Turbulent flow of water in a 3×3 rod bundle – Numerical results from RANS, URANS and LES

doi:10.1016/j.pnucene.2020.103516

Progress in Nuclear Energy

Volume 129, November 2020, 103516

https://doi.org/10.1016/j.pnucene.2020.103516 Get rights and content

Highlights

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The turbulent flow of water in a 3 × 3 rod bundle was studied numerically.
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Three numerical methodologies of RANS, URANS and LES were compared.
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First- and second-order turbulence statistics were provided.
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Large-scale flow pulsation was predicted by URANS and LES.

Abstract

The coolant flow behavior inside fuel bundles influences the subchannel mass and momentum exchange and the cladding temperature, which should be considered when designing fuel assemblies. In this paper, three numerical methodologies of RANS (Reynolds-Averaged Navier-Stokes), URANS (Unsteady Reynolds-Averaged Navier-Stokes) and LES (Large Eddy Simulation) were adopted to investigate the turbulent flow characteristics of water inside a 3 × 3 bare bundle at atmospheric pressure. Emphasis was focused on clarifying the features related to the flow through rod bundles, such as the distribution of mean flow, Reynolds stresses and the characteristics of large-scale flow pulsation. It was found that the prediction of RANS simulation deviates relatively large from the experimental data, on the other hand, the predictions given by URANS and LES are comparable and agree well with the experimental measurements. The time-averaged velocity, Reynolds stresses and turbulent kinetic energy were plotted along various lines of interest. The quasi-periodic large-scale flow pulsation was identified by URANS and LES, but the pulsation period and oscillation magnitude deviate slightly. Finally, power spectrum density was conducted for URANS and LES to study the axial and lateral velocity variations in the frequency domain.

Graphical abstract

Introduction

A conventional PWR (pressurized water-cooled reactor) fuel assembly consists of a 17 × 17 square array rod bundle and several spacer grids along the flow direction (Todreas and Kazimi, 2011). The spacer grid can provide a predetermined rod-to-rod spacing and prevent the occurrence of flow-induced vibration. Besides, strong transverse flow and mixing are created by the mixing vanes, which promotes the heat transfer between the fuel rods and the water coolant (Navarro and Santos, 2011). Another key phenomenon, i.e. quasi-periodic large-scale flow pulsation, may exist in rod bundles (Rehme, 1992; Meyer, 2010). Large-scale vortexes are generated by the turbulent shear stress as well as the strong velocity gradient in the gap region. While being transferred by the mainstream, these large vortexes form a line of vortex street which flows in and out the subchannel periodically, leading to strong cross flow and additional momentum and energy exchange between subchannels. This phenomenon is usually concerned in tight bundles which is characterized by small pitch-to-diameter ratios (P/D). In view of the complex flow and mixing phenomena induced by spacer grid and the rod bundle geometry, a thorough understanding is indispensable to the design and optimization of PWR fuel assemblies.

In recent years, a series of experiments have been conducted using laser-based flow visualization technique to reveal the coolant flow behavior in rod bundles. The studies of Hosokawa et al. (2012), Lee et al. (2013) and Wang et al. (2020) focused on analyzing the turbulent mixing process of water in small-scale 2 × 2 and 3 × 3 rod bundles without spacing devices. Based on the PIV (particle image velocimetry) measurements, the mean flow and turbulence statistics were provided. Several studies (Nguyen and Hassan, 2017; Li et al., 2019; Qu et al., 2019a; Qi et al., 2019; Xiong et al., 2020) payed attention to the transverse flow and local mixing resulted from the spacer grid inside 5 × 5 rod bundles. The dimension of the rod bundle mimicked the PWR fuel assembly, i.e. the rod diameter was set to 9.5 mm and the pitch was set to 12.6 mm. Flow redistribution, large velocity fluctuation and strong secondary flow were observed as the fluid passing through the spacer grid. The local disturbance decays exponentially along the flow direction after the fluid leaving the spacer grid.

