Unsteady RANS and LES Analyses of Hooper s Hydraulics Experiment in a Tight Lattice Bare Rod-bundle

Transcription

1 Unsteady RANS and LES Analyses of Hooper s Hydraulics Experiment in a Tight Lattice Bare Rod-bundle L. Chandra* 1, F. Roelofs, E. M. J. Komen E. Baglietto Nuclear Research and consultancy Group Westerduinweg 3, 1755 ZG, Petten, The Netherlands. Tel: , Fax: * chandra@nrg.eu CD-adapco, New York 60 Broadhollow Rd. Melville, NY ABSTRACT Several experiments have already reported the existence of flow oscillations in a tight lattice bare rod-bundle. This in-turn results in temperature oscillations, when heat transfer is also involved. Consequently, assessment of flow oscillations plays an important role in the design of future innovative reactor systems as proposed by the Generation IV International Forum. Literature review reveals that such flow oscillations have recently numerically been analyzed using Unsteady Reynolds Averaged Navier-Stokes (URANS) and Large Eddy Simulation (LES) techniques. The objective is to assess URANS and LES turbulence modelling techniques for application in tight rod bundles to determine: temperature oscillations arising from flow oscillations in a tight lattice rod bundle occurrence of flow induced vibrations To this purpose, as a first step this paper will present URANS and LES analyses of the hydraulics experiment performed by Hooper in a tight lattice bare rod-bundle (pitch-todiameter ratio is 1.107). These simulations are performed using STAR-CCM+. The numerical analyses reveal the existence of flow oscillation as observed in the experiment. This is concluded from the analyzed instantaneous velocities at a plane and the time dependent velocities at a point in the computational domain. As expected, for a given grid and time step, these results show that the employed LES approach resolves smaller structures compared to the employed URANS approach. The influence of the flow on the surface of the rods is assessed by analyzing the wall shear stress magnitude and its power spectra. Key words: URANS, LES, flow oscillation, rod-bundle. 1: Current address: Indian Institute of Technology, Rajasthan, India. 1 / 13

2 1. INTRODUCTION Six innovative reactor concepts are considered under Gen IV International Forum, [1]. Usually, in Computational Fluid Dynamics (CFD) analyses of fuel assembly subchannels, Reynolds Averaged Navier Stokes (RANS) is employed for evaluation of the reactor core in these systems. The applicability of RANS approaches has already been assessed for widely spaced rod-bundles, see e.g. [2], [3]. The isotropic first-order two-equation based k-ε or k-ω models are known to be incapable of capturing the secondary flows and resulting anisotropy, which are inherent in a rod-bundle. This necessitates the use of second-order Reynolds Stress Model (RSM) or non-linear anisotropic eddy viscosity based turbulence models as outlined e.g. by [4], [5], [6], [7]. Well-instrumented and detailed experiments by e.g. [8], [9] and [10] have provided valuable insight to the flow hydraulics in a rod-bundle. Such experiments benefit from the fact that the flow hydraulics mainly depends on the flow conditions and is largely independent of the fluids, see e.g. [11]. The hydraulics experiments by [10] and the thermal-hydraulics experiment by [8] have revealed the existence of flow oscillations or unsteadiness in a tightly spaced rod-bundle with pitch-to-diameter ratio (p/d) of 1.1 and 1.06, respectively. The flow oscillations can cause flow-induced vibration in a rod-bundle. It has been revealed by the thermalhydraulics experiment that these flow oscillations result in temperature oscillations. These temperature oscillations in turn can induce thermal shock or thermal fatigue damage to the walls of the rods in a bundle. To capture such time-dependent flow features an Unsteady RANS, a Large Eddy Simulation (LES), or even a Direct Numerical Simulation (DNS) approach is needed, see e.g. [12], [13]. Keeping the above aspects in mind this paper aims at: - Assessment of URANS and LES modelling approaches by analyzing Hooper s hydraulics experiment as described in [10]. - Analyses of obtained results to compare these two different approaches. The first section of the paper deals with the analyzed Hooper s hydraulics experiment [10], the second section describes the adopted CFD model for URANS and LES analyses, the third section deals with the obtained results and finally the last section summarizes and concludes the paper. 2. ANALYZED CASE To assess the capabilities of URANS and LES approaches, Hooper s hydraulics experiment [10] with a tight lattice bare rod-bundle having a p/d of 1.1 is selected. The cross section of this experimental geometry revealing six bare rods arranged in a square lattice is shown in Fig. 1. This six-rod cluster is supported by an external frame that maintains the dimensional accuracy without the need of additional spacer grids. This experiment is performed with air as a working fluid at a bulk Reynolds number (Re bulk ) of 2 / 13

