. 84 (2009) 1553–1557. [4] C.B. Baxi, Evaluation of helium cooling for fusion divertors, Fusion Eng. Des. 25 (1994) 263–271. [5] C.B. Baxi, C.P.C. Wong, Review of helium cooling for fusion reactor application, Fusion Eng. Des. 51–52 (1994) 319–324. [6] E. Diegele, R. Krüssmann, S. Malang, P. Norajitra, G. Rizzi, Modular helium cooled divertor for power plant application, Fusion Eng. Des. 66–68 (2003) 383–387. [7] A. Pizzuto, P.J. Karditsas, C. Nardi, S. Papastergiou, HETS performances in Helium cooled power plant divertor, Fusion Eng. Des. 75–79 (2005) 481–484. [8] T. Ihli, R. Kruessmann, I. Ovchinnikov, P. Norajitra, V. Kuznetsov, R. Giniyatulin, An advanced He-cooled divertor concept: design, cooling technology, and thermohydraulic analyses with CFD, Fusion Eng. Des. 75–79 (2005) 371–375. ´ Efficient helium cooling methods for nuclear fusion devices: status [9] T. Ihli, M. Ilic, and prospects, Fusion Eng. Des. 84 (2009) 964–968. [10] M.S. Tillack, A.R. Raffraya, X.R. Wanga, S. Malangb, S. Abdel-Khalikc, M. Yodac, et al., Recent US activities on advanced he-cooled w-alloy divertor concepts for fusion power plants, Fusion Eng. Des. 86 (2011) 71–98.
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[11] F. Arbeiter, S. Gordeev, V. Heinzel, V. Slobodtchouk, Analysis of turbulence models for thermohydraulic calculations of helium cooled fusion reactor components, Fusion Eng. Des. 81 (2006) 1555–1560. [12] B.H. Mills, J.D. Rader, D.L. Sadowski, S.I. Abdel-Khalik, M. Yoda, Experimental investigation of fin enhancement for gas-cooled divertor concepts, Fusion Sci. Technol. 60 (2011) 190–196. [13] M.D. Hageman, D.L. Sadowski, M. Yoda, S.I. Abdel-Khalik, Experimental studies of the thermal performance of gas cooled plate type divertor, Fusion Sci. Technol. 60 (2011) 228–232. [14] V. Widak, P. Norajitra, Optimization of He-cooled divertor cooling fingers using a CAD–FEM method, Fusion Eng. Des. 84 (2009) 1973–1978. [15] I. Ovchinnikov, R. Giniyatulin, T. Ihli, G. Janeschitz, A. Komarov, R. Kruessmann, et al., Experimental study of DEMO helium cooled divertor target mock-ups to
[16] [17]
[18] [19]
estimate their thermal and pumping efficiencies, Fusion Eng. Des. 73 (2005) 181–186. S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, New York, 1980. G. Xie, B. Sunden, W. Zhang, Comparisons of pins/dimples/protrusions cooling concepts for a turbine blade tip-wall at high Reynolds numbers, J. Heat Transfer 133 (2011) 0619021–06190219. ITER, Material Properties Handbook, 2001, ITER Document No. G. 74 MA 90011-10W 0.1. Y. Cengel, A. Ghajar, Heat and Mass Transfer Fundamentals & Applications, Tata McGraw-Hill, Noida, India, 2011.
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Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Numerical studies on helium cooled divertor finger mock up with sectorial extended surfaces Sandeep Rimza a,∗ , Kamalakanta Satpathy a , Samir Khirwadkar a , Karupanna Velusamy b a b
Divertor and First wall Technology Development Division, Institute for Plasma Research (IPR), Bhat 382428 Gandhinagar, Gujarat, India Mechanics and Hydraulics Division, Reactor Design Group (RDG), Indira Gandhi Centre for Atomic Research (IGCAR), Kalpakkam 603102, Tamilnadu, India
h i g h l i g h t s • • • • •
Studies on heat transfer enhancement for divertor finger mock-up. Heat transfer characteristics of jet impingement with extended surfaces have been investigated. Effect of critical parameters that influence the thermal performance of the finger mock-up by CFD approach. Effect of extended surface in enhancing heat removal potential with pumping power assessed. Practicability of the chosen design is verified by structural analysis.
