Z. C. Zheng

An improved direct-forcing immersed-boundary method for finite difference applications

A modified immersed-boundary method is developed using the direct-forcing concept. An improved bilinear interpolation/extrapolation algorithm is implemented for more accurate boundary forcing expressions and easier implementation. Detailed discussions of the method are presented on the stability, velocity interpolation on the immersed boundary, direct-forcing extrapolation to the grid points, resolution of the immersed boundary points, and internal treatment. The method can achieve second-order accurate solutions. The method is then applied to a finite-difference scheme to compute flow over a stationary cylinder, an oscillating cylinder, and a stationary sphere. The accuracy of the computational results is verified using numerous computational and experimental results in the literature.

Study of aircraft wake vortex behavior near the ground

Aircraft wake vortices have been modeled using an unsteady, two-dimensional laminar (constant eddy viscosity) approximation of the Navier-Stokes equations, to study the influence of ground coupling, stratification, and cross-wind on vortex system behavior and decay. Initialization and boundary conditions are developed and implemented systematically for a nonuniform grid representation of the semi-infinite domain containing a vortex pair. Subsequently, the physics of wake vortex interactions with the ground for different types of surface weather conditions are discussed.

Nonlinear spacing and frequency effects of an oscillating cylinder in the wake of a stationary cylinder

Nonlinear responses to a transversely oscillating cylinder in the wake of a stationary upstream cylinder are studied theoretically by using an immersed-boundary method at Re=100. Response states are investigated in the three flow regimes for a tandem-cylinder system: the “vortex suppression” regime, the critical spacing regime, and the “vortex formation” regime. When the downstream cylinder is forced to oscillate at a fixed frequency and amplitude, the response state of flow around the two cylinders varies with different spacing between the two cylinders, while in the same flow regime, the response state can change with the oscillating frequency and amplitude of the downstream cylinder. Based on velocity phase portraits, each of the nonlinear response states can be categorized into one of the three states in the order of increasing chaotic levels: lock-in, transitional, or quasiperiodic. These states can also be correlated with velocity spectral behaviors. The discussions are conducted using near-wake vel...

3D visualization of unsteady 2D airplane wake vortices

Air flowing around the wing tips of an airplane forms horizontal tornado-like vortices that can be dangerous to following aircraft. The dynamics of such vortices, including ground and atmospheric effects, can be predicted by numerical simulation, allowing the safety and capacity of airports to be improved. We introduce three-dimensional techniques for visualizing time-dependent, two-dimensional wake vortex computations, and the hazard strength of such vortices near the ground. We describe a vortex core tracing algorithm and a local tiling method to visualize the vortex evolution. The tiling method converts time-dependent, two-dimensional vortex cores into three-dimensional vortex tubes. Finally, a novel approach is used to calculate the induced rolling moment on the following airplane at each grid point within a region near the vortex tubes and thus allows three-dimensional visualization of the hazard strength of the vortices.<<ETX>>

A computational study of the effect of windscreen shape and flow resistivity on turbulent wind noise reduction

In this paper, numerical simulations are used to study the turbulent wind noise reduction effect of microphone windscreens with varying shapes and flow resistivities. Typical windscreen shapes consisting of circular, elliptical, and rectangular cylinders are investigated. A turbulent environment is generated by placing a solid circular cylinder upstream of the microphone. An immersed-boundary method with a fifth-order weighted essentially non-oscillatory scheme is implemented to enhance the simulation accuracy for high-Reynolds number flow around the solid cylinder as well as at the interface between the open air and the porous material comprising the windscreen. The Navier-Stokes equations for incompressible flow are solved in the open air. For the flow inside the porous material, a modified form of the Zwikker-Kosten equation is solved. The results show that, on average, the circular and horizontal ellipse windscreens have similar overall wind noise reduction performance, while the horizontal ellipse windscreen with medium flow resistivity provides the most effective wind noise reduction among all the considered cases. The vertical ellipse windscreen with high flow resistivity, in particular, increases the wind noise because of increased self-generation of turbulence.