Computational Fluid Dynamics (CFD) plays an essential role in thermal-hydraulic analyses of the rod bundle. Many numerical simulations were conducted to study the turbulent flow behavior of water induced by spacer grids, and to assess the capability of various CFD tools and models. During 2011–2013, extensive benchmark exercises have been carried out based on the MATiS-H experimental data released by KAERI. The effects of mesh type, turbulent model, numerical scheme, simulation methodology and boundary condition on the prediction accuracy have been evaluated. Detailed analyses are summarized in Smith et al. (2013). Bieder et al. (2014) found that, in Reynolds-Averaged Navier-Stokes (RANS) simulation, liner turbulence models can accurately predict the transverse flow created by the mixing vanes, but show large discrepancy to the experimental measurements at further downstream of the spacer grid where the interchannel exchange is governed by the anisotropic turbulence. In Podila et al. (2014), Unsteady Reynolds-Averaged Navier-Stokes (URANS) approach was utilized to capture the anisotropic turbulence in the rod bundle. It was found that URANS solution predicted the velocity distribution reasonably well, but underpredicted the turbulence intensity. Mikuž and Tiselj (2017) conducted an URANS simulation as well, but using an open-source code OpenFOAM and the SST k-ω model. The study signified that the turbulence intensity is obviously enhanced by the spacer grid. The authors claimed that their results are among the most accurate ones in the benchmark group. In Busco and Hassan (2018), Partially-Averaged Navier-Stokes (PANS) was employed to predict the flow in a 5 × 5 rod bundle with spacer grids. It was demonstrated that PANS is comparable to LES in predicting the flow field generated by the spacer grid, provided that a suitable cut-off criterion was chosen. Recently, the spectral element method was applied to investigate the turbulent flow and subchannel mixing of water in a 3 × 3 rod bundle (Ju et al., 2020). The turbulent mixing coefficient was obtained for various subchannels of the rod bundle. It was reported that the local wall effects should be considered in subchannel codes to get a reasonable result. In addition to small-scale rod bundles, subchannes were also considered as representative geometry to the fuel assembly. In this framework, the experiment performed by Hooper and Rehme (1984) was frequently reproduced numerically to: 1) study the turbulent flow behavior and gap vortex street in adjacent central subchannels, and 2) evaluate the performance of turbulence models as well as various modeling strategies (RANS, URANS, LES). Examples are the works reported by Chandra et al. (2010) and Shams and Kwiatkowski (2018).

Several numerical simulations were conducted using LES with the geometry of bare rod bundle without any spacer grids. Mikuž and Tiselj (2016) utilized the wall-adapting local eddy-viscosity (WALE) model and OpenFOAM to investigate the turbulent flow inside a 5 × 5 bundle. To reduce the required resource for LES, only a quarter of the bundle was considered as the control domain and its length was set to 2–4 D_h. The resolved velocity and fluctuations were compared with experimental measurements, demonstrating that the wall-resolved LES with WALE model is sufficiently accurate in simulating the flow through rod bundle, especially for the mean velocity profiles. The second-order statistics showed slightly larger deviation from the experimental data. Highly-resolved LES was performed by Lakehal (2018) using TransAT code to research the flow behavior in a subchannel. The turbulent flow characteristics such as the low Reynolds effects in the narrow gap as well as the strong transverse flow have been analyzed in details. Comparison between the LES results and the direct numerical simulation (DNS) exhibited a fairly good agreement. However, only first-order turbulence data were reported while higher-order statistics of the velocity fluctuations were not explored. Recently, Wang and Lu (2019) conducted a LES study about the flow phenomenon in a 4-rod bundle using STAR-CCM+. The root-mean-square (RMS) velocity and Reynolds stresses were found extremely anisotropic between adjacent rods. Secondary flow of the second kind and the Reynolds stress budget were presented.

From the literature mentioned above, it was found that most of the CFD studies carried out so far focused on revealing the transverse flow and local mixing produced by the spacer grids, using various modeling approaches, CFD codes and turbulence models. It should be noted that the strong disturbance and transverse mixing decayed exponentially as the flow passing through the spacer grid, and damped out at a distance of 4.5–10 D_h depending on the Reynolds number (Qi et al., 2019; Qu et al., 2019a, 2019b). In such cases, the anisotropic turbulence fluctuations become the dominant factor controlling the turbulent mixing process in the bare-bundle region. Besides, far from the spacer grid, the large-scale flow pulsation may be encountered which further enhances the cross flow mixing and momentum transfer. At present, however, the studies concerning the coolant flow behavior in bare bundles are insufficient. Finally, the direct comparison between various CFD methodologies in predicting the flow through a rod bundle is seldom discussed, which restricts the effective application of CFD tools in the fuel assembly design and optimization. In the present paper, the turbulent flow features of water inside a 3 × 3 rod bundle were numerically investigated using RANS, URANS and LES methodologies. The objectives of this paper are: 1) provides detailed first- and second-order turbulence information in a rod bundle; 2) promotes the understanding of the turbulent flow behaviors in rod bundles and 3) compares the performance of various CFD approaches and make a recommendation for further applications.

