H.S. Tang

An overset-grid method for 3D unsteady incompressible flows

A composite-grid numerical method is developed for simulating unsteady, three-dimensional (3D), incompressible flows in complex geometries. The governing equations are solved using a second-order accurate, finite-volume method based on the dual time-stepping artificial compressibility approach. Overset grids are employed to discretize arbitrarily complex geometries, and a new interface algorithm is developed to facilitate communication between neighboring grids. The algorithm is inspired by the necessary and sufficient conditions for satisfying global mass conservation in a composite domain and is simple to implement in 3D. Numerical experiments show that the new interpolation scheme is superior to straightforward, trilinear interpolation of all flow variables as it minimizes non-physical spurious oscillations in the overlap region, is less sensitive to grid refinement, and greatly enhances the computational efficiency of the iterative algorithm. The advantages of the new method are especially pronounced when adjacent overset subdomains are discretized with different spatial resolutions. The potential of the method as a powerful technique for simulating complex engineering flows is demonstrated by applying it to calculate vortex shedding from a circular cylinder mounted between two endplates and flow in a rectangular channel with two wall-mounted obstacles.

Unsteady circular tube flow of compressible polymeric liquids subject to pressure-dependent wall slip

A mathematical model is developed for the time-dependent circular tube flow of compressible polymeric liquids subject to pressure-dependent slip at the wall and applied to a poly (dimethyl siloxane) (PDMS). The parameters of pressure-dependent wall slip velocity and shear viscosity of the PDMS were determined using combinations of small-amplitude oscillatory shear, steady torsional and squeeze flows and were employed in the prediction of the time-dependent circular tube flow behavior of the PDMS. The numerical solutions suggest that a steady tube flow is generated when the flow boundary condition at the wall is stable, that is, either a contiguous stick (or weak slip) or a contiguous strong slip condition along the entire length of the wall. On the other hand, when the flow boundary condition changes from stick (or weak slip) to strong slip at any location along the length of the wall, undamped periodic oscillations in pressure and mean velocity are observed. The experimentally characterized and simulated tube flow curves of PDMS are similar and the simulation findings for flow stability are in general consistent with the experimentally observed flow instability behavior of PDMS.

Time-dependent tube flow of compressible suspensions subject to pressure dependent wall slip: Ramifications on development of flow instabilities

A mathematical model developed earlier for the time-dependent circular tube flow of compressible polymer melts subject to pressure-dependent wall slip [Tang and Kalyon, J. Rheol 52, 507–525 (2008)] was applied to the tube flow of polymeric suspensions with rigid particles. The model relies on the apparent slip mechanism for suspension flow with the additional caveat that the polymeric binder slips at the wall according to a pressure-dependent wall slip condition. The numerical simulations of the tube flow of concentrated suspensions suggest that steady flow is generated when the flow boundary condition at the wall is a contiguous strong slip condition along the entire length of the tube wall. The findings of the simulations are consistent with the experimental flow curves and flow instability data collected on suspensions of a poly (dimethyl siloxane), which itself exhibits wall slip, compounded with rigid and hollow spherical particles in the 10–40% by volume range. Increasing the concentration of rigid ...

On Nonconservative Algorithms for Grid Interfaces

In computations of fluid flows by domain decomposition methods, the necessity of conservation at grid interfaces is now widely claimed. In this paper we consider nonconservative algorithms for the interfaces. Our investigation begins with discussions about typical nonconservative interface treatments for one-dimensional calculations. The analysis shows that the conservation error of a numerical solution caused by a nonconservative interface matching has an upper bound when the solution itself is bounded. Furthermore, if the numerical solution converges as the mesh size goes to zero, it converges to a weak solution of the problem under certain conditions that may be detected numerically. Also, we acquire similar results for two-dimensional calculations on grids intersecting with each other in an arbitrary way. In order to illustrate the theoretical results, we present numerical examples and demonstrate that, under those conditions, conservation error reduces and accuracy for jumps as well as locations of discontinuities improves as the mesh size decreases.

