High-Fidelity CFD Modeling of Cryogenic Hydrogen Isotope Extrusion for Fusion Reactor Pellet Fueling

In reference [7] it is proved that the solution of the evolution Navier–Stokes equations in the whole of R 3 must be smooth if the direction of the vorticity is Lipschitz continuous with respect to the space variables. In reference [5] the authors improve the above result by showing that Lipschitz continuity may be replaced by 1/2-Holder continuity. A central point in the proofs is to estimate the integral of the term (ω · ∇)u · ω, where u is the velocity and ω = ∇ × u is the vorticity. In reference [4] we extend the main estimates on the above integral term to solutions under the slip boundary condition in the half-space R + 3 . This allows an immediate extension to this problem of the 1/2-Holder sufficient condition. The aim of these notes is to show that under the non-slip boundary condition the above integral term may be estimated as well in a similar, even simpler, way. Nevertheless, without further hypotheses, we are not able now to extend to the non slip (or adherence) boundary condition the 1/2-Holder sufficient condition. This is not due to the “nonlinear" term (ω · ∇)u · ω but to a boundary integral which is due to the combination of viscosity and adherence to the boundary. On the other hand, by appealing to the properties of Green functions, we are able to consider here a regular, arbitrary open set Ω.

A hybrid method of continuum and particle dynamics is developed for micro- and nano-fluidics, where fluids are described by a molecular dynamics (MD) in one domain and by the Navier–Stokes (NS) equations in another domain. In order to ensure the continuity of momentum flux, the continuum and molecular dynamics in the overlap domain are coupled through a constrained particle dynamics. The constrained particle dynamics is constructed with a virtual damping force and a virtual added mass force. The sudden-start Couette flows with either non-slip or slip boundary condition are used to test the hybrid method. It is shown that the results obtained are quantitatively in agreement with the analytical solutions under the non-slip boundary conditions and the full MD simulations under the slip boundary conditions.

A systematic study of the effect of the spanwise length and the sidewall boundary condition of a numerical wave flume (NWF) on direct numerical simulation of a plunging breaking wave is performed. To deal with the topological changes of free surfaces, a high-fidelity numerical model is employed to solve the Navier–Stokes equations together with the volume of fluid function. After verification by two-dimensional (2D) simulations of a plunging breaker on a sloping beach, ten NWFs with different spanwise extents and sidewall boundary conditions are studied. Special attention is devoted to the three-dimensionality of the plunging breaker. Compared with three-dimensional (3D) models, the 2D model accurately reproduces the dynamics of a breaking solitary wave in the early stage, but it is inadequate for the study of the post-breaking process. For a 3D NWF with nonslip sidewall boundary condition, the wave domain can be divided into two regions with different physical properties. In the near-wall region, the nonslip boundary condition on the sidewall plays a crucial role in the wave hydrodynamics, while in the central region, the properties of the breaking wave are similar to those for the periodic boundary condition, which provide a closer representation of the real sea environment. The spanwise length of the NWF plays only a minor role in simulations under the periodic boundary condition. Furthermore, lateral boundaries and spanwise length show more influences on a plunging breaker with larger incident wave steepness. This study provides valuable support for the design of numerical simulations of wave breaking.

We report on a molecular simulation study of the origin of nonslip or slip hydrodynamic boundary conditions in clay nanopores, focusing on the role of electrostatics. We simulate hydrodynamic and electro-osmotic flows and consider both charged (montmorillonite) and uncharged (pyrophyllite) clays. We further use two commonly used force fields to analyze the effect of local interactions, in particular, the effect of the polarity of the surface, in addition to the mere effect of the presence or absence of a net charge and counterions. For the 6 nm pore investigated here, the molecular velocity profile can be well described by continuum hydrodynamics only if (a) proper boundary conditions, with a slip or stagnation length determined from molecular simulation, are taken into account and (b) the ionic density profiles from MD simulations are used in the case of electro-osmotic flow, because the Poisson–Boltzmann equation fails to reproduce the ionic profiles, hence the force acting on the fluid. Among the considered force fields, only CLAYFF predicts a hydrophobic pyrophyllite and hydrophilic montmorillonite, as expected from experimental behavior. The nonslip or slip boundary conditions at clay surfaces strongly depend on electrostatic interactions of water molecules with the surface. The presence of a net charge results in an average electric field experienced by surface water molecules between the charged surface and the condensed layer counterions, which influences their orientation. The charge distribution inside the clay layer determines the polarity of the surface and hence the strength of hydrogen bonds donated by water molecules to surface oxygen atoms.

