Thermohydraulics of Rib-Roughened Helium Gas Running Cooling Channels for First Wall Applications

Transcription

1 EUROFUSION WPBB PR(15)01 S. Ruck et al. Thermohydraulics of Rib-Roughened Helium Gas Running Cooling Channels for First Wall Applications Preprint of Paper to be submitted for publication in Fusion Engineering and Design This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme under grant agreement No The views and opinions expressed herein do not necessarily reflect those of the European Commission.

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3 Thermohydraulics of Rib-Roughened Helium Gas Running Cooling Channels for First Wall Applications Sebastian Ruck, Frederik Arbeiter Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen, Germany Improved cooling channel designs of helium cooled first wall applications focus on efficient heat transfer enhancement and reduced material temperatures, even for high incident heat flux densities of more than 0.5 MW/m². To this end, thermohydraulics of turbulent flow in a non-uniformly heated, one-sided rib-roughened channel with squared, round-edged cross section were predicted by Detached Eddy Simulations (DES) at Reynolds numbers of Re Dh = 2.5E4, 5.0E4 and 10.5E4 respectively and at a heat up rate of q+=5.99e-3, 2.99E-3 and 1.42E-3, encompassing the envisaged operation envelope of helium cooled first wall cooling channels. The rib-roughened channel wall consists of centrally positioned, transversally oriented rib elements with a rib-pitch-to-rib-height-ratio of p/e=10, a rib-height-to-hydraulic-diameter-ratio of e/d h = and a rib-length-to-channel-width-ratio of l/w=0.6. Mean flow and heat transfer quantities, turbulent fluxes and flow structures were analyzed. Anisotropic, large-scale eddies originated in separated shear layers are shed vertically and laterally to the flow. Maximum heat transfer correlates with regions of maximum span- and crosswise turbulent fluctuations and is located at the rib leading edge. Minimum heat transfer occurs within the region of the counter-rotating vortex behind the rib. Keywords: DES, Rib-Roughened Channel, Helium-Cooling, Heat Transfer Enhancement. 1. Introduction High-pressure helium gas is a favorable heat transfer medium for cooling plasma-facing first wall applications of fusion power reactors. The heat generated by fusion is transferred from the plasma through the first wall to the 8-MPa-high-pressure helium gas flow. Improved channel designs with rib-roughened surfaces facilitate localized heat transfer augmentation and ensure reduced material temperatures and increased durability, even for the estimated (incident) high heat flux densities ranging from 0.14 MW/m 2 to 0.64 MW/m 2 [1]. The heat transfer augmentation is caused by the rib elements inducing a complex and highly three-dimensional unsteady flow field. Shear layer separation, flow reattachment, vortex shedding, unsteady secondary flow motion and boundary redevelopment dominate the flow physics in the ribroughened channel and significantly contribute to the heat transfer enhancement [2]. Unfortunately, ribroughened walls can cause inappropriate thermohydraulic conditions. The induced rib-wallroughness and the development of three-dimensional unsteady flow structures increase the flow resistance and pressure drop, and thus, the pumping power is raised for constant mass flow [3]. Furthermore, flow stagnation regions are developed at the rib-channel-wall corners or at recirculation zones [4]. An accompanying decrease in momentum and energy transport may cause surface temperature hot spots in unfavorable channel designs and lead to possible material damages. Detailed insight into the complex flow structures and an accurate prediction of heat transfer coefficients and friction factors is crucial for increasing the thermohydraulic performances and reducing the aforementioned shortcomings. Further improvements need to be focused on two main issues: a. heat transfer enhancement with modest pumping power increase, b. homogenous surface temperatures distributions without temperature hot spots and c. competitive and cost-efficient manufacturing. Numerous investigations of turbulent flows in heated channels with rib-roughened walls were carried out analysing the thermohydraulic performance for varying flow conditions and rib geometries. Wall temperatures and pressure drops were determined by thermocouple probes and pressure taps for uniformly heated rectangular channels with two-sided, opposite and x- sided rib-roughened walls, composed of parallel ribs with squared cross-section [3,5-10]. The averaged