Kunihiko Taira

Three-dimensional flows around low-aspect-ratio flat-plate wings at low Reynolds numbers

Three-dimensional flows over impulsively translated low-aspect-ratio flat plates are investigated for Reynolds numbers of 300 and 500, with a focus on the unsteady vortex dynamics at post-stall angles of attack. Numerical simulations, validated by an oil tow-tank experiment, are performed to study the influence of aspect ratio, angle of attack and planform geometry on the wake vortices and the resulting forces on the plate. Immediately following the impulsive start, the separated flows create wake vortices that share the same topology for all aspect ratios. At large time, the tip vortices significantly influence the vortex dynamics and the corresponding forces on the wings. Depending on the aspect ratio, angle of attack and Reynolds number, the flow at large time reaches a stable steady state, a periodic cycle or aperiodic shedding. For cases of high angles of attack, an asymmetric wake develops in the spanwise direction at large time. The present results are compared to higher Reynolds number flows. Some non-rectangular planforms are also considered to examine the difference in the wakes and forces. After the impulsive start, the time at which maximum lift occurs is fairly constant for a wide range of flow conditions during the initial transient. Due to the influence of the tip vortices, the three-dimensional dynamics of the wake vortices are found to be quite different from the two-dimensional von Karman vortex street in terms of stability and shedding frequency.

Effect of Tip Vortices in Low-Reynolds-Number Poststall Flow Control

We numerically investigate the application of steady blowing to three-dimensional stalled flows around low-aspect-ratio rectangular flat-plate wings at a Reynolds number of 300. The objective of this study is to explore techniques to enhance lift by directly modifying the dynamics of the wake vortices. Out of various combinations of forcing location and direction considered, we identify two configurations that provide significant lift enhancement. In these cases, actuation appears to strengthen the tip vortices for increased downward induced velocity upon the leading-edge vortices. This in turn moves the low-pressure core directly above the top surface of the wing to greatly enhance lift.

Modal Analysis of Fluid Flows: An Overview

Simple aerodynamic configurations under even modest conditions can exhibit complex flows with a wide range of temporal and spatial features. It has become common practice in the analysis of these flows to look for and extract physically important features, or modes, as a first step in the analysis. This step typically starts with a modal decomposition of an experimental or numerical dataset of the flow field, or of an operator relevant to the system. We describe herein some of the dominant techniques for accomplishing these modal decompositions and analyses that have seen a surge of activity in recent decades. For a non-expert, keeping track of recent developments can be daunting, and the intent of this document is to provide an introduction to modal analysis that is accessible to the larger fluid dynamics community. In particular, we present a brief overview of several of the well-established techniques and clearly lay the framework of these methods using familiar linear algebra. The modal analysis techniques covered in this paper include the proper orthogonal decomposition (POD), balanced proper orthogonal decomposition (Balanced POD), dynamic mode decomposition (DMD), Koopman analysis, global linear stability analysis, and resolvent analysis.

The leading-edge vortex and quasisteady vortex shedding on an accelerating plate

A computational inquiry focuses on leading-edge vortex (LEV) growth and shedding during acceleration of a two-dimensional flat plate at a fixed 10°–60° angle of attack and low Reynolds number. The plate accelerates from rest with a velocity given by a power of time ranging from 0 to 5. During the initial LEV growth, subtraction of the added mass lift from the computed lift reveals an LEV-induced lift augmentation evident across all powers and angles of attack. For the range of Reynolds numbers considered, a universal time scale exists for the peak when α≥30°, with augmentation lasting about four to five chord lengths of translation. This time scale matches well with the half-stroke of a flying insect. An oscillating pattern of leading- and trailing-edge vortex shedding follows the shedding of the initial LEV. The nondimensional frequency of shedding and lift coefficient minima and maxima closely match their values in the absence of acceleration. These observations support a quasisteady theory of vortex sh...

Stabilization of Ill-Posed Problems Through Thermal Rate Sensors

Reliance on conventional temperature and heat flux sensors in transient situations can inhibit predictiveness and lead to unsatisfactory results that require extensive post-processing procedures for reconstituting usable results. A mathematical formalism is presented to motivate the development of thermal rate sensors. Rate-based temperature and heat flux sensors can be designed in a manner without requiring any form of data differentiation. The proposed temperature and heat flux rate sensors can enhance both real-time and postprocessing investigations. A new sensor hierarchy is proposed that reduces and, in some cases, removes the often encountered ill-posed nature observed in numerous heat transfer studies. Four diverse examples are presented illustrating the power of rate-based data for enhancing stability and accuracy. Numerical regularization that is normally required for assuring stability can effectively be eliminated by data from thermal rate sensors. Additionally, in some investigations, these data forms can assist in identifying optimal regularization parameters. Data from rate-based sensors can make an immediate impact on a variety of aerospace, defense, and material science studies. Nomenclature A = constant, ◦ C/s 3 C = heat capacity, kJ/(kg ◦ C) D = differential operator, ∂/∂t f (t) = specified temperature function, Eq. (15b) G = Green’s function, Eq. (2b) g(t) = specified heat flux function, Eq. (15c) H = Heaviside step function, Eq. (8d) K = integral operator, Eq. (3b) k = thermal conductivity, W/(m ◦ C) L = fixed position, m M = number of data points N = number of space terms N j = difference norm, Eq. (20) P = number of time terms popt = optimal number of temporal terms Q = dimensionless heat flux QNP = approximate heat flux q �� = dimensional heat flux, W/m 2 q �� = discrete heat flux, W/m 2