A unified approach for nonslip and slip boundary conditions in the lattice Boltzmann method

At present, no clear guidelines exist for modeling non-water-cooled small modular reactors (SMRs) despite the rising need for high-fidelity simulation tools to support regulators and the industry. Most SMR concepts currently under the Canadian prelicensing review adopted non-water-cooled–reactor technologies [molten salt reactor (MSR), gas-cooled reactor, and liquid metal–cooled reactor] that are new for Canada. There is a need for a modeling tool set that is broadly applicable for the assessment of advanced technologies used in SMRs. Computational fluid dynamics (CFD) can be used in performance evaluation and safety analysis of non-water-cooled SMRs for modeling three-dimensional (3-D) fluid flow and heat transfer in geometries of arbitrary complexity without resorting to geometry-specific empirical correlations. This study investigates the capabilities of existing models within a commercial CFD code to simulate the flow and heat transfer characteristics in a MSR configuration. The Oak Ridge National Laboratory (ORNL) Molten Salt Reactor Experiment (MSRE) configuration was simulated in this study using a stand-alone CFD approach, and CFD predictions were assessed with ORNL data. Intricate geometry details within the MSRE core were included in the computational model to study the associated geometric effects. The results obtained in this study showcased the ability of CFD to predict 3-D effects within the computational domain especially at the lower plenums. The predicted trends for the temperature rise in the fuel and moderator within the core were in good agreement with the ORNL data. The results presented in this paper constitute the first step in developing Canadian Nuclear Laboratories’ capability for CFD modeling of non-water SMRs.

The slip boundary condition in the dynamics of solid particles immersed in Stokesian flows

Hydrodynamic journal bearings, coated with polytetrafluoroethylene (PTFE) and lubricated by water, have been widely used in ships and large-scale pumps, and the function is to maintain the stability of rotor system. However, slip velocity exists on the PTFE-coated surface, whose effect is still an open question. This study aims to investigate the static characteristics of water-lubricated hydrodynamic journal bearings under three-dimensional slip velocity boundary conditions. Firstly, under the non-slip boundary condition, the CFD (computational fluid dynamics) method with ANSYS Fluent is verified based on the Reynolds lubrication equation and the open literature. Then, a three-dimensional slip velocity equation that is based on the Navier slip velocity boundary condition is proposed and embedded into Fluent. Finally, the effects of slip length on the static characteristics are analyzed. Under the same eccentricity ratio, with the increase in slip length, the load capacity decreases due to the decrease of the pressure circumferential gradient, and the friction power decreases. Under the same eccentricity ratio and the same slip length, with the increase in the attitude angle, the load capacity and friction power increase. However, under the non-slip boundary condition, the effects of attitude angle on the load capacity and friction power are insignificant. This paper could provide a reference for studying slip velocity in the hydrodynamic journal bearing.

Obstructive sleep apnea syndrome (OSAS) may cause apneas or hypopneas, both physically and emotionally harmful to their sufferers. It has been realized that the periodic intermittent cessations of breathing or reductions in airflow resulted from OSAS is closely related to the developed pathological change in upper airways of the patients. In this paper, the authors present numerical simulations of airflows and fluid-solid interaction analysis for human upper airways. The objective of the research is to investigate airfield characteristics of the human upper airway by means of computational fluid dynamics (CFD) and the finite element (FE) method. The authors reconstruct three-dimensional models of the upper airway from the nostril to the epiglottis based on CT scanning images collected from two clinic volunteers. Based on the reconstruction three-dimensional CFD models that precisely preserve original configuration of upper airways are created. The CFD analysis is carried out by the FE method with boundary conditions of pressure at the nostril and of velocity at the top of vocal cord. The non-slip boundary conditions are used on the interior walls of the upper airway. With the CFD results the pressure and velocity distributions in the airflow field are quantitatively determined. For fluid-solid interaction analyses, the upper airway in the vicinity of the pharyngeal cavity is meshed using the reconstructed model. The fluid-solid interactive computations are performed for the healthy person and the OSAS patient. The results show that the hypertrophy of the soft palate remarkably escalates both the pressure and the deformation levels of the upper airway and hinders the airflow in the cavity channels.