friction factor and the Stanton number of the ribroughened walls increases for increasing rib-height and decreases for increasing rib-spacing. Whereas the Stanton number of the rib-roughened walls decreases for increasing Reynolds numbers, the averaged friction factor is Reynolds number independent. Mean velocity distributions and turbulent fluctuations were determined by laser Doppler measurements for turbulent channel flows with one-sided [4,11-14] and/or two-sided, opposite rib-roughened walls [2,4,12]. The temperature fields were measured by holographic interferometry [4,11] and liquid-crystal thermometry [2] and local heat transfer distribution along the rib-roughened and side walls were determined. Corresponding numerical simulations applying different approaches and turbulence models were carried out [15,4,11-14,16-23]. Local heat transfer is dominated by the separated and reattached shear layers and secondary flow motion. Minimum heat transfer coincides with the flow stagnation regions at concave rib-wall-corners and maximum local heat transfer corresponds to regions of author s sebastian.ruck@kit.edu

4 high turbulent kinetic energy and velocities at the rib top and in the vicinity of reattachment behind the rib. The present paper reports on turbulent flow and heat transfer characteristics in a non-uniformly heated, onesided rib-roughened cooling channel intended for helium cooled first wall applications. 2. Material and Methods 2.1 Turbulence modelling and numerical methods The applicability of computational methods for predicting turbulent flows with heat transfer depends strongly on its turbulence treatment. While the concept of Large Eddy Simulations (LES) is to resolve the largescales and to model the unresolved dissipation related small-scales, the Reynolds-Averaged-Navier-Stokes (RANS) approach bases on modelling the entirety of the turbulent scales and calculating the time-averaged mean flow quantities. Near-wall resolving LES are proven for predicting turbulent flows with heat transfer [20-22], but limited for engineering applications by its demanding grid requirements and its enormous numerical cost at high Reynolds numbers ( times higher compared to RANS [24]). Therefore, most of computational thermohydraulic predictions base on the Reynolds- Averaged-Navier-Stokes approach and isotropic eddyviscosity turbulence models. However, a multitude of studies comparing numerical and experimental results shows that RANS is inappropriate for thermohydraulic prediction of flows (in rib-roughened channels) with flow separation and reattachment [4,13,15,17,18,23]. Slight improvements in computational heat transfer predictions were obtained by algebraic Reynolds stress models which account for turbulence anisotropy [4], the v-2-f model [17] or differential stress models [18,19]. In the last decade, Detached Eddy Simulation has been established as a reliable computational method for turbulent flows at moderate numerical cost. It captures anisotropic turbulence in the separated flow regions, resolves transient effects and is not limited to timeaveraged global performance estimations. Thermohydraulics of turbulent flow in rib-roughened channels [23] at Re Dh =2E4 and over a heated backwardfacing step [25] at high Reynolds numbers Re h =2.8E4 were accurately predicted by DES. For the present study the delayed DES approach (DDES) [26] was applied. Turbulent and subgrid-scales are modelled by the k-ω- SST [27] and the DKEM model [28] respectively, with a turbulent Prandtl number of The DES constant of the k-ε-branch was 0.61 and of the k- ω-branch was Governing flow and energy equations were discretized with the finite volume method and solved by the pressure-based segregated solver [29]. The SIMPLE algorithm was applied for the pressure-velocity field coupling. For DES the convective term of the momentum equation was determined by the bounded central differencing scheme and the convective terms of turbulent kinetic energy, specific dissipation rate, density and energy equation were approximated by second order upwind discretization scheme. Pressure terms were interpolated by a second order scheme and the diffusion terms were second order central-differenced. For temporal integration the bounded second order implicit scheme was applied and the gradients were Least- Square-Cell-Based approximated. 