Shozo Koshigoe

Combustion-related shear-flow dynamics in elliptic supersonic jets

Abstract : An elliptic jet having an aspect ratio of 3:1 was studied and compared to a circular jet at three Mach numbers: M = 0.15, 1 and 1.3. Hot-wire measurements and Schlieren photography were employed in this study. The superior mixing characteristics of an elliptic jet relative to a circular jet, which were found in previous works in subsonic jets, prevail in the sonic jet and are further augmented by the shock structures of the supersonic underexpanded jet. The major and minor axes switch at a distance of 3 diameters from the nozzle, and the spreading rate of the minor axis side is twice that of a subsonic jet. The experimental data are supported by results of the linear instability analysis of the supersonic elliptic jet which show that the initial vortices are bending at the major axis side in a similar way to the process which occurs in a subsonic elliptic jet.

Initial Development of Noncircular Jets Leading to Axis Switching

This paper discusses the underlying mechanisms for the deformation of coherent structures which occurs in the initial stage of the axis switching of noncircular jets. The generalized shooting method is applied to jets with elliptic-core and equilateral-triangular-core regions of constant flow. The analysis reveals that in order to have the deformation, three requirements must be present in the behavior of the eigenmodes of noncircular jets: 1) the eigenfunctions are localized without excessive overlapping; 2) the amplification rates of the corresponding eigenmodes are comparable; and 3) sufficient phase speed difference exists between the eigenmodes. The qualitative behavior of the noncircular jets found through the numerical analysis is compared with experimental results and are in good correlation with them.

A new approach for active control of sound transmission through an elastic plate backed by a rectangular cavity

A new technique for controlling noise transmission into a cavity using piezoelectric actuators on an elastic plate is discussed. This study involves construction of a fully coupled acoustics/plate interaction model. This model is used to guide development of a new active noise control method. In real implementation, this approach does not require adaptive signal processing such as the least‐mean squares (LMS) method to minimize the acoustic energy in the cavity for control [Pan et al., J. Acoust. Soc. Am. 87, 2098–2108 (1990)]. It shares a similar concept with the plate velocity feedback control. However, the plate velocity feedback control is effective only for the plate controlled modes, whereas the new method is effective for both the plate and cavity controlled modes. A comparison of the simulations using the velocity feedback and the least mean squares method with the new technique will be discussed.

Wave structures in jets of arbitrary shape. III. Triangular jets

The generalized shooting method, previously developed for the analysis of spatial instability modes of arbitrary shape jets, is applied to incompressible jets with triangular core regions of constant flow. The instability modes of these jets are classified, and calculations are carried out for spatial growth rates, phase velocities, and velocity fluctuation eigenfunctions of three fundamental and two overtone modes. All of the calculated eigenfunctions show negligible velocity fluctuations at the triangle vertices, in good correlation with experimental findings.

Wave structures in jets of arbitrary shape. I: Linear inviscid spatial instability analysis

Green function methods are used to give a practical form of the Rayleigh linear inviscid instability analysis for jets of arbitrary mean flow profile. Simple illustrations of the general methodology are given for vortex‐sheet and continuous‐velocity‐profile shear layers. Some of the numerical results for elliptic jets are compared with those previously obtained from solutions of Mathieu’s equation in elliptic cylindrical coordinates.

Wave structures in jets of arbitrary shape. II. Application of a generalized shooting method to linear instability analysis

The shooting method, used in the linear instability analysis of plane shear layers, is generalized so as to be applicable to the case of straight three‐dimensional, inviscid, compressible jets of arbitrary mean flow profile. A jet is assumed to have a core region of constant flow W0 bounded by curve C, and an outer‐flow boundary C outside of which the flow is negligible. The instability eigenmodes are determined by using the Helmholtz surface integral relations between the incremental pressure and its normal derivative on C and C, together with finite difference approximate solutions of the Rayleigh differential equation in one region between C and C. Calculations typically require about 50 times less computer time than do equivalent integral‐equation methods. Numerical results are presented for incompressible jets with circular and elliptic core regions and several azimuthal variations of momentum thickness.

A time domain study of active control of sound transmission due to acoustic pulse excitation

A time domain model for simulating the noise transmission through an elastic plate into a rigid cavity has been developed. This model is used to study the noise attenuation capability of the filtered‐x least‐mean‐square (LMS) feedforward control algorithm for the case where the model is excited by an acoustic pulse. Piezoelectric transducers (PZT’s) are considered to be bonded on the elastic plate and are used as actuators in the control scheme. In this study, the fully coupled acoustic–plate interaction equations are solved using time‐dependent Green’s function techniques, where a time‐varying mean air density is considered. The effects of this variation on the transmission of sound and on the stability of the filtered‐x LMS adaptive controller are discussed.

Vortex deformation in elliptic‐core jets from the perspective of linear instability analysis

An attempt is made to identify the underlying mechanisms for the deformation of coherent structures that occurs in the initial state of axis switching of elliptic‐core jets. The generalized shooting method is applied to jets with elliptic‐core regions of constant flow. The analysis shows that there are three conditions on groups of eigenmodes of elliptic‐core jets which are necessary for the deformation. They are (1) proper localizations without excessive overlapping; (2) sufficiently large phase‐speed differences; and (3) comparable spatial amplification rates. The qualitative behaviors of elliptic‐core jets in relation to these three conditions are studied with respect to independent and joint variations of core eccentricity, azimuthal distribution of momentum thickness, and compressibility.

Implications of causality, time‐translation invariance, linearity, and minimum‐phase behavior for basilar‐membrane response functions

Several implications of the assumptions of causality (C), time-translation invariance (TTI), linearity (L), and minimum phase behavior (MPB) for basilar membrane (BM) frequency-response functions are derived. They are then used to: (1) test the consistency of calculated results for a two-dimensional cochlear model [S. T. Neely, J. Acoust. Soc. Am 69, 1386-1393 (1981)] and (2) check experimental data on the BM displacement/malleus displacement [W, S. Rhode, J. Acoust. Soc. Am. 67, 1969-1703 (1980)] for approximate consistency with these assumptions. Both the theoretical model results and experimental cochlear-partition response data are in fairly good accord with these assumptions.

Experiment in feedforward control for the reduction of sound transmission through an elastic plate backed by a rigid rectangular cavity

The payload compartment of space launch vehicles is an acoustically severe environment with sound pressure levels that often exceed 130 dB. Many of the design constraints for satellites are driven by the launch loads and any reduction in these loads would allow lighter spacecraft and significant cost savings because of reduced launch weight and testing requirements. In order to determine the levels of sound attenuation possible in such an application, a simple experimental apparatus consisting of a flexible plate backed by a rigid rectangular cavity has been built to mimic the behavior of a launch vehicle payload compartment. An external speaker is used to simulate the pressure loading caused by vehicle exhaust and turbulent flow around the launch vehicle. This paper provides a comparison of the harmonic disturbance attenuation capability and transient/convergence performance of a fixed analog feedforward and a filtered-x LMS adaptive feedforward controller for the cavity backed plate problem using piezoelectric ceramic actuators on the flexible plate and polyvinylidene fluoride pressure and plate vibration sensors. Controllers are developed for the first plate controlled mode and the first cavity controlled mode.