Unsteadiness in Flow over a Flat Plate at Angle-of-Attack at Low Reynolds Numbers

Flow over an impulsively started low-aspect-ratio flat plate at angle-of-attack is investigated for a Reynolds number of 300. Numerical simulations, validated by a companion experiment, are performed to study the influence of aspect ratio, angle of attack, and planform geometry on the interaction of the leading-edge and tip vortices and resulting lift and drag coecients. Aspect ratio is found to significantly influence the wake pattern and the force experienced by the plate. For large aspect ratio plates, leading-edge vortices evolved into hairpin vortices that eventually detached from the plate, interacting with the tip vortices in a complex manner. Separation of the leading-edge vortex is delayed to some extent by having convective transport of the spanwise vorticity as observed in flow over elliptic, semicircular, and delta-shaped planforms. The time at which lift achieves its maximum is observed to be fairly constant over dierent aspect ratios, angles of attack, and planform geometries during the initial transient. Preliminary results are also presented for flow over plates with steady actuation near the leading edge.

Lift Enhancement for Low-Aspect-Ratio Wings with Periodic Excitation

In an effort to enhance lift on low-aspect-ratio rectangular flat-plate wings in low-Reynolds-number post-stall flows, periodic injection of momentum is considered along the trailing edge in this numerical study. The purpose of actuation is not to reattach the flow but to change the dynamics of the wake vortices such that the resulting lift force is increased. Periodic forcing is observed to be effective in increasing lift for various aspect ratios and angles of attack, achieving a similar lift enhancement attained by steady forcing with less momentum input. Through the investigation on the influence of the actuation frequency, it is also found that there exists a frequency at which the flow locks on to a time-periodic high-lift state.

Vortex dynamics around pitching plates

Vortex dynamics of wakes generated by rectangular aspect-ratio 2 and 4 and two-dimensional pitching flat plates in free stream are examined with direct numerical simulation and water tunnel experiments. Evolution of wake vortices comprised of tip, leading-edge, and trailing-edge vortices is compared with force history for a range of pitch rates. The plate pivots about its leading edge with reduced frequency from π/8 to π/48, which corresponds to pitching over 1 to 6 chord lengths of travel. Computations have reasonable agreement with experiments, despite large differences in Reynolds number. Computations show that the tip effects are confined initially near the wing tips, but begin to strongly affect the leading-edge vortex as the motion of the plate proceeds, with concomitant effects on lift and drag history. Scaling relations based on reduced frequency are shown to collapse aerodynamic force history for the various pitch rates.

Network structure of two-dimensional decaying isotropic turbulence

The present paper reports on our effort to characterize vortical interactions in complex fluid flows through the use of network analysis. In particular, we examine the vortex interactions in two-dimensional decaying isotropic turbulence and find that the vortical interaction network can be characterized by a weighted scale-free network. It is found that the turbulent flow network retains its scale-free behavior until the characteristic value of circulation reaches a critical value. Furthermore, we show that the two-dimensional turbulence network is resilient against random perturbations but can be greatly influenced when forcing is focused towards the vortical structures that are categorized as network hubs. These findings can serve as a network-analytic foundation to examine complex geophysical and thin-film flows and take advantage of the rapidly growing field of network theory, which complements ongoing turbulence research based on vortex dynamics, hydrodynamic stability, and statistics. While additional work is essential to extend the mathematical tools from network analysis to extract deeper physical insights of turbulence, an understanding of turbulence based on the interaction-based network-theoretic framework presents a promising alternative in turbulence modeling and control efforts.

Temporal-Harmonic Specific POD Mode Extraction

Gilead Tadmor∗ and Daniel Bissex† Electrical & Computer Engineering, 440 DA, Northeastern University Boston, MA 02115, USA Bernd R. Noack‡ Inst. of Fluid Mechanics and Technical Acoustics Berlin University of Technology, Strase des 17. Juni, 10623 Berlin, Germany Marek Morzynski§ Institute of Combustion Engines and Transportation, Poznan University of Technology, Piotrowo 3, 60-965 Poznan, Poland Tim Colonius¶ and Kunihiko Taira‖ Engineering and Applied Science, California Institute of Technology, 1200 East California Boulevard, MS 104-44 Pasadena, CA 91125, USA