An overset grid method for integration of fully 3D fluid dynamics and geophysics fluid dynamics models to simulate multiphysics coastal ocean flows

It is now becoming important to develop our capabilities to simulate coastal ocean flows involved with distinct physical phenomena occurring at a vast range of spatial and temporal scales. This paper presents a hybrid modeling system for such simulation. The system consists of a fully three dimensional (3D) fluid dynamics model and a geophysical fluid dynamics model, which couple with each other in two-way and march in time simultaneously. Particularly, in the hybrid system, the solver for incompressible flow on overset meshes (SIFOM) resolves fully 3D small-scale local flow phenomena, while the unstructured grid finite volume coastal ocean model (FVCOM) captures large-scale background flows. The integration of the two models are realized via domain decomposition implemented with an overset grid method. Numerical experiments on performance of the system in resolving flow patterns and solution convergence rate show that the SIFOM-FVCOM system works as intended, and its solutions compare reasonably with data obtained with measurements and other computational approaches. Its unparalleled capabilities to predict multiphysics and multiscale phenomena with high-fidelity are demonstrated by three typical applications that are beyond the reach of other currently existing models. It is anticipated that the SIFOM-FVCOM system will serve as a new platform to study many emerging coastal ocean problems.

Analysis on creeping channel flows of compressible fluids subject to wall slip

Creeping channel flows of compressible fluids subject to wall slip are widely encountered in industries. This paper analyzes such flows driven by pressure in planar as well as circular channels. The analysis elucidates unsteady flows of Newtonian fluids subject to the Navier slip condition, followed by steady flows of viscoplastic fluids, in particular, Herschel–Bulkley fluids and their simplifications including power law and Newtonian fluids, that slip at wall with a constant coefficient or a coefficient inversely proportional to pressure. Under the lubrication assumption, analytical solutions are derived, validated, and discussed over a wide range of parameters. Analysis based on the derived solutions indicates that unsteadiness alters cross-section velocity profiles. It is demonstrated that compressibility of the fluids gives rise to a concave pressure distribution in the longitudinal direction, whereas wall slip with a slip coefficient that is inversely proportional to pressure leads to a convex pressure distribution. Energy dissipation resulting from slippage can be a significant portion in the total dissipation of such a flow. A distinctive feature of the flow is that, in case of the pressure-dependent slip coefficient, the slip velocity increases rapidly in the flow direction and the flow can evolve into a pure plug flow at the exit.

Coupling of CFD model and FVCOM to predict small-scale coastal flows

In order to accurately simulate small-scale coastal ocean phenomena, we propose to couple a computational fluid dynamics (CFD) model with the Unstructured Grid Finite Volume Coastal Ocean Model (FVCOM). The CFD model resolves small-scale flows, the FVCOM predicts large-scale background currents, and the resulting hybrid system is able to capture flow phenomena with spatial scales from centimeters to hundreds of kilometers. The coupling is two-way and realized using domain decomposition with aid of Chimera overset grids. Numerical examples are presented to demonstrate the feasibility and performance of the proposed hybrid approach.

Comments on algorithms for grid interfaces in simulating Euler flows

Abstract Some results concerning the algorithms for grid interfaces, which are crucial in simulating flows by zonal methods, are presented in this paper. It is indicated that the commonly used conservative interface scheme can ensure the discrete entropy condition, but it may be inconsistent and would bring a nonoverlapping solution on overlapping grids. A nonconservative interface matching obtained by interpolation can be monotonicity preserving, and it leads large conservation error when discontinuities are close to the interfaces. Methods for improvement of interface algorithms are also proposed.

Squeeze Flow Rheometry for Rheological Characterization of Energetic Formulations

The rheological characterization and the determination of the parameters describing the shear viscosity and wall slip behavior of energetic materials is a challenge. Some of the conventional rheometers including various rotational rheometers are not capable of deforming typical energetic formulations with their gel binders and high degrees of particulate fill. Other available rheometers are not conducive to rheological characterization of energetic formulations in the vicinity of the manufacturing operation with the data to be used immediately for quality control. Squeeze flow provides significant advantages in safety of materials handling and exposure as well as providing easy data generation for routine quality control of energetic formulations being processed. Here the basic hardware is reviewed along with the methods for the analysis of raw data to determine the parameters of the shear viscosity and the wall slip of energetic formulations. It is suggested that appropriate analytical and numerical analyses can indeed provide the basic wherewithal necessary for the solution of the inverse problem of squeeze flows to characterize the shear viscosity and the wall slip parameters provided that the issues of uniqueness and stability are properly addressed.

Hydrodynamic Effects of Solitary Waves Impinging on a Bridge Deck with Air Vents

AbstractAir vents in bridge decks are considered one potential measure for mitigating risk of damage to coastal bridges caused by extreme storm surge because they may reduce hydrodynamic uplift loa...