Physics

We introduce a simplified model of physiological coughing or sneezing, in the form of a thin liquid layer subject to a rapid (30 m/s) air stream. The setup is simulated using the Volume-Of-Fluid method with octree mesh adaptation, the latter allowing grid sizes small enough to capture the Kolmogorov length scale. The results confirm the trend to an intermediate distribution between a Log-Normal and a Pareto distribution P(d)??d ??.3 for the distribution of droplet sizes in agreement with a previous re-analysis of experimental results by one of the authors. The mechanism of atomisation does not differ qualitatively from the multiphase mixing layer experiments and simulations. No mechanism for a bimodal distribution, also sometimes observed, is evidenced in these simulations.

We describe a one-dimensional (1D) unsteady and viscous flow model that is derived from the momentum and mass conservation equations, and to enhance this physics-based model, we use a machine learning approach to determine the unknown modeling parameters. Specifically, we first construct an idealized larynx model and perform ten cases of three-dimensional (3D) fluid--structure interaction (FSI) simulations. The flow data are then extracted to train the 1D flow model using a sparse identification approach for nonlinear dynamical systems. As a result of training, we obtain the analytical expressions for the entrance effect and pressure loss in the glottis, which are then incorporated in the flow model to conveniently handle different glottal shapes due to vocal fold vibration. We apply the enhanced 1D flow model in the FSI simulation of both idealized vocal fold geometries and subject-specific anatomical geometries reconstructed from the MRI images of rabbits' larynges. The 1D flow model is evaluated in both of these setups and is shown to have robust performance. Therefore, it provides a fast simulation tool superior to the previous 1D models.

We study the three-dimensional turbulent Kolmogorov flow, i.e. the Navier-Stokes equations forced by a low-single-wave-number sinusoidal force in a periodic domain, by means of direct numerical simulations. This classical model system is a realization of anisotropic and non-homogeneous hydrodynamic turbulence. Boussinesq's eddy viscosity linear relation is checked and found to be approximately valid over half of the system volume. A more general nonlinear quadratic constitutive equation is proposed and its parameters estimated at varying the Taylor scale-based Reynolds number in the flow up to the value 200. This provides a Reynolds number-dependent quadratic closure for the Kolmogorov flow. The case of a forcing with a different shape, here chosen Gaussian, is considered and the differences with the sinusoidal forcing are emphasized.

The classical model for studying one-phase Hele-Shaw flows is based on a highly nonlinear moving boundary problem with the fluid velocity related to pressure gradients via a Darcy-type law. In a standard configuration with the Hele-Shaw cell made up of two flat stationary plates, the pressure is harmonic. Therefore, conformal mapping techniques and boundary integral methods can be readily applied to study the key interfacial dynamics, including the Saffman-Taylor instability and viscous fingering patterns. As well as providing a brief review of these key issues, we present a flexible numerical scheme for studying both standard and non-standard Hele-Shaw flows. Our method consists of using a modified finite difference stencil in conjunction with the level set method to solve the governing equation for pressure on complicated domains and track the location of the moving boundary. Simulations show that our method is capable reproducing the distinctive morphological features of the Saffman-Taylor instability on a uniform computational grid. By making straightforward adjustments, we show how our scheme can easily be adapted to solve for a wide variety of configurations, including cases where the gap between the plates is linearly tapered, the plates are separated in time, and the entire Hele-Shaw cell is rotated at a given angular velocity.

We present a unified variational mechanics framework for cavitating turbulent flows and structural motions via a stabilized finite element formulation. To model the finite mass transfer rate in cavitation phenomena, we employ the homogenous mixture-based approach via phenomenological scalar transport differential equations. Stable linearizations of the finite mass transfer terms for the mass continuity equation and the scalar transport equations are derived for robust and accurate implementation. The linearized matrices for the cavitation equation are imparted a positivity-preserving property to address numerical oscillations arising from high-density gradients typical of two-phase cavitating flows. The proposed formulation is strongly coupled in a partitioned manner with an incompressible 3D Navier-Stokes finite element solver, and the unsteady problem is advanced in time using a fully-implicit generalized- α time integration scheme. We first verify the implementation on the benchmark case of Rayleigh bubble collapse. We demonstrate the accuracy and convergence of the cavitation solver by comparing the numerical solutions with the analytical solutions of the Rayleigh-Plesset equation for bubble dynamics. We find our solver to be robust for large time steps and the absence of spurious oscillations in the pressure field. The cavitating flow solver is coupled with a hybrid URANS-LES turbulence model with a turbulence viscosity corrected for the presence of vapor. We validate the coupled solver for a very high Reynolds number turbulent cavitating flow over a NACA0012 hydrofoil section. Finally, the proposed method is solved in an Arbitrary Lagrangian-Eulerian framework to study turbulent cavitating flow over a pitching hydrofoil section and the coupled FSI results are explored for characteristic features of cavitating flows such as re-entrant jet and periodic cavity shedding.