3 about with an inlet uniform or bulk velocity of 10.3 m/s. The length of the experimental six-rod cluster is 9.14 m, which is equivalent to 128 hydraulic diameters. This is expected to be sufficient for obtaining a fully developed flow condition. This experiment measures time-dependent velocities with hot-wire anemometer probes positioned at (x,y) = (0, ±0.102m), in a plane that is about 126 hydraulic diameters from the inlet. These probes are placed in the smallest gap region between the rods. These measurements reveal the existence of flow oscillations or instabilities in the experiment. The estimated measurement uncertainty in the axial or main flow velocity component is about 15 % (see e.g. [14]). The experimental details are summarized in Table 1. Fig. 1: Cross section of the Hooper s hydraulic experiment with a tight lattice six-rod cluster ([10]). The red dotted lines are indicating the selected computational domain. Table 1. Conditions for Hooper s hydraulic experiment with pitch-to-diameter of 1.1 Rod-bundle arrangement Bulk Reynolds number Bulk velocity (m/s) Square Measuring plane 126 hydraulic diameter from inlet Experimental uncertainty 15 % in the main flow direction 3. CFD MODEL The selected region for the URANS and LES analyses of Hooper s hydraulics experiment is indicated with red dotted lines in Fig. 1. This modelled geometry is elaborated in Fig. 2. The length of this modelled geometry for CFD analyses is m, which is four times an average wavelength of oscillations as determined by [15]. The selected length corresponds to about 18 hydraulic diameters. The average wavelength is approximated from the ratio of bulk velocity 10.3 m/s to an average cycle frequency of flow oscillations. An average cycle frequency (f) of flow oscillations is obtained from its given graphical relationship with Re bulk in [10]. Analysis of this relationship provides a value of f close to 30 Hz for the defined experimental conditions. It is already explained that the 3 / 13

4 flow measurements include a certain error, and therefore, it can be expected that a relationship between Re bulk and f will also contain a certain amount of error. However, no details in this respect for the considered experiment are available. Flow Inlet Wall Outlet Fig. 2: Selected computational domain (left) and generated hexahedral mesh at the cross section (right) for CFD analyses of Hooper s hydraulics experiment. The generated cross-sectional grid for the present analyses is shown in Fig. 2. The wall near resolution of this grid exhibits an average y+ of the order of 2 for the closest grid point to the walls. The stretching factor in the boundary layer is about In other words, the selected grid resolves the wall near region at least in the radial direction. In general, the largest grid-width (=max ( x, y)) in the cross section as shown in this figure in terms of wall-units is about 20. Consequently, the generated cross-sectional mesh follows the recommendations for a suitable grid in nuclear applications involving heat transfer for Large Eddy Simulations (LES), see e.g. [16]. The maximum grid aspect ratio of the generated grid is 80. Furthermore, a practical guideline by [17] indicates that the generated wall-resolved grid is capable of representing the flow structures in the nearwall region and is suitable for LES. In the bulk region, the grid aspect ratio is about 8. The grid is having about 80 axial grid points in one average wavelength of the oscillations and consists of about 8.5 million computational hexahedral volumes. Such a grid resolution for capturing flow oscillations or unsteadiness restricts the selection of a larger computational domain. The generated grid is summarized in Table 2. It should be emphasized that the same grid is used for both URANS and LES simulations. Therefore, the obtained results allow us a direct comparison between these two approaches based on the selected numerical schemes and closure models. 4 / 13

