Donald B. Bliss

The instability of short waves on a vortex ring

A simple model for the experimentally observed instability of the vortex ring to azimuthal bending waves of wavelength comparable with the core size is presented. Short-wave instabilities are discussed for both the vortex ring and the vortex pair. Instability for both the ring and the pair is predicted to occur whenever the self-induced rotation of waves on the filament passes through zero. Although this does not occur for the first radial bending mode of a vortex filament, it is shown to be possible for bending modes with a more complex radial structure with at least one node at some radius within the core. The previous work of Widnall & Sullivan (1973) is discussed and their experimental results are compared with the predictions of the analysis presented here.

Theoretical and Experimental Study of the Stability of a Vortex Pair

The linear stability of the trailing vortex pair from an aircraft is discussed. The method of matched asymptotic expansions is used to obtain a general solution for the flow field within and near a curved vortex filament with an arbitrary distribution of swirl and axial velocities. The velocity field induced in the neighborhood of the vortex core by distant portions of the vortex line is calculated for a sinusoidally perturbed vortex filament and for a vortex ring. General expressions for the self-induced motion are given for these two cases. It is shown that the details of the vorticity and axial velocity distributions affect the self-induced motion only through the kinetic energy of the swirl and the axial momentum flux. The presence of axial velocity in the core reduces both the angular velocity of the sinusoidal vortex filament and the speed of the ring. The vortex pair instability is then considered in terms of the more general model for self-induced motion of the sinusoidal vortex. The presence of axial velocity within the core slightly decreases the amplification rate of the instability. Experimental results for the distortion and breakup of a perturbed vortex pair are presented.

Study of bulk reacting porous sound absorbers and a new boundary condition for thin porous layers

The effect of bulk reaction on the sound absorption properties of porous materials is studied theoretically and experimentally. Particular attention is focused on the important case of a layer of porous material attached to a rigid wall. In general, it is found that the surface of the porous material can be accurately represented by its normal incidence impedance only if a nondimensional flow resistance parameter is large, i.e., only under this condition is the bulk reaction effect negligible. A new boundary condition is proposed which accounts for the effect of bulk reaction when the thickness of the sound absorbing layer is smaller than the acoustic wavelength. The boundary condition relates the surface pressure and its second derivatives along the surface to the normal velocity. Sample calculations for a theoretical porous material show that the oblique incidence absorption coefficient can be calculated very accurately using this boundary condition. In practice, the boundary condition requires two expe...

Aeroelastic Wing with Leading- and Trailing-Edge Control Surfaces

It is well known that the effectiveness of a trailing-edge control surface can be substantially diminished due to the elastic twist of an airfoil or wing. This aeroelastic phenomenon is known as control surface reversal when the lift or roll rate vanishes at a sufficiently large ratio of flow dynamic pressure to wing stiffness. However, a leading-edge control surface can be used to counteract control surface reversal, and indeed, in principle, a leading-edge control surface may entirely cancel the tendency of the trailing-edge control surface to undergo reversal. Moreover, analysis shows that by using a simple control strategy one can use a combination of leading- and trailing-edge control surface rotations to maintain lift and roll effectiveness and minimize control surface rotations. The beneficial effects of leading-edge control surfaces on control surface reversal are known to practioners. However, the present simple model makes these especially transparent and suggests an advantageous strategy using a combination of leading- and trailing-edge control surfaces.

New free-wake analysis of rotorcraft hover performance using influence coefficients

Free-wake analyses of helicopter rotor wakes in hover using time stepping have been shown to encounter instabilities which preclude convergence to valid free-vortex solutions for rotor-wake geometries. Previous work has demonstrated that these convergence difficulties can be overcome by implementing a new free-wake analysis method based on the use of influence coefficients. The present paper reviews this approach and documents its incorporation into a hover performance analysis called Evaluation of Hover Performance using Influence Coefficients (EHPIC). The technical principles underlying the EHPIC code are described with emphasis on steps taken to develop the single-filament wake models used in previous work into a multifilament wake valid for realistic hover performance predictions. The coupling of the wake model to a lifting surface loads analysis is described, and sample problems are solved that illustrate the robustness of the method. Performance calculations are also undertaken for hover to illustrate the utility of EHPIC in the analysis of rotorcraft performance.