We construct a Poiseuille type flow which is a bounded entire solution of the nonstationary Navier-Stokes and the Stokes equations in a half space with non-slip boundary condition. Our result in particular implies that there is a nontrivial solution for the Liouville problem under the non-slip boundary condition. A review for cases of the whole space and a slip boundary condition is included.

This work studies the effects of hydrodynamic and thermal slip boundaries on Rayleigh-B′enard convection (RB convection) using lattice Boltzmann method (LBM). Firstly, the theoretical relations of the critical Rayleigh number (Rc) and corresponding wavenumber (ac) of RB convection with partially slippery boundary conditions on infinite horizontal plates are derived using the linear stability analysis. The results make previous studies by others under both slip and nonslip boundary conditions as special cases of the general relations. Secondly, before numerical study of the effects of various slip side walls on RB convection in a 2D box, a new implementation of partial slip boundary conditions in LBM is developed by using the parameter of tangential momentum accommodation coefficient (TMAC,σ). This new implementation utilizes the native expressions of velocity gradients in LBM and then eliminates the need for information of neighbor nodes to estimate the velocity and temperature gradients, which is inevitable for conventional numerical technique like finite-difference method. Thirdly, the numerical simulations show that the vertical slip side walls have similar impacts as the horizontal slip plates on the determination of Rc and the relations for infinite horizontal plates can be used as guidelines for the cases with side walls. The observations of pattern selection in the box with aspect ratio equal to 2 show that when σh (σ of horizontal plates) is less than 0.02, the preferred pattern is the one-roll mode. When σh ≥ 0.02, the fluid prefers the two-roll mode in which the fluid moves upwards in the center of the box if σv ≤ 0.1 (σ of vertical side walls), while the fluid switches the rotation directions if σv ≥ 0.2. The investigation of initial disturbance indicates the existence of the threshold of the initial amplitude for the desired mode. This result reveals the importance of initial conditions to RB convection.

Eu's GH(Genera1ized Hydrodynamic) equations are presented for analyzing a hypersonic flow over a double-cone geometry which shows various aerodynamic phenomena such as shock-shock interaction, shock-boundary layer interaction, etc. In order to analyze rarefied hypersonic flow, axisymrnetric generalized hydrodynamic equations are developed and validated by Rothe nozzle flow problem. Two kinds of solid surface boundary conditions nonslip and Langmuir's slip BC are examined, too. The hypersonic rarefied flow results acquired by GH equations are compared with experimental data and Navier-Stokes equations calculations with slip and nonslip boundary conditions. The calculations by GH equations show the more accurate flow predictions than those of NavierStokes equations, and GH equastion with some assumptions was able to be found that it is a useful tool to analyze rarefied hypersonic flows.

The aim of this work is to simulate the complex 3D hydrodynamics inside free-surface anti-roll tanks with obstacles and side sub-compartments. The case studies comprise a rectangular tank, a tank with a C-shaped section and a rectangular tank with baffles, for which experimental results are provided. The simulations have been performed for 3 and 6 degrees of roll, and for various filling levels. The Open Source Computational Fluid Dynamics (CFD) tool OpenFOAM has been used to carry out the simulations. Various turbulence models and boundary condition implementations have been used. It is shown in the paper that the k-ω SST model with slip boundary condition is the one that provides the best trade-off between accuracy and computational efficiency. In order for present results to be easily reproducible, the simulations files, also including the geometrical ones, are provided as supplementary material.

A techno-economic investigation of 2D and 3D configurations of fins and their effects on heat sink efficiency of MHD hybrid nanofluid with slip and non-slip flow

This paper investigates the role of slip boundary conditions in computational fluid dynamics modeling of material extrusion and layer deposition during 3D concrete printing. The mortar flow governed by the Navier-Stokes equations was simulated for two different slip boundary conditions at the extrusion nozzle wall: no-slip and free-slip. The simulations were conducted with two constitutive models: a generalized Newtonian fluid model and an elasto-viscoplastic fluid model. The cross-sectional shapes of up to three printed layers were compared to the experimental results from literature for different geometrical- and speed-ratios. The results reveal that employing free-slip boundary conditions at the extrusion nozzle wall improves layer-mimicking quality for both constitutive models, indicating the presence and importance of a lubricating layer of fine particles at the concrete-solid wall interface. This enhanced performance is primarily due to the observed decrease in extrusion pressure that minimizes layer height- and width-deviations compared to the experimental prints. Furthermore, the free-slip boundary conditions play an important role in predicting the multilayer prints, its deformation and groove shapes.