A second-order-accurate finite-volume method is developed for the solution of incompressible Navier–Stokes equations on locally refined nested Cartesian grids. Numerical accuracy and stability on locally refined nested Cartesian grids are achieved using a finite-volume discretization of the incompressible Navier–Stokes equations based on higher-order conservation principles – i.e., in addition to mass and momentum conservation, kinetic energy conservation in the inviscid limit is used to guide the selection of the discrete operators and solution algorithms. Hanging nodes at the interface are virtually slanted to improve the pressure–velocity projection, while the other parts of the grid maintain an orthogonal Cartesian grid topology. The present method is straight-forward to implement and shows superior conservation of mass, momentum, and kinetic energy compared to the conventional methods employing interpolation at the interface between coarse and fine grids.

In order to investigate effects of grid resolution on large-eddy simulation of flow over a heavy vehicle, large-eddy simulations over the vehicle with coarse grid and fine grid are conducted. In addition, comparison of drag coefficients with the experimental data obtained by a wind tunnel experiment is conducted. Both of the drag coefficients of coarse grid and fine grid large-eddy simulation show good agreement with the experimental data. Flow fields obtained by the coarse and the fine grid large-eddy simulation are compared in the vehicle frontal-face region, the vehicle rear wheel region, and the vehicle base region. Coarse grid large-eddy simulation shows good agreement with the fine grid large-eddy simulation in the vehicle front face region and the vehicle rear wheel region, since the flow over the present vehicle is dominated by flow separation which is geometrically pre-determined, not by the skin friction which is known to be sensitive to grid resolution.

Unsteady turbulent flow characteristics over a two-blade horizontal wind turbine rotor is analyzed using a large-eddy simulation technique. The wind turbine rotor corresponds to the configuration of the U.S. National Renewable Energy Laboratory (NREL) phase VI campaign. The filtered incompressible Navier-Stokes equations in a non-inertial reference frame fixed at the centroid of the rotor, are solved with centrifugal and Coriolis forces using an unstructured-grid finite-volume method. A systematic analysis of effects of grid resolution, computational domain size, and time-step size on simulation results, is carried out. Simulation results such as the surface pressure coefficient, thrust coefficient, torque coefficient, and normal and tangential force coefficients are found to agree favorably with experimental data. The simulation showed that pressure fluctuations, which produce broadband flow-induced noise and vibration of the blades, are especially significant in the mid-chord area of the suction side at around 70 to 95 percent spanwise locations. Large-scale vortices are found to be generated at the blade tip and the location connecting the blade with an airfoil cross section and the circular hub rod. These vortices propagate downstream with helical motions and are found to persist far downstream from the rotor.

Investigating the aerodynamic reduction of drag in heavy vehicles, such as trucks or tractor-trailers, has considerable significance given the strong influence on related industries. The underbody flow that passes through the underside of heavy vehicles induces considerable drag while interacting with rolling wheels and other structures. Nonetheless, the reduction of drag caused by underbody flow has received less attention than that attributed to upper and forebody flows. Side skirts are common underbody drag-reduction devices that consist of straight panels curtaining the underspace between the front and rear wheels to control the underbody flow in the ground clearance. In this study, we propose two different types of side skirts with flaps or additional inclined inner panels to maximize drag reduction. Effects of these devices are quantitatively evaluated by wind tunnel tests and computational fluid dynamics analysis. In wind tunnel tests with 1/8 scaled-down vehicle models, drag coefficient is reduced by more than 5% for both side skirts. Effects of various physical dimensions or angle variations on drag reduction are determined. Large-eddy simulation (LES) estimated similar drag reduction with reduced vortical activities, loss of streamwise momentum, strength of turbulent kinetic energy and global pressure difference, compared to the case without side skirts.

In order to gain better understanding for rheology of an isolated red blood cell (RBC) and a group of multiple RBCs, new continuum models for describing mechanical properties of cellular structures of an RBC and inter-cellular interactions among multiple RBCs are developed. The viscous property of an RBC membrane, which characterizes dynamic behaviors of an RBC under stress loading and unloading processes, is determined using a generalized Maxwell model. The present model is capable of predicting stress relaxation and stress–strain hysteresis, of which prediction is not possible using the commonly used Kelvin–Voigt model. Nonlinear elasticity of an RBC is determined using the Yeoh hyperelastic material model in a framework of continuum mechanics using finite-element approximation. A novel method to model inter-cellular interactions among multiple adjacent RBCs is also developed. Unlike the previous modeling approaches for aggregation of RBCs, where interaction energy for aggregation is curve-fitted using a Morse-type potential function, the interaction energy is analytically determined. The present aggregation model, therefore, allows us to predict various effects of physical parameters such as the osmotic pressure, the thickness of a glycocalyx layer, the penetration depth, and the permittivity, on the depletion and electrostatic energy among RBCs. Simulations for elongation and recovery deformation of an RBC and for aggregation of multiple RBCs are conducted to evaluate the efficacy of the present continuum modeling methods.