2.2 Computational Details The computational domain includes the setup of corresponding experiments and contains a fluid and a solid domain. It is displayed in Fig.1. The solid domain consists of the channel outer walls and a heating unit below the rib-roughened channel with a mounting support for a heating rod. It was divided by a plane positioned 3e below the rib-roughened channel wall, representing the plasma-faced first wall. The heating unit cross section was shape optimized by additional numerical studies, representing the heat flux distribution of a uniformly heated plasma-faced first wall. The fluid domain contains a non-heated smooth inlet domain, the heated one-side rib-roughened channel and a non-heated smooth outlet domain. The fluid domain cross section was 15e x 15e with round-edges of 2e radius. The ribroughened wall is faced to the heating unit. The fluid domain is composed of 16 centrally positioned, transversally oriented rib elements with a rib-height of e=1 mm, a rib-pitch-to-rib-height-ratio of p/e=10, a ribheight-to-hydraulic-diameter-ratio of e/d h = and a rib-length-to-channel-width-ratio of l/w=0.6. The fluid domain consists of 8.5E6 hexahedral cells. Local grid refinement was performed in the vicinity of the ribelements generating a focus region with almost isotropic cells. The boundary layers adjacent to smooth and ribroughened channel walls were resolved by 18 nodes with 4 nodes located inside the viscous sublayer yielding a wall-normal first spacing of z+<1. Fig. 1. Computational Domain

5 The inflow conditions were obtained separately by periodic, isothermal flow simulations of smooth channel domains with identical dimensions and boundary conditions as the inlet section of the rib-roughened channel domains. The inlet velocity was fully turbulent developed. Adiabatic conditions were assumed for the outer walls of the solid domain and a constant heat flux density was applied though the heating unit surface of the solid domain. The fluid was ideal gas and the solid was stainless steel [X6CrNiMoTi (316Ti)]. The specific heat capacity, thermal conductivity and fluid viscosity were temperature dependent functions [30,31]. Flow and heat transfer conditions were scaled from helium cooled first wall applications - with an inlet pressure of 8MPa, an fluid inlet temperature of 340 C, a mass flow rate of kg/s and a constant heat flux density at the plasma faced wall of 0.75MW/m 2 - by the Reynolds numbers and heat up rate at the ribroughened channel wall. The computations were carried out for a heat up rate of q+=5.99e-3, 2.99E-3 and 1.42E-3 respectively and Reynolds numbers of Re= 2.5E4, 5.0E4 and 1.05E5. 3. Results and Discussion The presented flow and heat distributions are timeaveraged and the overall values are time- and spaceaveraged. A time-average over ten flow-through times were carried out. For ensuring a fully developed flow field, data were captured between the 12th and 14th rib. The ribbed-side Nusselt number was calculated from the wall heat flux density and the wall temperatures at the rib-roughened wall (projected area and rib-side area): /! / ; with the spatial averaged fluid temperature, the hydraulic diameter! and thermal conductivity. The friction factor was determined from the streamwise pressure drop $ : % $! & ' ( /2 * +, ( with the channel cross section ', the mass flow rate +, and the density &. Nusselt numbers were normalized by the McAdams/Dittus-Boelter correlation / and the friction factors by Blasius correlation for fully developed turbulent flow in a smooth circular channel % /0 51.(. 3.1 Overall friction and heat transfer predictions The averaged overall friction factor ratios and Nusselt number ratios are summarized in Table 1. Correlations for heat transfer and friction prediction of channels with varying numbers of rib-roughened walls [7], combined with a friction roughness function of / and a heat transfer roughness function of (2 for channels with p/e=10 [3], were compared with the present simulation results. Table 1. Averaged friction factors and Nusselt numbers. Re f/f s Nu r /Nu s DES 2.5E DES 5.0E DES 1.05E [1,13] 2.5E [1,13] 5.0E [1,13] 1.05E For all simulations, flow resistance and heat transfer are increased by the rib-wall-roughness and the development of three-dimensional unsteady flow structures. Nusselt number ratios decrease and friction factor ratios increase slightly for increasing Reynolds numbers. The present results differ from previous RANS studies [16]. The correlated values agree with the present results reasonably for Re=2.5E4, better for Re=5.0E4 and well for Re=1.05E5. The Nusselt number and friction factor range is reduced and better estimations were obtained with a modified friction roughness functions taking the roughness Reynolds number 0 6 into account / The 0 6 dependency is referred to the strong contribution of spanwise flow motion to the heat and friction development for the present channel design. For increasing Reynolds Fig.2. Flow over ribs - structures visualized by iso-surfaces of the Q-Criterion and colored by the static pressure