a r t i c l e
i n f o
Article history: Received 11 February 2014 Received in revised form 10 June 2014 Accepted 4 July 2014 Available online 6 August 2014 Keywords: Jet-impingement CFD Sectorial extended surfaces Tile Thimble Fusion reactor
a b s t r a c t Jet impinging technique is an advance divertor concept for the design of future fusion power plants. This technique is extensively used due to its high heat removal capability with reasonable pumping power and for safe operation. In this design, plasma-facing components are fabricated with numerous fingers cooled by helium jets to reduce the thermal stresses. The present study is focused towards finding an optimum performance of one such finger mock-up through systematic computational fluid dynamics (CFD) studies. Heat transfer characteristics of jet impingement have been numerically investigated with sectorial extended surfaces (SES). The result shows that addition of SES enhances heat removal potential with minimum pumping power. Detailed parametric studies on critical parameters that influence thermal performance of the finger mock-up have been analyzed. Thermo-mechanical analysis has been carried out through finite element based approach to know the state of stress in the assembly as a result of large temperature gradients. It is seen that the stresses are within the permissible limits for the present design. The whole numerical simulation has been carried out using general-purpose CFD software (ANSYS FLUENT, Release 14.0, User Guide, Ansys, Inc., 2011). Benchmark validation studies have been performed against high-heat flux experiments (B. Konˇcar, P. Norajitra, K. Oblak, Appl. Therm. Eng., 30, 697–705, 2010) and a good agreement is noticed between the present simulation and the reported results. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Nuclear fusion programme is one of the most promising options to meet the increasing energy demand. However, there are interesting challenges in successful design of the fusion power plants. One among them is design of the divertor which is an important
∗ Corresponding author. Tel.: +91 8141511655. E-mail addresses: [email protected], [email protected] (S. Rimza), [email protected] (K. Satpathy), [email protected] (S. Khirwadkar), [email protected] (K. Velusamy). http://dx.doi.org/10.1016/j.fusengdes.2014.07.008 0920-3796/© 2014 Elsevier B.V. All rights reserved.
part of the fusion power plant that handles extremely high heat flux generated in interior of the core. The function of the divertor is to remove fusion ash, plasma impurities and unburned fuel from the reactor first wall which affects the quality of the plasma. Due to its location in the reactor, it must survive massive volumetric heating by neutron and surface heating results from radiation and all plasma exhaust. Usage of helium as coolant has favourable safety characteristics, and it is capable of efficient heat transfer. Different type of helium-cooled divertor concepts has already been proposed by Raffray et al. [3] for a fusion power plant application. One of the designs uses small tungsten fingers, cooled by high pressure helium jets. The challenges and the design issues
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Nomenclatures A Ac Ap Ae Ace heff hact Ke k ˙ m P Re q t T Tb Ti To Tc WHe
area of top surface wall, m2 area of cooled inner surface wall, m2 area of bare plate between the sectorial extended surface, m2 surface area of the sectorial extended surface, m2 cross section area of the sectorial extended surface, m2 effective heat transfer coefficient, W/(m2 K) actual heat transfer coefficient, W/(m2 K) thermal conductivity of the sectorial extended surface, W/(m K) turbulent kinetic energy, m2 /s2 mass flow rate, kg/s perimeter of the sectorial extended surface, m reynolds number heat flux incident on the cooled surface, W/m2 thickness of thimble, m temperature, K bulk temperature of the fluid, (Ti + To )/2, K inlet temperature of fluid, K outlet temperature of fluid, K average temperature of cooled surface, K pumping power for helium, W
Greek symbols ε rate of dissipation, m2 /s3 efficiency sectorial extended surface density of fluid, kg/m3 effectiveness of the sectorial extended surface Subscripts act actual b bulk cooled c ce cross section of extended surface e extended surface eff effective helium He i inlet o outlet p plate