5 Table 2. Generated mesh for URANS and LES analyses of Hooper s hydraulic experiment Computational volumes (million) 8.5 Average y+ (nearest node to the wall) ~ 2 Stretching factor in the boundary layer ~ 1.07 Maximum bulk grid-width in wall-units ~ 20 Maximum grid aspect ratio 80 (~160 wall-units) Grid aspect ratio in bulk 8 For the URANS and LES analyses, the STAR-CCM+ CFD code is used. The open boundaries of the modelled geometry are treated as rotationally periodic. These are indicated by the same types of arrows in Fig. 2. The inlet and outlet are treated as cyclic and a mass flow rate corresponding to a bulk velocity of 10.3 m/s is applied to sustain the flow and turbulence in the selected computational domain. The employed computational set up using a Finite Volume Method (FVM) consists of: - Implicit unsteady based segregated flow solver in which convection terms are discretized with a second-order (quadratic upwind for URANS and boundedcentral for LES) scheme in the continuity and momentum equations. - A stable first-order upwind scheme to discretize the convective terms in the transport equations of turbulent quantities such as k and ε for URANS analyses. - k-ε based non-linear quadratic anisotropic eddy-viscosity turbulence model for URANS analyses. - The Wall-Adapting Local Eddy-viscosity (WALE) model for LES analyses. - All y+-wall treatment, which is a hybrid treatment that attempts to emulate the high-y+ wall treatment for coarse meshes and the low-y+ wall treatment for fine meshes in both approaches. - A selected time step of t = 5x10-5 seconds results in a maximum Courant number of 0.5. This is much smaller than 1/f with f ~30 Hz for the present case i.e. t << 1/f. Note that [18] have employed an even smaller Courant number of about 0.2 for analyzing [8] experiment. For details on the employed scheme, turbulence models etc. refer to the STAR-CCM+ User Guide [19]. The discussed computational set-up is summarized in Table 3. 5 / 13

6 Table 3. Computational set-up for Hooper s hydraulics experiment with STAR-CCM+ Solver Turbulence model Numerical scheme for convective terms Time step Maximum convective Courant number Computed flow through times Inlet outlet Open boundaries URANS Implicit unsteady Segregated flow LES k-ε based non-linear anisotropic Wall-Adapting Local Eddyviscosity (WALE) model quadratic eddy-viscosity model All y+ wall treatment Continuity, momentum equations: Continuity, momentum equations: Second-order upwind scheme Bounded-central scheme Turbulence equations: First order --- upwind scheme for URANS 5E-5 seconds Cyclic: Forced with mass flow rate Rotationally periodic 4. RESULTS The URANS and LES computations are carried out for a total time of 1.5s and 2.6s, respectively. This corresponds to about 12 and 22 flow-through times, respectively, in the modelled geometry with a bulk velocity of 10.3 m/s. The first 2-3 flow-through times based results are not considered for the analyses in both approaches. The URANS and LES analyzed axial velocity fluctuations at a certain point (z = m, x = m) are shown in Fig. 3. This also includes the recorded response of hot-wire anemometer probes as given in [10]. Following can be inferred from this figure: - URANS and LES analyzed axial velocity fluctuations are mostly within ± 1.5 m/s. Some of the analyzed values are as high as ± 2m/s. In other words, the fluctuations are almost % of the axial bulk flow velocity of 10.3m/s. This is not negligible and could cause flow induced vibrations of the six-rod cluster. - LES analysis reveals a higher frequency of axial velocity fluctuation in comparison to URANS analysis. This indicates that wider ranges (or scales) of flow structures are captured with LES than that of RANS approach, as expected. - Experimental measurement reveals that the axial velocity fluctuations are mostly within ± 1.3 m/s. 6 / 13