SIMULATION OF TURBULENT WIND NOISE REDUCTION BY POROUS WINDSCREENS USING HIGH-ORDER SCHEMES

The purpose of the study is to investigate the wind noise reduction provided by microphone windscreens at different frequencies of the impinging turbulence. The windscreen is assumed to be a cylindrically shaped porous medium. This paper uses a high-order scheme to improve the accuracy at the interface between air and porous medium. The computational scheme is based on a modified immersed-boundary method with distributed forcing terms. The simulation results show that, for low-frequency turbulence, the windscreens with low flow resistivity are more effective in noise reduction, while for high-frequency turbulence, the windscreens with high flow resistivity are more effective.

Numerical stabilities and boundary conditions in time-domain Eulerian simulations of acoustic wave propagations with and without background flow

A thorough numerical analysis is performed for time-domain simulation of acoustic wave propagations in the atmosphere, with the ground modeled as a porous medium. Two types of computational grid arrangement for the simulation, i.e., the staggered grid and the collocated grid, are considered. It is proved that the computational schemes based on these two grids are identical under certain finite differencing procedures. The numerical stability analysis is studied that applies to both of the grids. Non-reflecting, absorbing boundary conditions are used at the free-space boundary. Simulations on the collocated grid are then carried out for a model problem of sound propagation in the air/ground to confirm the equivalency of the two grids and to investigate the effectiveness of non-reflecting boundary conditions. The results are compared with the data in the literature and with bench-mark simulation, and very good agreements have been achieved.

A collision model for a large number of particles with significantly different sizes

A collision model, modified from the Smoluchowski model, is developed for simulating coagulation and growth of a large number of aerosol particles with significantly different sizes. In this collision model, the particle-size distribution is discretized in volume bins, and the total mass among all the bins is conserved. In situations with significantly different particle sizes, the present model reduces the number of bins compared with the previous models, thus reducing the computational cost. By comparing the results of the present model with the exact solution of Smoluchowskis original model, the accuracy of the solution is not sacrificed. Therefore, this model enables the real-time simulation of three-dimensional, two-phase flow when flow/particle interactions need to be considered. After implementation with a flow solver, the model is further validated with the data from a smoke-reduction experiment in a room-scale chamber using flow-injected nanoparticle aggregates.

Betz Invariants and Generalization of Vorticity Moment Invariants

The widely used Betz invariants can be categorized as invariants of vorticity moments or impulses in plane motion for mostly inviscid vortex flow. These invariants have served as a foundation of vortex roll-up process analysis as well as benchmarks to estimate numerical simulation errors for vortex flow. The analysis starts from a more general integral divergence relation in rational mechanics to extend the analysis for both inviscid and viscous vortex flow cases, with or without finite boundaries. Conditions for the existence of the Betz invariants and their extensions to include viscous effects are discussed. These extensions can be used as analytical means for theoretical modeling of complicated vortex systems, especially in flows with viscous effects and finite boundaries. The goal of this study is to clearly establish when the Betz invariants and the generalized vorticity moment invariants are applicable. The approach uses rigorous mathematical analysis, and the physical interpretations of the results are discussed. A trailing vortex pair is used as an example to illustrate the applications of the theoretical study

Research on energy extraction characteristics of an adaptive deformation oscillating-wing

Oscillating foil machines represent a type of flow energy harvesters which perform pitching and plunging motions simultaneously to harness the energy from incoming stream. In this paper, a new adaptive deformation oscillating wing was proposed and the theoretical performance of such a concept was studied here through unsteady two-dimensional simulations using an in-house developed computational fluid dynamics code. During operation, the proposed oscillating foil whose initial shape is symmetric can be deformed into a cambered foil, which aims to produce large lift force. Our numerical results suggest that the power efficiency of the proposed oscillating foil can be about 16.1% higher than the conventional oscillating foil without deformation. In addition, the effects of the maximum bending displacement and effective angle of attack on the efficiency of proposed oscillating foil were also discussed in this work.