associated with the helium cooling viz., manifold sizes, pumping power, and leak prevention are studied by Baxi [4]. It was demonstrated that, the manifold sizes and the pumping power can be reduced to acceptable levels as per the design criteria. Baxi and Wong [5] reviewed various heat transfer enhancement techniques (viz., swirl tape, roughening, porous media etc.) to reduce the flow, pumping power and pressure requirements in helium cooling for fusion reactor applications. A modular helium cooled divertor for power plant application was studied by Diegele et al. [6] with an improved heat transfer technique. The result showed that the design has the potential of removing high heat flux (∼15 MW/m2 ). High Efficiency Thermal Shield (HETS) concept that relies on an abrupt change of momentum of the fluid was proposed by Pizzuto et al. [7]. The numerical studies along with experiments indicate that HETS solution is viable in order to attain a good heat transfer with limited pumping power. An advanced He-cooled divertor concept (DEMO) was studied by Ihli et al. [8] with modular target plate design through CFD simulations and achieved best cooling performance with jet impingement technique. Various cooling technologies for future fusion power plants were studied by
Ihli and Ilic´ [9]. Among different cooling technologies, V-rib based surface roughness approach for the first wall, the multiple impingement cooling techniques were identified as a suitable advantageous method. A comprehensive review of varying helium cooled divertor concepts for fusion power plant applications was reported by Tillack et al. [10]. In their review, they summarized recent US efforts on fusion power plants through analytical and experimental studies. Key issues were identified and future R&D (viz., fabrication, joining, material behaviour and reliability) has been widely discussed. Thermal hydraulic characteristics of fusion reactor components were analyzed by Arbeiter et al. [11] through various turbulence models using CFD code STAR–CD, and the results were validated against experiments. It is seen that, k–ε turbulence model with damping functions gives more accurate results for high heat flux test module. In order to increase the turbulence in the gas, thermal performance of the divertor design was experimentally studied by Mills et al. [12]. The objective of their studies is to assess the effect of fin’s addition on the thermal performance. Effect of fins on the heat transfer coefficient of plate-type divertor was investigated by Hageman et al. [13]. The results suggested that, adding fins nearly double the effective heat transfer coefficient. Thermal stress is regarded as an important limit for performance of the fusion power plants. Towards this, Widak and Norajitra [14] numerically investigated the thermo-mechanical aspect through finite element (FE) approach. Experimental study of DEMO helium cooled divertor target mock-ups has been done by Ovchinnikov et al. [15]. The objective of their study is to estimate thermal and pumping efficiencies of the divertor and concluded that, helium distributed cartridge options have high heat flux removing capability within mass flow ranges of 5–15 g/s. From the above literatures, it is observed that various designs for helium cooled divertor have been discussed but limited heat transfer enhancement techniques have been addressed. It is evident that manufacturing difficulties and high pressure drop associated with divertor design is of main concern. Towards this, a new type of sectorial extended surface (SES) has been proposed. This particular design is easy to manufacture and cost effective. The main objective of this paper is to numerically evaluate how addition of SES affects the thermal hydraulics performance of finger type divertor. In this regard, solution methodologies along with governing equations are presented in Section 2. As a precursor, benchmark validation studies have been performed for cooling finger against high heat flux experiments [2]. Effective heat transfer coefficients and pressure losses related to different heat fluxes, flow rates are numerically studied and are presented in Section 3. Enhancement of heat transfer is analyzed by introducing SES. Comparative studies for fluid flow features viz., turbulence kinetic energy, temperature and heat flux distributions are presented in Section 4. Finally, major conclusions have been arrived and are presented in Section 6.