7 It should be emphasized that the measurement of axial velocity component involves an error of the order of 15% (see e.g. [14]). In other words, the measured axial velocity fluctuation can vary within ± 1.5 m/s including the explained experimental error. Moreover, although it has been outlined that appropriate measures have been taken, it should be noted that there are always several possible reasons for uncertainties in a CFD analysis, such as, generated grid, selected domain, turbulence model, boundary conditions and the selected approaches etc. Even with all these practical aspects of differences between experimental and computational approaches, it can be safely stated that the calculated values agree well with the experimentally measured axial velocity fluctuation. These are summarized in Table 4. Table 4. Experimental and CFD analyzed axial velocity fluctuations Axial velocity fluctuations (m/s) Experimentally measured URANS and LES analyzed ± 1.5 (± 1.3 ± 15%) ± URANS LES -1 Axial-velocity fluctuation (m/s)- URANS -1.5 Axial-velocity fluctuation (m/s)- LES z = m, x = m u: Axial velocity component (at 126 hydraulic diameter, x = ±.102 m Fig. 3: URANS analyzed (top) and Experimentally measured (bottom) axial velocity fluctuations for the Hooper s hydraulics experiment. 7 / 13

8 A three dimensional perspective of URANS and LES analyzed axial velocity is shown in Fig. 4. This figure shows: - A wavy pattern that can be inferred from the regions with different axial velocities in the analyzed mid-plane. These are indicated by arrows in the figure. As expected, the velocity is lower in the smallest gap region and higher in a region close to the open boundaries. - The presence of smaller flow structures in the LES computed flow field in comparison to URANS computed flow field. For instance, small plumes of low velocity are observed at the inlet section in LES and are not visible with URANS computation. The presence of smaller flow structures in LES is attributed to smaller values of analyzed turbulent eddy viscosity in comparison to URANS. In general, analyzed effective viscosity with LES is lower than that of URANS with the generated grid and employed computational frame-work. Fig 4: URANS (left) and LES (right) analyzed axial velocity after about 1s of computational time. Power Spectral Densities (PSD) of the URANS and LES analyzed axial velocity fluctuations at two different measurement points are shown in Fig. 5. The CFD software STAR-CCM+ is used for computing PSD. The analyzed axial velocity fluctuations over six and eight flow-through times are employed for this purpose in the adopted URANS and LES approaches, respectively. These indicate: - The PSD peaks are observed in the production frequency range of Hz for URANS and in the range of Hz for LES analyzed axial velocity fluctuations. These can be inferred as frequencies associated with the dominant amplitudes (e.g. ± 1.5 m/s) of axial velocity fluctuations. 8 / 13

9 - Based on a graphical relationship between frequency and bulk Reynolds number ([10]) it can be deduced that an average characteristic frequency of such large scale structures is about 30 Hz. The LES analyzed results shows a closer resemblance with the experimental observation than that of URANS analyzed results.this indicates the presence of large scale structures that contribute to a higher production of turbulence energy or power in the indicated frequency ranges. - It can be observed that the energy of turbulent structures with a frequency, say, 300 Hz is much smaller in URANS in comparison to LES. This can be attributed to a higher eddy-viscosity in the URANS approach compared to LES. This means, smaller scales with such a high frequency in URANS are not sustainable whereas they still exist in LES. At the same time, energy contents of turbulent structures with frequency below 100 Hz are comparable in URANS and LES. In other words, URANS will be useful for applications where lower frequencies or larger or mean flow structures are relevant. Fig 5: Power Spectral Density (PSD) analyzed from URANS (left) and LES (right) analyzed axial velocity fluctuations. It can be expected that the flow oscillation may even influence the wall shear stress. In order to determine the influence of flow oscillations on the wall shear stress, its magnitude is noted over time at a point in the lower wall at the smallest gap between the rods. The time dependent wall shear stress magnitude (in Pa) is shown in Fig. 6. This shows that: - Oscillations exist in wall shear stress magnitude. - URANS analyzed wall shear stress magnitude has a higher lower limit of 0.2 Pa than that of about 0.1 Pa in LES analyzed wall shear stress magnitude. - LES analyzed wall shear stress has a higher amplitude of oscillation (varying between 0.1 to 0.4 Pa) than that of URANS analyzed wall shear stress (varying between Pa). It can be emphasized that an oscillating wall shear stress is not desirable in a rod-bundle as it can challenge the integrity of the reactor core by damaging the fuel rods surface. 9 / 13