An acoustic boundary element method based on energy and intensity variables for prediction of high-frequency broadband sound fields

A boundary element method is formulated in terms of time-averaged energy and intensity variables. The approach is applicable to high modal density fields but is not restricted to the usual low-absorption, diffuse, and quasiuniform assumptions. A broadband acoustic energy/intensity source is the basic building block for the method. A directivity pattern for the source is derived to account for local spatial correlation effects and to model specular reflections approximately. A distribution of infinitesimal, uncorrelated, directional sources is used to model the boundaries of an enclosure. These sources are discretized in terms of boundary elements. A system of equations results from applying boundary conditions in terms of incident, reflected, and absorbed intensity. The unknown source power for each element is determined from this system of equations. A two-dimensional model problem is used to demonstrate and verify the method. Exact numerical solutions were also obtained for this model problem. The resul...

Prediction of Viscous Trailing Vortex Structure from Basic Loading Parameters

An analytical method has been developed to predict the structure of a fully developed trailing vortex with a viscous core. Vortex structure is calculated from the load distribution on the generating wing and fundamental conservation laws are satisfied. The present rollup model implicitly addresses viscous effects in the vortex core region by assuming a turbulent mixing process in the core during formation. Mixing theory suggests the appropriate functional form of the solution velocity profiles within this region, with constants that are determined uniquely by the method for arbitrary wing loading distributions. Important structural properties such as vortex strength, core size, and peak swirl velocity are calculated directly from these solution constants. The viscous core model was validated against two recent experimental studies, which provided new insight into vortex growth

An acoustic boundary element method using analytical/numerical matching

Analytical/numerical matching (ANM) is a hybrid scheme combining a low-resolution global numerical solution with a high-resolution local solution to form a composite solution. ANM is applied to a harmonically oscillating body to calculate the radiated acoustic field and the associated fluid loading. The approach utilizes overlapping smoothed dipoles, and local corrections to calculate the dipole strength distribution along the surface of the body. A smoothing length scale is introduced that is larger than the smallest physical scale, and smaller than the largest physical scale. The global low-resolution solution is calculated numerically using smoothed dipole solutions to the wave equation, and converges quickly. Local corrections are done with high-resolution local analytical solutions. The global numerical solution is asymptotically matched to the local analytical solutions via a matching solution. The matching solution cancels the global solution in the near field, and cancels the local solution in the...

A discussion of modal uncoupling and an approximate closed-form solution for weakly coupled systems with application to acoustics

Modal analysis is often used to solve problems in acoustics, leading to a system of coupled equations for the modal amplitudes. A common practice in analytical work utilizing modal analysis has been to assume that weak modal coupling is negligible, thereby enabling the modal coefficients to be solved independently in closed form. The validity of this assumption, as well as the order of the error from neglecting modal coupling, is discussed. It is possible to incorporate the principal effects of weak modal coupling in a very simple way without solving the fully coupled system. An approximate closed-form solution for weakly coupled systems of equations is developed. The procedure gives insight into the errors incurred when coupling is neglected, and shows that these errors may be unacceptably large in systems of practical interest. A model problem involving a pipe with an impedance boundary condition is solved when the one-dimensional sound field is harmonically driven, and when it undergoes reverberant dec...

Role of Artificial Viscosity in Euler and Navier-Stokes Solvers

A method is proposed to determine directly the amount of artificial viscosity needed for stability using an eigenvalue analysis for a finite difference representation of the Navier-Stokes equations. The stability and growth of small perturbations about a steady flow over airfoils are analyzed for various amounts of artificial viscosity. The eigenvalues were determined for a small time-dependent perturbation about a steady inviscid flow over a NACA 0012 airfoil at a Mach number of 0.8 and angle of attack of 0 deg. The method has been applied to inviscid flows here, but as discussed is also applicable to viscous flows. The movement of the eigenvalue constellation with respect to the amount of artificial viscosity is studied. The stability boundaries as a function of the amount of artificial viscosity from both the eigenvalue analysis and the time-marching scheme are also presented. The eigenvalue procedure not only allows for determining the effect of varying amounts of artificial viscosity, but also for the effects of different forms of artificial viscosity. Nomenclature a = speed of sound e = total energy per unit volume 7 = identity matrix / = Jacobian of transformation M = Mach number p - pressure Re = Reynolds number, p^ V^ c/fi^ t = nondimensional physical time u,v = Cartesian velocity components x,y = physical Cartesian coordinates a = angle of attack 6 = finite difference operator eEf e/ = coefficients of artificial viscosity X = eigenvalues IJL = viscosity coefficient £, r/ = transformed coordinates p = density T = transformed time