2. Solution Methodology 2.1. Design description The whole divertor is divided into a number of small volumes known as cassettes, which are independently cooled. The plasma facing components of the divertor are splitted into a number of finger mock-ups in order to reduce the thermal stress, as presented in Fig. 1. Each mock-up consists of small hexagonal tile made up of tungsten (W) with sacrificial layers used as the thermal shield. Tiles are brazed to another material of tungsten alloy (WL-10) known as the thimble. A steel cartridge carrying the nozzle is placed concentrically inside the thimble. Fluid enters through the nozzle and
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Fig. 1. (a) Schematic of test section and (b) cross sectional view (all dimensions are in mm).
flows radially outwards through the space between cartridge and the thimble. Thermo-hydraulic performance of the mock up has been studied with addition of extended surfaces which is placed between cartridge and the thimble with a supporting plate of 1 mm thickness, as depicted in Fig. 2. The circumferential pitch was varied from first row to last row that leads to reduce the expense of machining to cover the top cooled surface. Extended surfaces are angularly constructed at every 30◦ sector, resulting 36 numbers of extended surface with 1 mm thickness, 0.8 mm pitch and 2 mm height. Circumferential gap between the extended surfaces are maintained at 0.4 mm. WL-10 is used as the material for SES due to its favourable machining property. The most important design criterion is to keep thimble temperature above ductile brittle transition
temperature (DBTT, ∼600 ◦ C) and below re-crystallization temperature (RCT, ∼1300 ◦ C). The brazing filler temperature of tiles and thimble should not exceed 1050 ◦ C [2] and pumping power should be ∼10% of incident power. The aim of this design is to reduce the temperature of the thimble as low as possible below brazing melting point at the expense of small pressure drop. 2.2. Governing equations The steady state forms of continuity, momentum and energy equations for an incompressible fluid used for the present numerical simulation are described in [16]. To resolve the Reynolds stresses, realizable k–ε turbulence model is employed with buoyancy, because it accurately predicts the performance for separation,
Fig. 2. (a) Bottom and (b) 3D view of SES (all dimensions are in mm).
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Fig. 3. (a) Geometry of cooling finger mock-up for validation (b) global grid pattern and (c) close-up view of CFD mesh. Table 1 Grid sensitivity analysis. Mesh
Control volume
Minimum grid spacing (mm)
Maximum tile temperature (◦ C)
Maximum thimble temperature (◦ C)
CPU time per iterations (s)
M1 M2 M3 M4
2.5 × 105 3.5 × 105 5 × 105 6 × 105
0.2 0.15 0.1 0.08
1687 1675 1651 1649
1087 1064 1004 1003
3 5 8 12
Maximum tile and thimble temperature reported [2] = 1660.3 ◦ C, 1010.73 ◦ C
recirculation, and flows involving boundary layers under pressure gradients [1] and also used to simulate flow and heat transfer in pin fin channel [17]. Pressure-velocity coupling between the incompressible Navier–Stokes and continuity equations is resolved using the Semi Implicit Pressure Linked Equations (SIMPLE) algorithm. To declare convergence at any iteration, the absolute errors in the discretized momentum and continuity equations are set to be 10−4 where as for energy, it is set to be 10−6 .
2.3. Boundary condition Due to exist of symmetry, a 30◦ sector model is considered for the present numerical simulation. Temperature dependent material properties are taken into consideration for the tile, thimble, and supporting plate with extended surfaces [18] whereas constant material properties are considered for cartridge. Carrier fluid (helium) is considered to be steady incompressible. Initial
Fig. 4. (a) Comparison between Helium pressure drop & temperature difference with heat flux. (b) Comparison maximum tile and thimble temperature against different heat flux.
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Fig. 5. Temperature distribution for mass flow rate of 6.8 g/s with a heat flux of 10 MW/m2 (a) reported results [2] and (b) present simulation.
temperature and pressure of the fluid are 600 ◦ C and 10 MPa, respectively [2]. The boundary conditions for the present 3D numerical simulations are as follows:
• No-slip conditions are imposed on the walls and at the extended surfaces. 3. Benchmark Validation
• Symmetry boundary conditions are imposed on the 30◦ cut sections. • Adiabatic boundary conditions are imposed on outer sides of the domain. • Top surface of the domain is imposed with constant heat flux. • Specified mass flow rate and temperature are considered at the inlet where as the outlet is specified with constant pressure.
Benchmarking the numerical calculation against suitable experimental data is of vital importance in CFD studies. To this end, the reference finger geometry of [2] is considered for the validation where high heat flux experiments [15] have been reported. The computational domain with the global grid patterns considered in the validation studies are depicted in Fig. 3.
