Burns turbulent dispersion considers the dispersed phase as a passive scalar

The Burns turbulent dispersion force is the most commonly used turbulent dispersion in the twofluid RANS bubbly-flow literature. However, its derivation is based on a series of hypothesis that are difficult to justify in industrial flows. It is shown that in low-void fraction vertical pipe flow, the Burns turbulent dispersion formulation is equivalent to considering the radial movement of the gas phase like a passive scalar that follows turbulent eddies. This is not apparent in the derivation of the force. As bubbles in pressurized water reactor (PWR) conditions have a low Stokes number (∼ 10−1), considering bubbles are transported by turbulence is a good approximation for bubble dispersion in pipe flow. Therefore, the Burns turbulent dispersion force is appropriate to represent bubble dispersion in low-void fraction PWR flows

A Diameterless Boiling-Flow Multiphase CFD Framework for Nuclear Reactor Conditions

We develop a two-fluid Euler-Euler CFD framework based on the PolyMAC numerical scheme in CEA’s open-source TrioCFD code. Interfacial momentum closure terms are selected and validated using bubbly adiabatic experiments on vertical flows. The local experimental bubble diameter is enforced to avoid the use of interfacial area closures. Independently, it is shown that in a high-pressure developed boiling pipe flow, changing the entrance temperature while measuring flow characteristics at the outlet is equivalent to changing the distance from the inlet where the flow characteristics are measured. This enables us to simulate the DEBORA experiment, an ascending boiling R12-freon flow in a tube, using a 3D map of the experimental diameter. Atmospheric-pressure closure terms are shown not to be able to reproduce measured void fraction profiles. We propose a new set of closures that is based on the hypothesis that bubbles are deformable in nuclear reactor conditions. This enables us to avoid bubble diameter modeling through an interfacial area transport equation or population balance model, as in system-scale codes extensively used in the nuclear industry. Void fraction predictions are improved compared with the baseline set of closures

Building a boiling-flow multiphase CFD framework for interfacial area and heat transfer modeling

International audienceMultiphase CFD's predictions for boiling flow are limited by available models for interfacial heat transfer and area. Both terms are greatly interdependent.Much research has relied upon adiabatic experiments on bubbly flow to determine the contribution of coalescence and breakup terms on the interfacial area independently of heat transfer. These models are often applied to boiling flows.We develop a 2-fluid Euler-Euler CFD framework based on the PolyMAC numerical scheme in CEA's open-source TrioCFD code. We implement a $k- \omega$ turbulence model, along with an original adaptive wall law treatment. Interfacial momentum closure terms are selected and validated using bubbly adiabatic experiments on vertical flows. The local experimental bubble diameter is enforced to limit interactions with interfacial area closures.We simulate the Debora experiment, an ascending boiling freon flow in a tube.We enforce the experimental diameter to isolate condensation from coalescence and breakup effects. The long-term goal is to run simulations using independently selected coalescence-fragmentation and heat transfer closures

CFD simulations of boiling flows in nuclear reactor conditions

International audienceDespite decades of work in the thermal hydraulics community, modeling interfacial area in boiling bubbly flows remains a challenge for multiphase CFD. However, bubble diameters are required for many momentum and heat transfer closures. Simulating flows without access to experimental bubble diameters is therefore difficult. This is problematic for design applications or extreme conditions as in Pressurized Water Reactors (PWR's). Here, we build a two-fluid CFD framework to compare different approaches to interfacial area. We select momentum closures, implement them in an open-source code and validate them using experiments with known bubble diameters. In the medium-term, we will compare interfacial area transport equations

Heat Flux Partition based on Onset of Significant Void

The thermal log-law is valid in flow boiling with a value of the additive constant that evolves as the flow develops. Using a multiphase flow cross-literature database, this constant is shown to be -7 at the point of onset of significant void (OSV). This means that at the OSV the liquid is at saturation temperature up to y+ = 30. The OSV predictions using this model have a similar mean average error as the Saha and Zuber 1974 correlation for one less fitted constant for channel, pipe and annular flows for pressure from 1 to 147bar and Peclet numbers from 3,500 to 400,000. This model is used to build a heat flux partitioning (HFP) inspired from system-scale codes. It predicts the distribution of the heat flux between the liquid phase and the evaporation term, and must be coupled with an empirical boiling total heat flux correlation to replace a traditional HFP. This partition provides more coherent flux distribution between the evaporation and liquid terms than Kurul and Podowski based approaches and improves void fraction predictions in high-subcooling regions on the DEBORA database and on experiments by Bartolomei et al

Critical density for the stability of a 2D magnet array

Confining a given number of magnets with vertically aligned moments on a non-magnetic surface creates a 2D magnet array, self-organized by repulsive forces in a hexagonal crystal-like network. Increasing areal density leads to a dramatic collapse of the structure where magnets finally stick together. We study the origin of this collapse and its critical density both experimentally, by either increasing the number of magnets or reducing the area, and theoretically, by using a dipole model. We suggest the collapse occurs when magnetic forces or torques created by irregularities overcome gravity. Transition from torque-driven to force-induced mechanism is observed when the critical density increases

A nonlinear beam model to describe the postbuckling of wide neo-Hookean beams

Wide beams can exhibit subcritical buckling, i.e. the slope of the force-displacement curve can become negative in the postbuckling regime. In this paper, we capture this intriguing behaviour by constructing a 1D nonlinear beam model, where the central ingredient is the nonlinearity in the stress-strain relation of the beams constitutive material. First, we present experimental and numerical evidence of a transition to subcritical buckling for wide neo-Hookean hyperelastic beams, when their width-to-length ratio exceeds a critical value of 12%. Second, we construct an effective 1D energy density by combining the Mindlin–Reissner kinematics with a nonlinearity in the stress-strain relation. Finally, we establish and solve the governing beam equations to analytically determine the slope of the force-displacement curve in the postbuckling regime. We find, without any adjustable parameters, excellent agreement between the 1D theory, experiments and simulations. Our work extends the understanding of the postbuckling of structures made of wide elastic beams and opens up avenues for the reverse-engineering of instabilities in soft and metamaterials