Section snippets

Governing equations

In the methodology of LES, large eddies, which are closely related to the Reynolds number and physical geometry, are predicted by solving the governing equations. On the other hand, small eddies are believed to be isotropic and universal, and hence are modeled using a subgrid scale (SGS) model. Generally, the variables in LES could be decomposed into a resolved part and a modeled part by using a filter function. For example, the instantaneous velocity $u_{i}$ equals to the resolved one ${\overline{u}}_{i}$ plus the

Governing equations

In the methodology of RANS/URANS, a variable is decomposed into a time-averaged part plus a fluctuation part. Taking velocity for example, the instantaneous one $u_{i}$ equals to the time-averaged one ${\tilde{u}}_{i}$ plus the fluctuation one $u^{'}$ , i.e. $u_{i} = {\tilde{u}}_{i} + u^{'}$ . Note that the overbar “~” stands for time averaging. The Reynolds-averaged mass and momentum equations can be described as: $\frac{\partial {\tilde{u}}_{i}}{\partial x_{i}} = 0$ $\frac{\partial {\tilde{u}}_{i}}{\partial t} + \frac{\partial ({\tilde{u}}_{i} {\tilde{u}}_{j})}{\partial x_{j}} = - \frac{1}{ρ} \frac{\partial \tilde{p}}{\partial x_{i}} + \frac{\partial}{\partial x_{j}} [ν (\frac{\partial {\tilde{u}}_{i}}{\partial x_{j}} + \frac{\partial {\tilde{u}}_{j}}{\partial x_{i}})] - \frac{\partial {\tilde{τ}}_{i j}}{\partial x_{j}}$ where ${\tilde{τ}}_{i j}$ is the Reynolds stress to be modeled using a

Explanations of the unsteady simulation

As already described, the length of the domain for LES was 20 D_h to reduce the computational hardware resource. Thus, it is necessary to examine whether the chosen length is sufficiently long without bringing about extra periodicity. This is usually done by analyzing the streamwise two-point velocity correlation (Busco and Hassan, 2018). Normalized by the RMS velocity, the two-point correlation is given by: $R_{i i} (x_{p}, η) = \frac{\overline{u_{i}^{'} (x_{p}) u_{i}^{'} (x_{p} + η)}}{\sqrt{\overline{u_{i}^{' 2} (x_{p})}} \sqrt{\overline{u_{i}^{' 2} (x_{p} + η)}}}$ where R_ii is the two-point correlation, x_p

Conclusions

In this paper, three methodologies of RANS, URANS and LES were adopted to investigate the fluid flow behavior in a 3 × 3 bare bundle. The numerical predictions were directly compared with experimental measurements. The following conclusions can be reached according to the analyses.

(1)
Most of the turbulent scales were resolved in the present LES, and the modeled part of the flow is trivial. For URANS simulation, the resolved and modeled portions are in the same order of magnitude and contribute

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This research was financially supported by National Natural Science Foundation of China (11605057) and the Fundamental Research Funds for the Central Universities (2018MS046).

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Turbulent flow of water in a 3×3 rod bundle – Numerical results from RANS, URANS and LES

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Governing equations

Governing equations

Explanations of the unsteady simulation

Conclusions

Declaration of competing interest

Acknowledgements

Prog. Nucl. Energy

Int. J. Heat Fluid Flow

Nucl. Eng. Des.

Int. J. Heat Mass Tran.

Nucl. Eng. Des.

Prog. Nucl. Energy

Nucl. Eng. Des.

Ann. Nucl. Energy

Nucl. Eng. Des.

Int. J. Heat Fluid Flow

Prog. Nucl. Energy

Int. J. Heat Fluid Flow

Prog. Nucl. Energy

Ann. Nucl. Energy

Nucl. Eng. Des.

Ann. Nucl. Energy