Fig. 6. (a) Sectional top view of turbulence kinetic energy distribution (m2 /s2 ) around SES (b) bottom view of 30◦ sector of SES (c) velocity distribution (m/s).
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Fig. 7. Temperature distribution of cooling finger design (a) without SES and (b) with SES.
3.1. Grid sensitivity analysis In a CFD simulation, establishing grid size towards independent nature of the solution is an essential first step. In this regard, an attempt is made to determine the optimum mesh for the present numerical simulations. Different mesh sizes employed for the grid sensitivity study are shown in Table 1 along with maximum tile and thimble temperature. It can be noticed that the difference between temperature distributions of tiles and thimbles obtained from mesh M3 and M4 are small. The percentage of deviation in temperature among M3 and M4 are 0.12% and 0.09%, respectively. Though the change is a small but computational effort is significantly higher for M4 as compared to M3 thus justifying the use of mesh M3 for further investigations. 3.2. Parametric studies
in details. Fig. 6 depicts distribution of turbulence kinetic energy with the presence of SES. It is seen that, maximum kinetic energy occurs at the nozzle entrance due to high velocity at the centre. The sectional top view of velocity distribution around SES is depicted in Fig. 6(c). Symmetric eddies are formed in between the extended surfaces due to flow obstruction, which is similar to flow across bluff bodies. Flow by-pass occurs through the gap between the wall of the extended surfaces and the channel wall which is clearly seen from the figure. Formations of eddies leads to increase in turbulence activity and hence increases the rate of heat transfer. Temperature distributions for without and with SES are shows in Fig. 7. It is observed that the temperature of tile and thimble are reduced for SES as compared to without extended surface. It is due to enhance the rate of heat transport by SES as a result of increasing in surface area. The total surface heat flux across the supporting plate and SES for the above cases is depicted in Fig. 8. It is seen that the inclusion of
Systematic studies for various mass flow rates with different heat flux have been performed using mesh M3. This particular grid is chosen after performing a detailed grid sensitivity study as discussed in Section 3.1. The outcomes of the parametric studies are depicted in Fig. 4(a) and (b). It has been observed that tile, thimble and helium temperature difference continuously increases with heat fluxes whereas the pressure drop remains almost constant as expected. Temperature distributions across tile, thimble and the helium temperature difference of the present simulation at varying heat fluxes is in good agreement with the reported results [2]. Analysis has been performed for nominal mass flow rate and is validated against the reported result. The temperature distributions in the solid and fluid regions are presented in Fig. 5. The maximum tile temperature occurs at the outer corner of the surface, and the maximum thimble temperature is noticed just above the central jet. 4. Results and Discussions 4.1. Comparative studies for flow & heat transfer analysis Comparative analysis for without and with SES have been carried out and presented for mass flow rate of 5 g/s with heat flux value of 10 MW/m2 . Flow and heat transfer features are described
Fig. 8. Total heat flux (W/m2 ) at solid-fluid interface (a) without SES and (b) with SES.
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Fig. 9. Maximum temperature as function of mass flow rate at different heat loads (a) tile and (b) thimble.
Fig. 10. Effect of Reynolds number on (a) heat transfer coefficient and (b) pressure drop at different heat loads.
extended surface increases heat flux distribution and heat transfer rate as compared to without extended surface as more surface area available for fluid to interact with the solid.
be corrected for the non homogeneous temperatures above the SES by average fin efficiency () as:
4.2. Extraction of thermal parameters
heff Ac = hact Ap + Ae
The effective heat transfer coefficient (heff ) for the case without SES is determined based on the temperature difference between the cooled surface wall and the bulk fluid as: heff =
q A (Tc − Tb ) Ac q
(4.2.1)
where represents an upper bound of average heat flux incident on the cooled surface. In order to determine heff , with SES, it must
(4.2.2)
where ‘hact ’ actual heat transfer coefficient. For the finger mockup without SES, hact = heff . Assuming no gap between inner steel cartridge and extended surfaces, an adiabatic boundary condition was assumed over the tip of the extended surfaces to determine ‘’ [19] from:
= tanh ml/ml
where m =
hact P Ke Ace
(4.2.3)
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Fig. 11. (a) Comparisons of tiles and (b) thimble maximum temperature for with and without SES at different heat loads.