10 Wall shear stress magnitude (Pa) URANS LES Wall-shear-stress-URANS Wall-shear-stress-LES Time (s) Fig 6: URANS and LES analyzed wall shear stress magnitude (Pa) at a point lower wall in the smallest gap between the rods, indicated by an arrow in the right figure. Fig 7: Power Spectral Density (PSD) of URANS (left) and LES (right) analyzed wall shear stress magnitude The PSD of URANS and LES analyzed wall shear stress magnitude are shown in Fig. 7. These are obtained from monitored signals over seven flow-through times. These reveal distinct peaks in a frequency range of Hz for both approaches. In other words, the signals of wall shear stress magnitude as shown in Fig. 6 have dominant amplitudes in this frequency range. If this time response of dominant wall shear stress (in this frequency range) is below a characteristics response time of the material of which the fuel rods are made, then the material may adjust having enough time to react on the changes of wall shear stress. In case this time response of dominant wall shear stress (in the indicated frequency range) is higher than that of a characteristic response time of the material of which the fuel rods are made, then the material may not be able to react on the changes of wall shear stress. Otherwise, it can be expected that the material will react to the changes in wall shear stress and will not be able to adjust to these changes. It can be noted that dominant frequencies of axial velocity fluctuations and wall shear stress magnitudes are quite comparable values that indicate a possible relationship between these quantities. However, at this moment this is purely qualitative. For a 10 / 13

11 quantitative statement further analyses are needed by recording velocity at a point closest to the monitor point for wall shear stress magnitude. Such oscillatory wall shear stresses can damage the fuel rods surface, and therefore, the safety or integrity of such a rodbundle need special attention. It can also be expected that such flow oscillations will also produce temperature oscillations at the fuel rods surface. These can in turn result in thermal shocks or thermal fatigue damage to the surface. 5. SUMMARY AND CONCLUSIONS This paper aims at assessment of URANS and LES approaches by analyzing Hooper s hydraulic experiment with a tight lattice bare rod-bundle. For this purpose, a CFD model is constructed comprising of a domain that allows the use of periodicity as a boundary condition, a grid that is generated following the practical requirements for LES and resolves the wall-near region, and numerical schemes for both these approaches. The analyses of URANS and LES computed results reveal the following: - URANS and LES analyzed axial velocity fluctuations are mostly within ± 1.5 m/s and agree well with the experimentally obtained limits of ± 1.3 m/s ± 15%. - The axial velocity fluctuations are % of the bulk velocity, which is significant. This could cause flow induced vibration of such a tight lattice rodbundle. - As expected, LES captures a wider range of turbulent structures or scales in comparison to URANS. - The frequency range corresponding to the power spectra peaks of LES analyzed axial velocity fluctuations is closer to the experiment in comparison to URANS. - In URANS, the smaller turbulent structures contain much lower energy (or power) compared to LES. Therefore, such smaller structures in URANS are not sustained whereas they exist in LES. - It is expected that URANS will be useful for applications where mean or large flow structures are relevant. - Analyses of wall shear stress magnitude at a point in bare rods surface reveal oscillations. They also contain distinct peaks in their analyzed power spectra. This indicates a possible relationship between flow oscillations and wall shear stress magnitude oscillations. Further analyses are needed for a quantitative assessment. - Oscillations in wall shear stress at the fuel rods surface are not desirable as they can cause damage to the fuel rods surface and therefore special attention to the safety of such a reactor core is necessary. - Flow oscillations can cause temperature oscillations when heat transfer is involved. This in turn can cause thermal shocks or thermal fatigue damage to the surface of fuel rods, depending on the frequencies of dominant amplitudes of oscillations. - Flow oscillations and their consequences need special attention in a tight lattice rod-bundle with spacer grids. 11 / 13