Numerical simulations of fully-developed turbulent flow through a straight square duct at three Reynolds numbers of 190, 300, and 550 based on the friction velocity averaged over the duct perimeter and duct half width are reported. The effect of Reynolds number on the mean and turbulence statistics and secondary flow is investigated. The mean streamwise-velocity profiles along the wall bisector are found to obey a logarithmic scaling when they are normalized by the friction velocity at the mid-wall. Magnitudes and spatial distributions of the peak production and diffusion terms in the mean streamwise-vorticity equation normalized by the wall units are found to be unaffected by the Reynolds-number variation when they are considered in wall-unit coordinates.

A computational analysis of vortex-shedding-induced vibration of a flexible splitter plate behind a cylinder at a low Reynolds number is conducted to understand effects of the length and flexibility of a splitter plate on the drag and lift of a cylinder and vibration of the attached plate. The drag and lift coefficients, the Strouhal number of vortex shedding, and the magnitude of tip displacements of a flexible splitter plate are found to be intricate functions of the plate flexibility. The deflection shape of a flexible splitter plate is dependent on the length of the plate, while the deflection magnitude is a function of the bending stiffness and natural frequencies of the corresponding plate. It is concluded in the present work that the Strouhal number of vortex shedding or the frequency of plate deflection is difficult to estimate using natural frequencies of the plate, which are calculated by inducing free vibration, since the fluid loading is distributed non-uniformly over the plate rather than concentrated at the tip of the plate. The present study suggests that the flexibility of a splitter plate, in general, adversely modulates the drag and lift forces acting on the cylinder surface while it promotes the oscillation of the plate.

A dynamic global-coefficient mixed subgrid-scale eddy-viscosity model for large-eddy simulation of turbulent flows in complex geometries is developed. In the present model, the subgrid-scale stress is decomposed into the modified Leonard stress, cross stress, and subgrid-scale Reynolds stress. The modified Leonard stress is explicitly computed assuming a scale similarity, while the cross stress and the subgrid-scale Reynolds stress are modeled using the global-coefficient eddy-viscosity model. The model coefficient is determined by a dynamic procedure based on the global-equilibrium between the subgrid-scale dissipation and the viscous dissipation. The new model relieves some of the difficulties associated with an eddy-viscosity closure, such as the nonalignment of the principal axes of the subgrid-scale stress tensor and the strain rate tensor and the anisotropy of turbulent flow fields, while, like other dynamic global-coefficient models, it does not require averaging or clipping of the model coefficient for numerical stabilization. The combination of the global-coefficient eddy-viscosity model and a scale-similarity model is demonstrated to produce improved predictions in a number of turbulent flow simulations.

A fully-implicit ghost-cell immersed boundary method for simulations of flow over complex moving bodies on a Cartesian grid is presented. The present immersed boundary method is highly capable of controlling the generation of spurious force oscillations on the surface of a moving body, thereby producing an accurate and stable solution. Spurious force oscillations on the surface of an immersed moving body are reduced by alleviating spatial and temporal discontinuities in the pressure and velocity fields across non-grid conforming immersed boundaries. A sharp-interface ghost-cell immersed-boundary method is coupled with a mass source and sink algorithm to improve the conservation of mass across non-grid conforming immersed boundaries. To facilitate the control for the temporal discontinuity in the flow field due to a motion of an immersed body, a fully-implicit time-integration scheme is employed. A novel backward time-integration scheme is developed to effectively treat multiple layers of fresh cells generated by a motion of an immersed body at a high CFL number condition. The present backward time-integration scheme allows to impose more accurate and stable velocity vectors on fresh cells than those interpolated. The effectiveness of the present fully-implicit ghost-cell immersed boundary method coupled with a mass source and sink algorithm for reducing spurious force oscillations during simulations of moving body problems is demonstrated in a number of test cases.

Large-eddy simulations of turbulent channel flow at Reτ = 395 are performed using explicit filtering. Two different subfilter-scale models, the dynamic Smagorinsky mixed model and the dynamic global-coefficient mixed model, are formulated in accordance with the explicitly filtered governing equations. The use of explicit filtering separates the filtering operation from discretization, thereby producing a grid-independent solution. In explicit-filter large-eddy simulations, both the dynamic Smagorinsky mixed and the dynamic global-coefficient mixed subfilter-scale models are found to produce solutions close to the non-filtered direct numerical simulation data when explicit-filter widths in the streamwise and spanwise directions and at the center of the channel in the wall normal direction are about four times the grid spacings for direct numerical simulation. Solutions obtained using explicit-filter large-eddy simulation are compared with solutions obtained using implicit-filter large-eddy simulation in a range of filter and grid resolution. Explicit-filter large-eddy simulations performed on gradually refined grids with a fixed set of explicit-filter widths are found to produce grid-converged solutions for both models. Similarly in implicit-filter large-eddy simulation, predictive capabilities of subfilter-scale models in explicit-filter large-eddy simulation are found to be interfered with truncation errors when the ratio of the explicit-filter width to the grid spacing is small.