Effectiveness () of the extended surface is defined as the ratio of heat transfer rate by SES to the without extended surface is written as: =
Ae × Ac
(4.2.4)
The corresponding pumping power (W) was then determined by: WHe =
˙ × pHe m He
(4.2.5)
where the symbols have their usual meanings and are described in the nomenclature.
Fig. 12. Comparisons of (a) effective wall heat transfer coefficient and (b) pressure drop for with and without SES at optimized heat loads.
4.3. Assessment of performance for flow parameters (without SES) The prime motive of this investigation is to find optimum mass flow rate at an acceptable pressure drop for cooling of finger mock-up. Towards this, numerical studies have been performed without considering SES at different heat fluxes value, viz., 8, 10 and 12 MW/m2 over a wide range of mass flow rates (5–20 g/s). Temperature distributions on the surface of tile and thimble for various mass flow rates for given heat loads are depicted Fig. 9(a) and (b), respectively. Fig. 9 shows that, tile and thimble brazing temperature are within design limits for lower heat flux value of 8 MW/m2
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Fig. 14. Comparison of pumping power with and without SES as function of mass flow rate.
4.4. Performance analysis with extended surfaces Thermal-hydraulics performance of finger mock-up has been analyzed to find the effectiveness of SES at specified heat load conditions describe in Section. 4.3. Four cases (Flow with & without SES) are analyzed with two heat flux, viz., 8 and 10 MW/m2 . Coolant mass flow rate is varied from 5 to 20 g/s. Maximum temperature values on tiles and thimble without, and with SES at different mass flow rates are depicted in Fig. 11. It is observed that, tiles and thimble temperature reduces with an increase in flows rate. The temperature values along the tiles and thimble with SES are significantly lower than that without SES. With the presence of SES, lesser mass flow rates (5 g/s for heat flux of 8 MW/m2 and 7.3 g/s for 10 MW/m2 ) are adequate to keep thimble temperature within the desire limits. Fig. 12 represents the variation of effective heat transfer coefficient (heff ) and pressure drop for without and with SES at different
Fig. 13. (a) Comparison of efficiency () and (b) effectiveness () with SES.
with mass flow rate of ∼10 g/s, whereas for higher heat flux (10–12 MW/m2 ), flow rate in the range of 14–19 g/s is required to keep thimble temperature within the design limits (1050 ◦ C). From the above figure, it implies that without SES, cooling finger will require very high mass flow rate and hence pumping power will be high to maintain the desired constraint. Fig. 10(a) and (b) represents heat transfer coefficient and pressure drop as a function of Reynolds number (Re). With increasing Re, both heff and pHe increases, however there is no appreciable effect observed with variation in heat flux due to the temperature variation of cooled wall surface.
Fig. 15. Comparison of mass flow rate without and with SES for different heat flux values.
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Fig. 17. Comparison of effective wall heat transfer coefficient for without and with SES as a function of pumping power.
4.5. Design analysis of divertor finger mock-up The dependence of pumping power on the proposed design of finger mock-up has been investigated for various mass flow rates and is presented in Fig. 14. It is seen that, the pumping power continuously increases with mass flow rate for a constant heat flux 10 MW/m2 ). Dashed line marks the design limit on pumping power. From the figure, clearly the mass flow rate should not exceed 10 g/s for the finger mock up without SES, which contradicts our earlier statements (Fig. 9b, Section 4.3). So the reference design is unable to tolerate 10 MW/m2 unless extended surface is added to it. It is also seen that, with the addition SES, even a lower mass flow rate ∼7.3 g/s is adequate to maintain the desired pumping power and thimble temperature limit for the above heat load. The maximum heat flux to be accommodated by finger mockup at allowable tile/thimble filler temperature constraint has been estimated as:
q =
Fig. 16. Comparison of pumping power (a) without SES and (b) with SES as a function of heat flux.