12 6. ACKNOWLEDGEMENT The authors gratefully acknowledges the support from Dutch Ministry of Economic Affairs and the seventh framework program THINS Project No. FP sponsored by the European Commission. 7. REFERENCES 1. GIF Introduction to Generation IV nuclear energy system and the international forum (2008). 2. X. Cheng and N. I. Tak CFD analysis of thermal hydraulic behavior of heavy liquid metals in sub-channels Nuclear Engineering & Design 236, (2006). 3. D. Chang and S. Tavoularis Numerical simulation of turbulent flow in a 37-rod bundle Nuclear Engineering & Design 237, pp (2007). 4. W. K. In, C. H. Shin, D. S. Oh, and H. Chun CFD Simulation of the turbulent flow and heat transfer in a bare rod bundle Proc. ICAPP, Pittsburgh, USA, Paper 4179 (2004). 5. E. Baglietto and H. Ninokata, Turbulence model evaluation for heat transfer simulation in tight lattice fuel bundles Proc. NURETH-10, Seoul, Korea (2003). 6. G. Grötzbach Anisotropy and buoyancy in nuclear turbulent heat transfer critical assessment and needs for modelling FZKA 7363, Karlsruhe, Germany (2007). 7. H. Ninokata, H. and Merzari, E., Computational fluid dynamics and simulation-based-design approach for tight lattice nuclear fuel pin subassemblies, Proc. NURETH-12, Log no: KN#6, Pennsylvania, USA. 8. T. Krauss and L. Meyer Experimental investigation of turbulent transport of momentum and energy in a heated rod bundle Nuclear Engineering & Design 180, (1998). 9. V. Vonka Measurement of secondary flow vortices in a rod bundle Nuclear Engineering & Design 106, (1988). 10. J. D. Hooper and K. Rehme Large-scale effects in developed turbulent flow through closely- spaced rod arrays J. Fluid Mech. 145, (1984). 11 B. Arien, Assessment of computational fluid dynamic codes for heavy liquid metals. ASCHLIM EC-Con. FIKW-CT Final Report (2004). 12. E. Baglietto RANS and URANS simulations for accurate flow predictions inside fuel rod bundles Proc. ICAPP, Nice, France, Paper 7310 (2007). 13. H. Ninokata, N. Atake, E. Baglietto, T. Misawa and T. Kano, Direct numerical simulation of turbulence flows in a subchannel of tight lattice fuel pin bundles of nuclear reactors, (2004). 14. S. V. Möller, On phenomena of turbulent flow through rod bundles Exp. Therm. and Fl. Sc. 4, 5-35 (1991). 15. E. Merzari, H. Ninokata, and E. Baglietto Unsteady Reynolds averaged navierstokes simulation for an accurate prediction of the flow insight tight rod bundles 12 / 13

13 Proc. NURETH-12, Pennsylvania, USA, Log number 213 (2007). 16. G. Grötzbach, Updating the resolution requirements for turbulence simulations in nuclear heat transfer Proc. NURETH13, Kanazawa, Japan, Paper no: N13P1276 (2009). 17. U. Piomelli and J. Chasnov Large eddy simulations: theory and simulations In: A Henningson, K. Hallback, L. Alfredson and M. Johansson (Eds.), Transition and Turbulence Modelling, Kluwer Academic Publishers (1996). 18. H. Ninokata, E. Merzari, E. and A. Khakim Analysis of low Reynolds number turbulent flow phenomena in nuclear fuel pin subassemblies of tight lattice configuration Nuclear Engineering & Design, 239, (2009). 19. STAR-CCM+ User guide, Published by: CD-Adapco (2009). 13 / 13