Figure 1: A photo of a Westinghouse 17x17 commercial nuclear fuel assembly (left), the simulation results (center) and a photo of a fuel assembly being removed from the TVA Watts Bar reactor core during a refueling outage.
A team of CASL scientists from Los Alamos National Laboratory and Westinghouse Electric Corporation (WEC) collaborated on an assessment of calculation approaches for forcing inputs to grid-to-rod fretting (GTRF) using Hydra-TH, Star-CCM+, and WEC’s proprietary VITRAN (VIbration TRansient Analysis – Nonlinear) code. A series of computational fluid dynamics simulations were completed for the commercial-power reactor fuel, designed by Westinghouse Electric Corporation and operated by Tennessee Valley Authority in Watts Bar Unit 1 (illustrated in Figure 1). The calculated flow field rod excitation forces were applied as input to evaluate the sensitivity of the fuel-rod assembly dynamics to the turbulent fluid forces.
Mark Christon, Jozsef Bakosi and Lori Pritchett-Sheats of LANL carried out a series of isothermal turbulent flow calculations on both 3x3 and 5x5 rod bundle geometries.
The turbulence models assessed in the study included implicit large-eddy simulation (ILES), Reynolds-averaged Navier-Stokes (RANS) models (e.g., the Spalart-Allmaras model), and detached-eddy simulation (DES), a blended LES/RANS method. Details on the turbulence models used are described in the Hydra-TH Theory Manual (LA-UR-12-23181).
For the study, the flowing water was specified at 394.2 K (942.0 kg/m3 and 2.32x10-4 kg/m/s) with an inlet velocity of 5 m/s axially, with no cross-flow applied. A physical duration of 1.0 second was selected for the simulations. Time-averaged statistics were collected beginning at 0.2 sec, after the turbulent flow reached a statistically stationary state (fluctuation around a clearly defined mean).
Figure 2 provides an illustration of the 3M cell Cubit mesh.
All calculations were performed in a time-accurate way using the neutrally dissipative second-order trapezoidal rule time-integrator. A fixed CFL condition was used for all calculations in conjunction with implicit second-order treatment of the advective and diffusive terms.
Various statistics of the fluctuating flow field were analyzed and compared to data from computations carried out by Westinghouse using Star-CCM+ and from experiments at Texas A&M University. The available results showed good agreement with both simulations and experiments. Comparing different approaches to compute turbulent flows, the team concluded that low-order RANS models do not appear to be appropriate to provide time-accurate pressure force fluctuations at the resolution required for the GTRF problem.
Results from Hydra-TH and STAR-CCM+ are in reasonable agreement, and show that the mixing vanes are the main source of turbulence that generates the excitation forces on the fuel rod. The excitation forces decay along the span downstream of the spacer grid. The Hydra-TH results with 14 million cells are relatively close to the STAR-CCM+ results with 48 million cells. Results from both Hydra-TH and STAR-CCM+ show the force in the X-component is slightly lower than the Z-component.
WEC engineer Roger Lu used the CFD-calculated RMS forces as inputs to the WEC VITRAN code. VITRAN is a specialized code developed by Westinghouse to simulate flow-induced vibration and fretting wear of a fuel rod. The non-linear dynamic VITRAN model includes a single fuel rod and its associated grid supports (represented as springs and gaps), as shown in Figure 3, and calculates the rod frequency response and motion, the support impact forces (normal and friction forces), the sliding and sticking distances, and the work rates based. Inputs to the code include the hydraulic excitation forcing function (the power spectral density, or PSD) and the power history of the fuel rod to calculate rod-to-grid gaps, cladding creep-down, spring relaxation, and grid lateral growth. The model uses the normal work rate to calculate the rod wear rates and the scar depths using empirical wear coefficients. High-flow velocity and turbulence imposes stochastic and fluctuating pressure (force) on the fuel rod surface and induces fuel rod vibration. The PSD is used to describe the fluctuating pressure. Experimentally measuring the PSD and the related correlation length on the fuel rod surface is very difficult, and it recent years, due to the significant increase in computing capability, CFD has been introduced to calculate PSD using numerical techniques. In this study, the hydraulic forcing functions were supplied by the Hydra‑TH and STAR-CCM+ calculations.
The VITRAN model includes six spacer grids. For these calculations, the input and boundary conditions were applied consistent with the VIPER loop test used for comparison. All grid cells were assumed to have zero preload and zero gap. The VITRAN results show that the CFD modeling methodologies used by Hydra-TH and STAR-CCM+, while different, produce comparable RMS forces. Both codes show very good agreement. However, it would be desirable to perform additional computations with Hydra-TH using higher resolution meshes to test the sensitivity of the RMS forces. Less than 2% difference in the wear work-rate was observed between the cases run with Hydra‑TH loads and STAR-CCM+ loads.
Why Large-Eddy Simulation?
From the engineering viewpoint the most useful information that can be obtained from simulations of turbulent flows are statistical and integrated quantities derived from the fluctuating flow field. Examples of statistics are the mean velocity, the root-mean-square (RMS) pressure, and the turbulent kinetic energy spectrum. Examples of integrated quantities are the mean drag or mean lift on an airplane wing or the PSD distribution of the fluctuating forces that load the fuel rods in a pressurized water nuclear reactor. The current engineering practice for the GTRF problem is to compute turbulent flow solving the RANS equations augmented by a turbulence model. RANS models directly compute the statistics by solving for only the mean field values and, depending on the model, the second moments. For example, the κ-ε model is a popular way to approximate the effects of fluctuations on the mean velocity. However, it is important to appreciate that the main goal of the κ-ε model is to provide closure for mean velocity via the time scale ~k/ε. Consequently, one can expect a statistically meaningful description of the mean but less so of the fluctuations (e.g., k or ε, themselves) only their effect on the mean. If the second moments (e.g., the fluctuation about the mean) are also important, a model with a higher level of description is required. Figure 4 provides an illustration of the results obtained for the ILES, DES and RANS models.
Numeca's Hexpress/Hybrid mesh generator, a.k.a. “Spider,” was used for the first time to generate hybrid meshes for the GTRF problem. A method for quantitative assessment of complex unstructured meshes with no-slip walls was developed and used to assess a series of meshes generated for the GTRF problem by two mesh generators.
Arguably the most important quantity for coupling to a structural code is the fluctuations of the pressure force loading the rod. The RMS forces were calculated on a series of 3 meshes with increasing mesh resolution. Using the same algorithm and code, the team found that the predicted RMS forces, integrated for the whole rod, an order of magnitude larger using the higher-quality Spider meshes compared to Cubit meshes. The rod force distributions computed with Hydra-TH and STAR-CCM+ are quite comparable, albeit using relatively coarse meshes with Hydra.
The study concluded that the displacement, acceleration and wear work-rates computed with VITRAN indicate there is little sensitivity to using RMS forces computed with Hydra-TH or STAR-CCM+ as input. The RMS force comparison indicated that the CFD methods used by Hydra-TH and STARCCM+, although different, predict transient forces that show very good agreement, and the mixing vanes result in significant turbulent mixing which generates the unsteady excitation forces on fuel rod. The excitation forces generated by mixing vanes decay along the span downstream the grid. The study additionally noted that a minimum mesh resolution of approximately 7 to 14 million cells is required to achieve RMS pressures that are of reasonable fidelity for the subsequent VITRAN calculations.