Jeff D. Eldredge

The absorption of axial acoustic waves by a perforated liner with bias flow

The effectiveness of a cylindrical perforated liner with mean bias flow in its absorption of planar acoustic waves in a duct is investigated. The liner converts acoustic energy into flow energy through the excitation of vorticity fluctuations at the rims of the liner apertures. A one-dimensional model that embodies this absorption mechanism is developed. It utilizes a homogeneous liner compliance adapted from the Rayleigh conductivity of a single aperture with mean flow. The model is evaluated by comparing with experimental results, with excellent agreement. We show that such a system can absorb a large fraction of incoming energy, and can prevent all of the energy produced by an upstream source in certain frequency ranges from reflecting back. Moreover, the bandwidth of this strong absorption can be increased by appropriate placement of the liner system in the duct. An analysis of the acoustic energy flux is performed, revealing that local differences in fluctuating stagnation enthalpy, distributed over a finite length of duct, are responsible for absorption, and that both liners in a double-liner system are absorbant. A reduction of the model equations in the limit of long wavelength compared to liner length reveals an important parameter grouping, enabling the optimal design of liner systems.

On the roles of chord-wise flexibility in a flapping wing with hovering kinematics

The aerodynamic performance of a flapping two-dimensional wing section with simplified chord-wise flexibility is studied computationally. Bending stiffness is modelled by a torsion spring connecting two or three rigid components. The leading portion of the wing is prescribed with kinematics that are characteristic of biological hovering, and the aft portion responds passively. Coupled simulations of the Navier- Stokes equations and the wing dynamics are conducted for a wide variety of spring stiffnesses and kinematic parameters. Performance is assessed by comparison of the mean lift, power consumption and lift per unit power, with those from an equivalent rigid wing, and two cases are explored in greater detail through force histories and vorticity snapshots. From the parametric survey, four notable mechanisms are identified through which flexible wings behave differently from rigid counterparts. Rigid wings consistently require more power than their flexible counterparts to generate the same kinematics, as passive deflection leads to smaller drag and torque penalties. Aerodynamic performance is degraded in very flexible wings undergoing large heaving excursions, caused by a premature detachment of the leading-edge vortex. However, a mildly flexible wing has consistently good performance over a wide range of phase differences between pitching and heaving - in contrast to the relative sensitivity of a rigid wing to this parameter - due to better accommodation of the shed leading-edge vortex into the wake during the return stroke, and less tendency to interact with previously shed trailing-edge vortices. Furthermore, a flexible wing permits lift generation even when the leading portion remains nearly vertical, as the wing passively deflects to create an effectively smaller angle of attack, similar to the passive pitching mechanism recently identified for rigid wings. It is found that an effective pitch angle can be defined that accounts for wing deflection to align the results with those of the equivalent rigid wing.

Acoustic modeling of perforated plates with bias flow for Large-Eddy Simulations

The study of the acoustic effect of perforated plates by Large-Eddy Simulations is reported. The ability of compressible Large-Eddy Simulations to provide data on the flow around a perforated plate and the associated acoustic damping is demonstrated. In particular, assumptions of existing models of the acoustic effect of perforated plate are assessed thanks to the Large-Eddy Simulations results. The question of modeling the effect of perforated plates is then addressed in the context of thermo-acoustic instabilities of gas turbine combustion chambers. Details are provided about the implementation, validation and application of a homogeneous boundary condition modeling the acoustic effect of perforated plates for compressible Large-Eddy Simulations of the flow in combustions chambers cooled by full-coverage film cooling.

Passive locomotion of a simple articulated fish-like system in the wake of an obstacle

The behaviour of a passive system of two-dimensional linked rigid bodies in the wake of a circular cylinder at Re = 100 is studied computationally. The three rigid bodies are connected by two frictionless hinges, and the system (‘fish’) is initially aligned with a streamwise axis three diameters behind the cylinder. Once flow symmetry is broken, the wake rolls up into a K ´ arm ´ an vortex street in which the fish is stably trapped, and the passing large-scale vortices induce an undulatory shape change in the articulated system. It is found that, for certain fish lengths relative to cylinder diameter, the fish is propelled upstream toward the cylinder. Furthermore, the fish is propelled equally effectively when the hinges are locked, confirming that induced body undulation is not necessary for achieving a net thrust. An analysis of the forces on constituent bodies shows that leading-edge suction and negative skin friction on the forward portion of the fish are in competition with positive skin friction on the aft portion; propulsion is achieved when the forebody contributions dominate those on the aftbody. It is shown that the so-called ‘suction zone’ behind the cylinder that enables this passive propulsion is double the length of that without a fish present.

Axisymmetric simulations of libration-driven fluid dynamics in a spherical shell geometry

We report on axisymmetric numerical simulations of rapidly rotating spherical shells in which the axial rotation rate of the outer shell is modulated in time. This allows us to model planetary bodies undergoing forced longitudinal libration. In this study we systematically vary the Ekman number, 10−7≤E≲10−4, which characterizes the ratio of viscous to Coriolis forces in the fluid, and the libration amplitude, Δϕ. For libration amplitudes above a certain threshold, Taylor–Gortler vortices form near the outer librating boundary, in agreement with the previous laboratory experiments of Noir et al. [Phys. Earth Planet. Inter. 173, 141 (2009)]. At the lowest Ekman numbers investigated, we find that the instabilities remain spatially localized at onset in the equatorial region. In addition, nonzero time-averaged azimuthal (zonal) velocities are observed for all parameters studied. The zonal flow is characterized by predominantly retrograde flow in the interior, with a stronger prograde jet in the outer equatori...