A three-dimensional (3D) scanning velocimetry system is developed to quantify the 3D configurations of particles and their surrounding volumetric, three-component velocity fields. The approach uses a translating laser sheet to rapidly scan through a volume of interest and sequentially illuminate slices of the flow containing both tracers seeded in the fluid and particles comprising the aggregation of interest. These image slices are captured by a single high-speed camera, encoding information about the third spatial dimension within the image time-series. Where previous implementations of scanning systems have been developed for either volumetric flow quantification or 3D object reconstruction, we evaluate the feasibility of accomplishing these tasks concurrently with a single-camera, which can streamline data collection and analysis. The capability of the system was characterized using a study of induced vertical migrations of millimeter-scale brine shrimp (Artemia salina). Identification and reconstruction of individual swimmer bodies and 3D trajectories within the migrating aggregation were achieved up to the maximum number density studied presently, 8? 10 5 animals per m 3 . This number density is comparable to the densities of previous depth-averaged 2D measurements of similar migrations. Corresponding velocity measurements of the flow indicate that the technique is capable of resolving the 3D velocity field in and around the swimming aggregation. At these animal number densities, instances of coherent flow induced by the migrations were observed. The accuracy of these flow measurements was confirmed in separate studies of a free jet at R e D =50 .

A spacetime outlook on Computational Fluid Dynamics is advocated: models in fluid mechanics often have the spacetime correlation property, which should be inherited and preserved in the corresponding numerical algorithms. Starting from the fundamental formulation of fluid mechanics under continuum hypothesis, this paper defines the meaning of spacetime correlation of the models, establishes the fundamental principle of finite volume schemes, expounds the necessity of spacetime coupling of algorithms, as well as realizes the physical and mathematical unification of basic governing equations of fluid mechanics and finite volume schemes. In practice, the design methodology of spacetime coupling high order numerical algorithms is presented, and the difference from spacetime decoupling method is compared. It should be pointed out that most of the contents in this paper are suitable for computational fluid dynamics under the assumption of continuous medium, and some are only suitable for compressible flow.

Wormlike micelles are self-assemblies of polymer chains that can break and recombine reversibly. In this paper, we derive a thermodynamically consistent two species micro-macro model of wormlike micellar solutions by employing an energetic variational approach. The model incorporates a breakage and combination process of polymer chains into the classical micro-macro dumbbell model for polymeric fluids in a unified variational framework. We also study different maximum entropy closure approximations to the new model by "variation-then-closure" and "closure-then-variation" approaches. By imposing proper dissipation in the coarse-grained level, the closure model, obtained by "closure-then-approximation", preserves the thermodynamical structure of both mechanical and chemical parts of the original system. Several numerical examples show that the closure model can capture the key rheological features of wormlike micellar solutions in shear flows.

In the lattice Boltzmann method (LBM), the widely utilized wall boundary is the bounce-back (BB) boundary, which corresponds to the no-slip boundary. The BB boundary prevents the LBM from capturing the accurate shear drag on the wall when addressing high Reynolds number flows using coarse-grid systems. In this study, we proposed a "wall-function bounce (WFB)" boundary that incorporates a wall function into the LBM's boundary condition and overcomes the limitation of the BB. The WFB boundary calculates the appropriate shear drag on the wall using a wall function model, and thereafter modifies distribution functions to reflect the shear drag. The Spalding's law was utilized as the wall function in WFB. Simulations of turbulent channel flow at R e τ =640 and 2003 using the LBM-based large-eddy simulation (LBM-LES) were conducted to validate the effectiveness of the proposed boundary condition. The results indicate that the BB boundary underestimated the time-averaged velocity in the buffer layer at R e τ =640, and the averaged velocity in the entire domain at R e τ =2003, when using coarse-grid systems. However, WFB obtained the proper shear drag on the wall and thus, compensated for the underestimation and agreed better with the experimental or DNS data, especially at the first-layer grid. In addition, WFB improved the Reynolds normal stress in the near-wall region to some extent. The distributions of shear stress on the wall by WFB was analogous to those by the wall model function in the finite volume method.

A scheme for the solution of fluid-structure interaction (FSI) problems with weakly compressible flows is proposed in this work. A novel hybridizable discontinuous Galerkin (HDG) method is derived for the discretization of the fluid equations, while the standard continuous Galerkin (CG) approach is adopted for the structural problem. The chosen HDG solver combines robustness of discontinuous Galerkin (DG) approaches in advection-dominated flows with higher order accuracy and efficient implementations. Two coupling strategies are examined in this contribution, namely a partitioned Dirichlet-Neumann scheme in the context of hybrid HDG-CG discretizations and a monolithic approach based on Nitsche's method, exploiting the definition of the numerical flux and the trace of the solution to impose the coupling conditions. Numerical experiments show optimal convergence of the HDG and CG primal and mixed variables and superconvergence of the postprocessed fluid velocity. The robustness and the efficiency of the proposed weakly compressible formulation, in comparison to a fully incompressible one, are also highlighted on a selection of two and three dimensional FSI benchmark problems.