Re. It is notice that ‘heff ’ for both the cases increase with the rise in Re, but the increase is much faster with the presence of SES. This is due to increasing in surface area that enhances turbulence in flow and hence improves the effective heat transfer coefficient. Similarly, the values of pressure drop increase in the presence o f SES as compared to that without extended surfaces as seen from Fig. 12(b) as expected. Variation in efficiency () and effectiveness () with mass flows rate are depicted in Fig. 13. It is seen that both and are maximum at lower mass flow rate, and they start decreasing continuously mass flow further increases. This particular behaviour expected as both these factors inherently depend on hact . From the above comparison, it is implied that extended surfaces potentially enhance the thermal performance of the finger mock-up.
(Tc − Ti )
A/heff Ac + t/K
(4.5.1)
where t and K denote the thickness and thermal conductivity of the thimble, respectively. Fig. 15 depicts the variation of heat flux with mass flow rate for the cases with and without SES at 10 MW/m2 . It is observed that prototypical flow rates conditions for fusion power plant (∼7.3 g/s) with SES can accommodate a heat flux of 10 MW/m2 whereas it is only ∼4.5 MW/m2 without SES. In order to accommodate high heat flux exceeding 10 MW/m2 with the present design, melting limits of the tile/thimble brazing filler material should be increased. Parametric studies on pumping power without and with SES are analyzed for two different pumping power limits, viz., 10–15% of the total power removed from the tile and thimble. The corresponding results are depicted in Fig. 16. It is observed that with extended surface, finger mock-up can tolerate up to a maximum heat load of 10–11.2 MW/m2 at the expense of pumping powers 10% and 15% of the incident power. However, without the extended surfaces, it can abide by a highest load of only 5 MW/m2 . Fig. 17 compare the effective heat transfer coefficient obtained for heat flux 10 MW/m2 with pumping power for with and without extended surface. From the figure, it is found that at identical
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Fig. 18. 30◦ sector cooling finger mock-up (a) temperature distribution (b) Von-Mises stress distribution.
required pumping power, the mock-up with extended surface offer a higher heat transfer coefficient and thereby higher heat transfer enhancement. From all these parametric studies, it is evident that the use of extended surface in the finger mock up significantly increase the thermal performance associated with low additional pressure drop. To respect pumping power and thimble temperature limit, low mass flow rates (∼7.3 g/s) is adequate for the present design. It can also accommodate higher heat flux, if melting temperature limit of the tile and thimble brazing filler material further increased. 5. Thermo-Mechanical Analysis In order to verify the practicability of design, thermomechanical investigations are carried out using finite element based tools [1]. Towards this, nodal temperatures and pressure obtained from the CFD optimization studies are imported to the FEM software for structural analysis. For the entire solid domain, temperature dependent material properties [18] are considered, and frictionless boundary condition is considered at the bottom. Fig. 18 represented temperature distribution around the extended surface as well as the Von-Mises stress for the optimized geometry. Fig. 18(a) illustrate the maximum temperature occur at top of the mock up and also the temperature distribution around the extended surface is non homogeneous. It is seen that the maximum stress develops at the tile-thimble interface. However, the stresses developed in present design are within the permissible limit (Fig. 18b). 6. Conclusions The fluid flow and heat transfer characteristics of divertor cooling finger mock-up are investigated through jet impinging technique with sectorial extended surfaces (SES). The main objective of the present study is to numerically evaluate how addition of SES affects the thermal hydraulics performance of finger type divertor. Towards this, systematic studies by modelling of one such cooling finger have been carried out. As a first precursor, grid sensitivity analyses have been performed through a 30◦ sector model,
and the optimized grid has been arrived. In the second stage, flow and heat transfer features have been investigated and are compared with the published experimental and computational data. The calculated and measured values of the tile and thimble surface temperatures show good agreement with the reported results. Numerical investigations showed that addition of SES greatly increases thermal-hydraulic performance of the finger mock-up. Performance analysis indicates that present mock-up design should be acceptable for mass flow rate less than 7.3 g/s (Rejet ∼ 1,11,000) to ensure desired pumping power and thimble temperature limits. Adding the array of extended surface, double the maximum heat flux that can accommodated by the finger mock-up. This design can also accommodate high heat flux, if melting temperature limit of the tile and thimble brazing temperature are increased further. Thermo-mechanical analysis has been carried out for the finger mock-up through finite element based approach. It is seen that, all the stresses are within the permissible limit.
