Shizhao Wang

An immersed boundary method based on the lattice Boltzmann approach in three dimensions, with application

The immersed boundary (IB) method originated by Peskin has been popular in modeling and simulating problems involving the interaction of a flexible structure and a viscous incompressible fluid. The Navier-Stokes (N-S) equations in the IB method are usually solved using numerical methods such as FFT and projection methods. Here in our work, the N-S equations are solved by an alternative approach, the lattice Boltzmann method (LBM). Compared to many conventional N-S solvers, the LBM can be easier to implement and more convenient for modeling additional physics in a problem. This alternative approach adds extra versatility to the immersed boundary method. In this paper we discuss the use of a 3D lattice Boltzmann model (D3Q19) within the IB method. We use this hybrid approach to simulate a viscous flow past a flexible sheet tethered at its middle line in a 3D channel and determine a drag scaling law for the sheet. Our main conclusions are: (1) the hybrid method is convergent with first-order accuracy which is consistent with the immersed boundary method in general; (2) the drag of the flexible sheet appears to scale with the inflow speed which is in sharp contrast with the square law for a rigid body in a viscous flow.

An immersed boundary method based on discrete stream function formulation for two- and three-dimensional incompressible flows

An immersed boundary method is proposed in the framework of discrete stream function formulation for incompressible flows. In order to impose the non-slip boundary condition, the forcing term is determined implicitly by solving a linear system. The number of unknowns of the linear system is the same as that of the Lagrangian points representing the body surface. Thus the extra cost in force calculation is negligible if compared with that in the basic flow solver. In order to handle three-dimensional flows at moderate Reynolds numbers, a parallelized flow solver based on the present method is developed using the domain decomposition strategy. To verify the accuracy of the immersed-boundary method proposed in this work, flow problems of different complexity (decaying vortices, flows over stationary and oscillating cylinders and a stationary sphere, and flow over low-aspect-ratio flat-plate) are simulated and the results are in good agreement with the experimental or computational data in previously published literatures.

Effects of geometric shape on the hydrodynamics of a self-propelled flapping foil

The hydrodynamics of a free flapping foil is studied numerically. The foil undergoes a forced vertical oscillation and is free to move horizontally. The effect of chord-thickness ratio is investigated by varying this parameter while fixing other ones such as the Reynolds number, the density ratio, and the flapping amplitude. Three different flow regimes have been identified when we increase the chord-thickness ratio, i.e., left-right symmetry, back-and-forth chaotic motion, and unidirectional motion with staggered vortex street. It is observed that the chord-thickness ratio can affect the symmetry-breaking bifurcation, the arrangement of vortices in the wake, and the terminal velocity of the foil. The similarity in the symmetry-breaking bifurcation of the present problem to that of a flapping body under constraint is discussed. A comparison between the dynamic behaviors of an elliptic foil and a rectangular foil at various chord-thickness ratios is also presented.

A lift formula applied to low-Reynolds-number unsteady flows

A lift formula for a wing in a rectangular control volume is given in a very simple and physically lucid form, providing a rational foundation for calculation of the lift of a flapping wing in highly unsteady and separated flows at low Reynolds numbers. Direct numerical simulations on the stationary and flapping two-dimensional flat plate and rectangular flat-plate wing are conducted to assess the accuracy of the lift formula along with the classical Kutta-Joukowski theorem. In particular, the Lamb vector integral for the vortex force and the acceleration term of fluid for the unsteady inertial effect are evaluated as the main contributions to the unsteady lift generation of a flapping wing.

Unsteady Thin-Airfoil Theory Revisited: Application of a Simple Lift Formula

The physical foundations of unsteady thin-airfoil theory are explored in the general framework of viscous flows. The thin-airfoil lift formula is derived by using the simple lift formula that contains the vortex lift and the lift associated with the fluid acceleration. From a broader perspective, the thin-airfoil lift formula could be applicable even when the flow around an airfoil is moderately separated, from which the classical von Karman–Sears lift formula can be recovered as a reduced case. The quantitative relationship between boundary layer and lift generation is discussed. Direct numerical simulations of low-Reynolds-number flows over a flapping flat-plate airfoil are conducted to examine the accuracy and limitations of the thin-airfoil lift formula.