6 Fig. 3. Nusselt number ratios numbers this dependency is reduced. In general, the results indicate, that correlations for heat transfer and friction prediction of squared channels with varying numbers of rib-roughened walls are applicable to channel design without continuous ribs. 3.2 Flow flied For investigating the transient flow field, instantaneous and time-averaged results are analyzed. Vortex structures of the flow at Re Dh =1.05E5, visualized by iso-surfaces of the Q-Criterion and colored by the static pressure, are displayed in Fig. 2. According to flow and heat experiments in one-sided rib-roughened channels [2], the flow field can be classified into a low pressure zone and a high pressure zone respectively, behind and in front of the rib. This was observed for all Reynolds numbers. The flow field is highly three-dimensional and dominated by shear layer separation and reattachment, recirculation and secondary flow motion. The flow impacts on the upstream rib-front surface and is deflected side- and upwards. It is accelerated in vertical and lateral direction with corresponding local velocity maxima at the lateral upper rib-end. Flow separates at the leading top- and side-edge forming shear layers and reattaches on the rib-top and rib-side surface, before it detaches again. Recirculation regions are developed on the rib-top and at rib-side surface. Anisotropic, largescale flow structures are originated in the shear-layers. Vortical flow structures are shed vertically and laterally to the core flow due to the up- and sideward flow motion in the vicinity of the leading edge. The sudden crosssection expansion decelerates the flow. Thus, the flow separated on the rib-top surface is deflected towards the lower channel wall and the flow structures separated on the rib-side surface move centrally downward. Shear layers reattach at the lower channel wall surrounding the beneath located highly unsteady main recirculation region. The downward and central flow motion behind the rib yields a constriction of the recirculation region with a reduction of its streamwise elongation in lateral direction. Eddies impinge on the lower channel wall or sweep further downstream without wall-interaction. The impinging eddies break up and move further downstream or upstream into the recirculation region induced by the adverse pressure gradient. Similar flow motion was captured for separated and reattached turbulent flows over a heated backward-facing step [32]. The overriding eddies are entrained by the core flow or impact on the successive rib. In front of the rib, flow detaches from the lower wall forming additional recirculation regions. The mean recirculation regions are characterized by recirculation vortices on the rib-top and rib-side surfaces, in front and behind the rib. The main recirculation region behind the rib contains a spacious recirculation vortex and a small counter-rotating vortex close to the rib-rear surface. The expansion and strength of all vortices vary. 3.3 Heat Transfer The Nusselt number ratios of the rib-roughened wall at Y/e=0.0 and Y/e=2.5 for the entire Reynolds number range are shown in Fig. 3. The distributions differ from RANS studies [4,11,17] and show several similarities with LES computations [21,22]. The heat transfer increases rapidly along the rib-front surface and reaches its maximum slightly below the leading-edge (B). A short gradient alternation of the steeply rising curve indicates regions of mean flow deceleration. Peak values at the leading edge vary from / - =3.6 for Re=1.05E5 at Y/e=0.0 to / - =5.2 for Re=2.5E4 at Y/e=2.5. Heat transfer enhancement correlates with the shedding of flow structures at the rib edges. These eddies transport hot fluid from the heated rib towards the core flow and, in reversed direction, cold fluid is transferred from the core flow towards the rib-roughened wall. According to experimental [2,12] and large-scale resolving computational investigations [22,23], it was found, that maximum heat transfer correlates with regions of maximum span- and crosswise turbulent fluctuations (: ;< / ;= >0.3,? ;< / ;= >0.2 ) at the rib-top. Heat transfer decreases further downstream and rises to a local maximum at the rear-edge of the rib (C). The corresponding peak values remain nearly constant for the Reynolds number range. At the rear-rib surface heat transfer is reduced and drops gradually within the region of the counter-rotating vortex. It reaches the absolute minimum for Re=2.5E4 and 5.0E4, and a local minimum for Re=1.05E5 respectively, slightly downstream of the concave rib-channel-wallcorner (D). At the stagnation region between the