References [1] ANSYS FLUENT, Release 14.0, User Guide, Ansys, Inc., Lebanon, US, 2011. [2] B. Konˇcar, P. Norajitra, K. Oblak, Effect of nozzle sizes on jet impingement heat transfer in He-cooled divertor, Appl. Therm. Eng. 30 (2010) 697–705. [3] A.R. Raffray, S. Malang, X. Wang, Optimizing the overall configuration of He cooled W-alloy divertor for a power plant, Fusion Eng. Des. 84 (2009) 1553–1557. [4] C.B. Baxi, Evaluation of helium cooling for fusion divertors, Fusion Eng. Des. 25 (1994) 263–271. [5] C.B. Baxi, C.P.C. Wong, Review of helium cooling for fusion reactor application, Fusion Eng. Des. 51–52 (1994) 319–324. [6] E. Diegele, R. Krüssmann, S. Malang, P. Norajitra, G. Rizzi, Modular helium cooled divertor for power plant application, Fusion Eng. Des. 66–68 (2003) 383–387. [7] A. Pizzuto, P.J. Karditsas, C. Nardi, S. Papastergiou, HETS performances in Helium cooled power plant divertor, Fusion Eng. Des. 75–79 (2005) 481–484. [8] T. Ihli, R. Kruessmann, I. Ovchinnikov, P. Norajitra, V. Kuznetsov, R. Giniyatulin, An advanced He-cooled divertor concept: design, cooling technology, and thermohydraulic analyses with CFD, Fusion Eng. Des. 75–79 (2005) 371–375. ´ Efficient helium cooling methods for nuclear fusion devices: status [9] T. Ihli, M. Ilic, and prospects, Fusion Eng. Des. 84 (2009) 964–968. [10] M.S. Tillack, A.R. Raffraya, X.R. Wanga, S. Malangb, S. Abdel-Khalikc, M. Yodac, et al., Recent US activities on advanced he-cooled w-alloy divertor concepts for fusion power plants, Fusion Eng. Des. 86 (2011) 71–98.
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[11] F. Arbeiter, S. Gordeev, V. Heinzel, V. Slobodtchouk, Analysis of turbulence models for thermohydraulic calculations of helium cooled fusion reactor components, Fusion Eng. Des. 81 (2006) 1555–1560. [12] B.H. Mills, J.D. Rader, D.L. Sadowski, S.I. Abdel-Khalik, M. Yoda, Experimental investigation of fin enhancement for gas-cooled divertor concepts, Fusion Sci. Technol. 60 (2011) 190–196. [13] M.D. Hageman, D.L. Sadowski, M. Yoda, S.I. Abdel-Khalik, Experimental studies of the thermal performance of gas cooled plate type divertor, Fusion Sci. Technol. 60 (2011) 228–232. [14] V. Widak, P. Norajitra, Optimization of He-cooled divertor cooling fingers using a CAD–FEM method, Fusion Eng. Des. 84 (2009) 1973–1978. [15] I. Ovchinnikov, R. Giniyatulin, T. Ihli, G. Janeschitz, A. Komarov, R. Kruessmann, et al., Experimental study of DEMO helium cooled divertor target mock-ups to
[16] [17]
[18] [19]
estimate their thermal and pumping efficiencies, Fusion Eng. Des. 73 (2005) 181–186. S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, New York, 1980. G. Xie, B. Sunden, W. Zhang, Comparisons of pins/dimples/protrusions cooling concepts for a turbine blade tip-wall at high Reynolds numbers, J. Heat Transfer 133 (2011) 0619021–06190219. ITER, Material Properties Handbook, 2001, ITER Document No. G. 74 MA 90011-10W 0.1. Y. Cengel, A. Ghajar, Heat and Mass Transfer Fundamentals & Applications, Tata McGraw-Hill, Noida, India, 2011.