Angelo Frisani

On the Immersed Boundary Method: Finite Element Versus Finite Volume Approach

A projection approach is presented for the coupled system of time-dependent incompressible Navier-Stokes equations in conjunction with the Immersed Boundary Method (IBM) for solving fluid flow problems in the presence of rigid objects not represented by the underlying mesh. The IBM allows solving the flow for geometries with complex objects without the need of generating a body fitted mesh. The no-slip boundary constraint is satisfied applying a boundary force at the immersed body surface. Using projection and interpolation operators from the fluid volume mesh to the solid surface mesh (i.e., the “immersed” boundary) and vice versa, it is possible to impose the extra constraint to the incompressible Navier-Stokes equations as a Lagrange multiplier in a fashion very similar to the effect pressure has on the momentum equations to satisfy the divergence-free constraint. The projection operation removes the immersed boundary surface slip and non-divergence-free components of the velocity field. The boundary force is determined implicitly at the inner iterations of the fractional step method implemented. No constitutive relations for the immersed boundary objects fluid interaction are required, allowing the formulation introduced to use larger CFL numbers compared to previous methodologies. An overview of the immersed boundary approach is presented showing third order accuracy in space and second order accuracy in time when the simulation results for the Taylor-Green decaying vortex are compared to the analytical solution using the Immersed Finite Element Method (IFEM). For the Immersed Finite Volume Method (IFVM) a ghost-cell approach is used. Second order accuracy in space and first order accuracy in time are obtained when the Taylor-Green decaying vortex test case is compared to the analytical solution. The numerical results are compared with the analytical solution also for adaptive mesh refinement (for the IFEM) showing an excellent error reduction. Computations were performed using IFEM and IFVM approaches for the time-dependent incompressible Navier-Stokes equations in a two-dimensional flow past a stationary circular cylinder at Re = 20, and 40, where shedding effects are not present. The drag coefficient and the recirculation length error compared to the experimental data is less than 3–4%.Simulations for the two-dimensional flow past a stationary circular cylinder at Re = 100 were also performed. For Re numbers above 46, unsteadiness generates vortex shedding, and an unsteady flow regime is present. The results shown are in excellent quantitative and qualitative agreement with the flow pattern expected. The numerical results obtained with the discussed IFEM and IFVM were also compared against other immersed boundary methodologies available in literature and simulation performed with the commercial computational fluid dynamics code STAR-CCM+/V5.02.009 for which a body fitted finite volume numerical discretization was used. The benchmark showed that the numerical results obtained with the implemented immersed boundary methods are very close to those obtained from STAR-CCM+ with a very fine mesh and in a good agreement with the other IBM techniques. The IBM based of finite element approach is numerically more accurate than the IBM based on finite volume discretization. In contrast, the latter is computationally more efficient than the former.Copyright

Computational Fluid Dynamics Analysis of Very High Temperature Gas-Cooled Reactor Cavity Cooling System

Abstract The design of passive heat removal systems is one of the main concerns for the modular very high temperature gas-cooled reactors (VHTR) vessel cavity. The reactor cavity cooling system (RCCS) is a key heat removal system during normal and off-normal conditions. The design and validation of the RCCS is necessary to demonstrate that VHTRs can survive to the postulated accidents. The computational fluid dynamics (CFD) STAR-CCM+/V3.06.006 code was used for three-dimensional system modeling and analysis of the RCCS. A CFD model was developed to analyze heat exchange in the RCCS. The model incorporates a 180-deg section resembling the VHTR RCCS experimentally reproduced in a laboratory-scale test facility at Texas A&M University. All the key features of the experimental facility were taken into account during the numerical simulations. The objective of the present work was to benchmark CFD tools against experimental data addressing the behavior of the RCCS following accident conditions. Two cooling fluids (i.e., water and air) were considered to test the capability of maintaining the RCCS concrete walls’ temperature below design limits. Different temperature profiles at the reactor pressure vessel (RPV) wall obtained from the experimental facility were used as boundary conditions in the numerical analyses to simulate VHTR transient evolution during accident scenarios. Mesh convergence was achieved with an intensive parametric study of the two different cooling configurations and selected boundary conditions. To test the effect of turbulence modeling on the RCCS heat exchange, predictions using several different turbulence models and near-wall treatments were evaluated and compared. The comparison among the different turbulence models analyzed showed satisfactory agreement for the temperature distribution inside the RCCS cavity medium and at the standpipes walls. For such a complicated geometry and flow conditions, the tested turbulence models demonstrated that the realizable k-ε model with two-layer all y+ wall treatment performs better than the other k-ε and k-ω turbulence models when compared to the experimental results and the Reynolds stress transport turbulence model results. A scaling analysis was developed to address the distortions introduced by the CFD model in simulating the physical phenomena inside the RCCS system with respect to the full plant configuration. The scaling analysis demonstrated that both the experimental facility and the CFD model achieve a satisfactory resemblance of the main flow characteristics inside the RCCS cavity region, and convection and radiation heat exchange phenomena are properly scaled from the actual plant.