7 counter-rotating and the main recirculation vortex, heat transfer reaches a local minimum for Re=2.5E4 and 5.0E4, and the absolute minimum for Re=1.05E5. The different location of absolute minimum heat transfer is referred to a Reynolds number dependent flow development behind the rib. Further downstream heat transfer rises within the recirculation region and Nusselt number ratios are decreases for increasing Reynolds numbers. Similar to the thermohydraulics of heated backward-facing step flow [25,26], the heat transfer enhancement is caused by the impingement of separated turbulent eddies, breaking down the boundary layer and thinning the viscous sublayer adjacent to the channel. Downstream of mean reattachment, the impact of the eddies are reduced and boundary layers are redeveloped leading to heat transfer reduction. In front of the rib, heat transfer rises steeply. It is followed by a local minimum above the concave rib-channel-wall-corner (A) coinciding with regions of low flow velocities and flow stagnation. The heat transfer rise upstream the rib agree qualitatively well with comparable LES results [21] and experimental findings [13,14]. In contrast to previous RANS studies of rib-roughened channel walls [4], temperature hot spots are only expected downstream of the concave rib-channel-wall-corner. The reduction of heat transfer loss in front of the rib is referred to the strong spanwise flow motions due the presented channel design without continuous rib and to the scale-resolving numerical approach. All peak values decrease for increasing Reynolds numbers. Further design improvements need to be focused on the reduction of the absolute heat transfer minimum in the rear of the ribs. 4. Conclusion For the first time, heat transfer in a non-uniformly heated, one-sided rib-roughened channel with squared, round-edged cross section was predicted by Detached Eddy Simulations. The transient flow field, overall friction and heat transfer predictions and the local heat transfer were analyzed. The main findings are summarized as follows. a. Correlations for heat transfer and friction prediction of channels with varying numbers of rib-roughened walls [7], combined with friction and heat transfer roughness function of channels with p/e=10 [3] show acceptable agreement with the simulation results. For the presented geometry, a friction roughness functions of / is derived. The present heat transfer and friction factors differ from previous RANS studies [16]. b. The flow field is highly three-dimensional and dominated by shear layer separation and reattachment, recirculation and secondary flow motion. Anisotropic, large-scale flow structures are originated in the shear-layers shed vertically and laterally to the core flow due to the up- and sideward flow motion. These eddies transport hot fluid from the heated rib towards the core flow and, in reversed direction, cold fluid is transferred from the core flow towards the rib-roughened wall. c. Maximum heat transfer occurs at the rib leading edge and correlates with regions of maximum spanand crosswise turbulent fluctuations. d. Minimum heat transfer occurs within the region of the counter-rotating vortex behind the rib. e. Large-scale flow structures, friction factors and heat transfer are well resolved by the DES at flow conditions of helium cooled first wall applications. Hence, it is suggested for the thermal design of ribroughened helium gas running cooling channels of first wall applications. The present channel design is promising for cooling channels of first wall applications, but further improvements focusing on the rib design are important to reduce temperature hot spots in the vicinity of the ribs. Acknowledgement This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme under grant agreement No The views and opinions expressed herein do not necessarily reflect those of the European Commission. References [1] R. Wenning et al., DEMO Exhaust Challenges Beyond ITER, Proceedings 42nd EPS Conference on Plasma Physics, Lisbon, Portugal, 2015 [2] G. Rau et al., The Effect of Periodic Ribs on the Local Aerodynamic and Heat Transfer Performance of a Straight Cooling Channel, J. Turbomach. 120 (1998) [3] J. C. Han, Heat Transfer and Friction in Channels With Two Opposite Rib-Roughened Walls, J. Heat Transfer 106 (1984) [4] T.-M. 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