Numerical and experimental study of the fluid dynamics of a flapping wing with low order flexibility

A simple canonical problem for understanding the role of flexibility in flapping wing flight is investigated numerically and experimentally. The problem consists of a two-dimensional two-component wing structure connected by a single hinge with a damped torsion spring. One component of the wing is driven with hovering flapping wing kinematics, while the other component responds passively to the fluid dynamic and inertial/elastic forces. Numerical simulations are carried out with the viscous vortex particle method with strongly coupled body dynamics. The experiments are conducted in a water tank with suspended particles for flow visualization. The system is analyzed in several different kinematic test cases that are designed to span a broad parametric range of flapping. Hinge deflection is used as the primary metric for comparison; the agreement between computation and experiment is very good in all cases. The trajectories of shed vortices are also compared, again with favorable agreement. Fluid forces and...

An inviscid model for vortex shedding from a deforming body

We study finite-time blow-up for pseudo-relativistic Hartreeand Hartree-Fock equations, which are model equations for the dynamical evolution of white dwarfs. In particular, we prove that radially symmetric initial configurations with negative energy lead to finite-time blow-up of solutions. Furthermore, we derive a mass concentration estimate for radial blow-up solutions. Both results are mathematically rigorous and are in accordance with Chandrasekhar’s physical theory of white dwarfs, stating that stellar configurations beyond a certain limiting mass lead to “gravitational collapse” of these objects. Apart from studying blow-up, we also prove local well-posedness of the initial-value problem for the Hartreeand Hartree-Fock equations underlying our analysis, as well as global-in-time existence of solutions with sufficiently small initial data, corresponding to white dwarfs whose stellar mass is below the Chandrasekhar limit.

A Vortex Particle Method for Two-Dimensional Compressible Flow

A vortex particle method is developed for simulating two-dimensional, unsteady compressible flow. The method uses the Helmholtz decomposition of the velocity field to separately treat the irrotational and solenoidal portions of the flow, and the particles are allowed to change volume to conserve mass. In addition to having vorticity and dilatation properties, the particles also carry density, enthalpy, and entropy. The resulting evolution equations contain terms that are computed with techniques used in some incompressible methods. Truncation of unbounded domains via a nonreflecting boundary condition is also considered. The fast multipole method is adapted to compressible particles in order to make the method computationally efficient. The new method is applied to several problems, including sound generation by corotating vortices and generation of vorticity by baroclinic torque.

A numerical study of compressible turbulent boundary layers

Compressible turbulent boundary layers with free-stream Mach number ranging from 2.5 up to 20 are analyzed by means of direct numerical simulation of the Navier–Stokes equations. The fluid is assumed to be an ideal gas with constant specific heats. The simulation generates its inflow condition using the rescaling-recycling method. The main objective is to study the effect of Mach number on turbulence statistics and near-wall turbulence structures. The present study shows that supersonic/hypersonic boundary layers at zero pressure gradient exhibit close similarities to incompressible boundary layers and that the main turbulence statistics can be correctly described as variable-density extensions of incompressible results. The study also shows that the spanwise streak’s spacing of 100 wall units in the inner region y + 15 still holds for the considered high Mach numbers. The probability density function of the velocity dilatation shows significant variations as the Mach number is increased, but it can also be normalized by accounting for the variable-density effect. The compressible boundary layer also shows an additional similarity to the incompressible boundary layer in the sense that without the linear coupling term, near-wall turbulence cannot be sustained.

Résumé of the AIAA FDTC Low Reynolds Number Discussion Group's Canonical Cases

The AIAA Fluid Dynamics Technical Committee’s Low Reynolds Number Discussion Group has introduced several “canonical” pitch motions, with objectives of (1) experimental-numerical comparison, (2) assessment of closed-form models for aerodynamic force coefficient time history, and (3) exploration of the vast and rather amorphous parameter space of the possible kinematics. The baseline geometry is a flat plate of nominally 2.5% thickness and round edges, wall-to-wall in ground test facilities and spanwise-periodic or 2D in computations. Motions are various smoothings of a linear pitch ramp, hold and return, of 40 and 45 amplitude. In an attempt to discern acceleration effects, sinusoidal and linear-ramp motions are compared, where the latter have short runs of high acceleration and thus high noncirculatory lift and pitch. Parameter variations include comparison of the flat plate with an airfoil and ellipse, variation of reduced frequency, pitch pivot point location and comparison of pitch to quasi-steady equivalent plunge. All motions involve strong leading edge vortices, whose growth history depends on pitch pivot point location and reduced frequency, and which can persist over the model suction-side for well after motion completion. Noncirculatory loads were indeed found to be localized to phases of motion where acceleration was large. To the extent discernable so far, closed-form models of lift coefficient on the pitch upstroke are relatively straightforward, but not so on the downstroke, where motion history effects complicate the return from stall. Broad Reynolds number independency, in flowfield evolution and lift coefficient, was found in the 10 to 10 range.