ANALYSIS OF LEAKS THROUGH MICROCHANNEL CRACKS USING RELAP5-3D

Abstract The purpose of the present work is to study the flow leakage through postulated microchannels. In the framework of the leak before break, it is reasonable to assume that a detectable leak develops before a large break occurs. A large pressure difference may exist between the crack inlet and outlet; the fluid residence time is so brief that thermodynamic equilibrium conditions cannot be reached within the crack. Using RELAP5-3D system code, the modified Henry’s homogeneous nonequilibrium model was adopted to simulate the fluid condition at the choked point. In channels with large L/DH, mechanical equilibrium between the phases is usually reached. On the other hand, because of the small residence time, thermal equilibrium may not be achieved. Thus, the critical flow through the crack is kinematically homogeneous, but thermodynamically in nonequilibrium conditions. In this investigation, various channel cross-flow areas were considered, each having a sensitivity study performed in reference to the wall roughness. In this approach it was possible to analyze the dependence of channel pressure drop as a function of the Reynolds number and wall roughness. For high values of the Reynolds number, the pressure drop showed very little influence of the Reynolds number over the fluid conditions inside the microchannel. On the other hand, the wall roughness strongly influences the channel pressure drop and, consequently, the critical mass flow rate through the crack. The RELAP5-3D wall friction correlation was compared with various available models in the literature, such as John et al. (1987), modified Karman, Nikuradse (1933), and Button et al. (1978). These correlations predict similar values for the friction factor. The RELAP5-3D model was also in agreement with modified Karman correlation for the studied wall roughness values. However, it underestimated the friction factor with respect to John’s formula. This indicates that the crack critical mass flow rate predicted by RELAP5-3D is larger than that calculated using John’s correlation.

Analysis of RCCS Heat Exchange for Benchmarking of CFD Codes

One of the main concerns for modular Very High Temperature Gas-Cooled Reactors (VHTR) is the design of passive heat removal systems from the reactor vessel cavity. The Reactor Cavity Cooling System (RCCS) is an important heat removal system during normal and up-normal conditions. The design and validation of the RCCS is necessary to demonstrate that HTGRs can survive the postulated accidents. Here we investigate this using the Computational Fluid Dynamics (CFD) STAR-CCM+ V3.06.006 code to simulate the Pressurized Conduction Cooling (PCC) and Depressurized Conduction Cooling (DCC) accident scenarios. Heat is transported by radiation and free convection from the Reactor Pressure Vessel surface to the cooling panels or standpipes. The standpipes are cooled by natural circulation of air or forced circulation of water flowing through the pipes. A representative VHTR RCCS configuration was considered, represented experimentally by a 180° scaled model facility that was used to measure temperature and velocity distributions inside the cavity. The CFD model constructed incorporated the features of the experimental facility. Using the vessel temperature profile obtained from the experimental facility as boundary conditions in the CFD simulations, different tests were performed increasing the vessel average wall temperature progressively. Grid independence was achieved and different turbulence models and near-wall treatments were tested. For the standpipes, simulations with both natural circulation of air and forced circulation of water were performed. A reasonable agreement between the experimental results and the CFD simulations was achieved for the temperature distributions in the RCCS cavity. Also the standpipes external wall temperature was close to the experimental data. The fraction of heat exchange due to radiation determined by STAR-CCM+ code was in reasonable agreement with the experimental results. The k-e turbulence models results were compared against the other turbulence models (i.e., the k-ω, Reynolds Stress Transport, and Spalart-Allmaras). Some differences were found between the turbulence models used. The k-e turbulence models showed in general better performance than the k-ω and Spalart-Allmaras models if compared with the Reynolds Stress Transport (RST) results and experimental data. Among the k-e turbulence models, the Realizable k-e turbulence models with two-layer all-y+ near wall treatment performed better than the standard and the Abe-Kondoh-Nagano (AKN) k-e models with Low-Reynolds Number low-y+ and all-y+ near wall treatments, if compared to both the RST and experimental results. The RST model was expected to perform better than the other models considering the strong anisotropy of the Reynolds stress tensor close to the vessel wall. The discrepancy between the experimental data with the RST model predictions may be due to the need for finer computational mesh model. A scaling analysis was developed to address the distortion introduced by the experimental facility and CFD model in simulating the physics inside the RCCS system with respect to the real plant configuration. The scaling analysis demonstrated that both the experimental facility and CFD model give a satisfactory reproduction of the main flow characteristics inside the RCCS cavity region, with convection and radiation heat exchange phenomena being properly scaled from the real plant to the model analyzed.Copyright