Lift enhancement by dynamically changing wingspan in forward flapping flight

Dynamically stretching and retracting wingspan has been widely observed in the flight of birds and bats, and its effects on the aerodynamic performance particularly lift generation are intriguing. The rectangular flat-plate flapping wing with a sinusoidally stretching and retracting wingspan is proposed as a simple model for biologically inspired dynamic morphing wings. Numerical simulations of the low-Reynolds-number flows around the flapping morphing wing are conducted in a parametric space by using the immersed boundary method. It is found that the instantaneous and time-averaged lift coefficients of the wing can be significantly enhanced by dynamically changing wingspan in a flapping cycle. The lift enhancement is caused by both changing the lifting surface area and manipulating the flow structures responsible to the vortex lift generation. The physical mechanisms behind the lift enhancement are explored by examining the three-dimensional flow structures around the flapping wing.

Study of the shock motion in a hypersonic shock system turbulent boundary-layer interaction

Wall pressure fluctuations and surface heat transfer signals have been measured in the hypersonic turbulent boundary layer over a number of compression-corner models. The distributions of the separation shock oscillation frequencies and periods have been calculated using a conditional sampling algorithm. In all cases the oscillation frequency distributions are of broad band, but the most probable frequencies are low. The VITA method is used for deducing large scale disturbances at the wall in the incoming boundary layer and the separated flow region. The results at present showed the existence of coherent structures in the two regions. The zero-cross frequencies of the large scale structures in the two regions are of the same order as that of the separation shock oscillation. The average amplitude of the large scale structures in the separated region is much higher than that in the incoming boundary layer. The length scale of the separation shock motion region is found to increase with the disturbance strength. The results show that the shock oscillation is of inherent nature in the shock wave/turbulent boundary layer interaction with separation. The shock oscillation is considered to be the consequence of the coherent structures in the separated region.

Evaluation of lift formulas applied to low-Reynolds-number unsteady flows

Different lift decompositions into the elemental terms are compared based on direct numerical simulations of a flapping flat plate and a flapping rectangular wing at low-Reynolds-number flows. The simple lift formula is given as a useful approximate form that has the vortex force and local acceleration terms. The accuracy of the simple lift formula in lift estimation is quantitatively evaluated in comparison with the general force formulas based on the fully resolved two- and three-dimensional unsteady velocity fields and the planar velocity fields at several spanwise locations in simulated particle-image-velocimetry measurements. In addition, the mathematical connections between the different force formulas are discussed.

Flow Past Two Freely Rotatable Triangular Cylinders in Tandem Arrangement

In this paper we investigate the interaction of two freely rotatable triangular cylinders that are placed in tandem in a laminar flow. To study how the spacing between the two cylinders may influence the dynamic behavior of the cylinders and vortical structure of the flow, we have performed a series of numerical simulations of the two-cylinder-flow system. In all the simulations, the dimensionless moment of inertia and Reynolds number are fixed to 1.0 and 200, respectively. Four cases with the spacing ratio (L/D) of 2.0, 3.0, 4.0, and 5.0 are studied. With the increase of spacing, three different states of motion of the system are found. At L/D 2.0, oscillatory rotation (swinging in both directions) is observed. At L/D 3.0 both cylinders exhibit quasi-periodic autorotations. At L/D 4.0 and 5.0, a more complicated pattern (irregular autorotation) is observed. For each case, the time history of angular velocity, the phase portrait (angular acceleration versus angular velocity,) and the spectra of the moments of forces on both cylinders are plotted and analyzed. The vortical structures in the near and far wake are visualized. Physical interpretations for various phenomenon observed are presented whenever possible. [DOI: 10.1115/1.4004637]

Lift enhancement by bats' dynamically changing wingspan

This paper elucidates the aerodynamic role of the dynamically changing wingspan in bat flight. Based on direct numerical simulations of the flow over a slow-flying bat, it is found that the dynamically changing wingspan can significantly enhance the lift. Further, an analysis of flow structures and lift decomposition reveal that the elevated vortex lift associated with the leading-edge vortices intensified by the dynamically changing wingspan considerably contributed to enhancement of the time-averaged lift. The nonlinear interaction between the dynamically changing wing and the vortical structures plays an important role in the lift enhancement of a flying bat in addition to the geometrical effect of changing the lifting-surface area in a flapping cycle. In addition, the dynamically changing wingspan leads to the higher efficiency in terms of generating lift for a given amount of the mechanical energy consumed in flight.