Subsonic Mode Research Articles

DISTRIBUTED ANECHOIC SYSTEM USING ELECTRICALLY ACTIVE FLUID

A novel application of electrorheological fluid as a potential candidate for externally controllable anechoic material is discussed. The mechanism postulated is a resonant interaction of the incident compressional waves with the subsonic shear modes of the system. The energy dissipation is expected due to the existence of a loss modulus of the system.

Nonlinear evolution of subsonic and supersonic disturbances on a compressible free shear layer

We consider the effects of a nonlinear–non-equilibrium–viscous critical layer on the spatial evolution of subsonic and supersonic instability modes on a compressible free shear layer. It is shown that the instability wave amplitude is governed by an integro-differential equation with cubic-type nonlinearity. Numerical and asymptotic solutions to this equation show that the amplitude either ends in a singularity at a finite downstream distance or reaches an equilibrium value, depending on the Prandtl number, viscosity law, viscous parameter and a real parameter which is determined by the linear in viscid stability theory. A necessary condition for the existence of the equilibrium solution is derived, and whether or not this condition is met is determined numerically for a wide range of physical parameters including both subsonic and supersonic disturbances. It is found that no equilibrium solution exists for the subsonic modes unless the temperature ratio of the low-to high-speed streams exceeds a critical value, while equilibrium solutions for the most rapidly growing supersonic mode exist over most of the parameter range examined.

A comprehensive analysis of the viscous incompressible flow in quasi‐three‐dimensional aerofoil cascades

AbstractA rigorous model of the fully elliptic flow over the blade‐to‐blade stream surface in an annular aerofoil cascade is developed. The model accuracy stems from its precise simulation of the meridional hub‐to‐casing flow effects, including those of the shear stress components that are created by the spanwise velocity gradients. These stresses are unprecedentedly introduced in the flow‐governing equations in the form of source terms and are modelled as such. The final set of flow‐governing equations are solved using the Galerkin weighted residual method coupled with a biquadratic finite element of the Lagrangian type. The flow solution is verified against the numerical results of a fully three‐dimensional flow model and a set of experimental data, both concerning a low‐aspect‐ratio stator of an axial flow turbine under a low Reynolds number and subsonic flow operation mode. The numerical results in this case show well predicted aerofoil loading and pitch‐averaged exit flow conditions. Also evident is a substantial capability of the analysis in modelling such critical regions as the wake subdomain. It is further proven that the new terms in the governing equations enhance the quality of the numerical predictions in this class of flow problems.

On the existence of interfacial (Stoneley) waves in bonded piezoelectric half-spaces

A new definition of the piezoelectric limiting speed, based on the piezoelectrically stiffened acoustical tensor is introduced. The Stoneley wave problem is readily formulated for bonded piezoelectric half-spaces in both the Φ and F representations introduced by Lothe & Barnett. The notion of the F piezoelectric interfacial impedance tensor, which is an extension of the elastic interfacial impedance tensor, is used to show that a maximum of two subsonic Stoneley waves can occur. A definite existence criterion for a single subsonic piezoelectric Stoneley mode is given, and a numerical scheme that searches for Stoneley modes, when they exist for a given geometry and material combination, is also presented along with a numerical example for two joined cadmium sulphide half-spaces.

Experiment on multiple fuel supplies to air breathing rocket combustors

An experimental study on multiple fuel supplies to cylindrical subsonic mode combustors of air breathing rockets was made for the purpose of reducing combustor length. The experiment consisted of two parts, one in which all the fuel was supplied through a rocket with multiple nozzles and the other in which a portion of the fuel was directly fed into a secondary combustor with the rest being supplied through a rocket with a single nozzle. The results are compared with each other and with those of a reference experiment in which a rocket with a single nozzle without fuel injection was used. In the case with multiple nozzles, mixing and combustion efficiencies were higher than those in the reference experiment for the same combustor length. They collapse to a single curve against the combustor length nondimensionalized by the rocket nozzle exit diameter, except for the combustion efficiencies for unstable combustion. Increase of the injection mass flow rate makes mixing and combustion efficiencies rise, but it soon becomes less effective beyond a certain limit. Combustion instability observed in the reference case for long combustors is suppressed in both cases.

Long-Range Acoustic Scattering by Surface Inhomogeneities Beneath a Turbulent Boundary Layer

Low-frequency turbulent boundary layer eddies inject a power Ps into the elastic structure over which the boundary layer is formed which generally greatly exceeds the acoustic power Pa directly radiated by the eddies (acoustically equivalent to quadrupoles). The power Ps remains trapped in the surface and an adjacent fluid layer and propagates in subsonic surface wave modes until it encounters a rib, or edge, or other surface inhomogeneity, from which a power Pe is scattered to the far field. While Pe is again small compared with Ps, it may nonetheless greatly exceed Pa, and in that case the dominant acoustic mechanism is associated with the long-range coupling between the quadrupole eddy and the remote inhomogeneity via subsonic surface waves. That interaction, and the acoustic fields produced by it, are examined in detail in this paper for the inhomogeneities represented by a simple line support rib, a simple point support rib, and an edge to a plane elastic plate, either with or without an adjacent rigid baffle, and with a range of edge conditions. Under conditions of “light” fluid loading, the long-range coupling mechanism seems unlikely to be of importance, but at low frequencies and under “heavy” fluid loading it appears that, even for large separations between an eddy and an inhomogeneity, the long-range coupling generates an acoustic field far in excess of that radiated by the same boundary layer turbulence over a homogeneous surface.

Mechanisms of the generation of external acoustic radiation from pipes due to internal flow disturbances

Extensive spectral measurements of the internal wall pressure fluctuations, pipe wall acceleration, and external acoustic radiation due to the disturbance of a fully developed turbulent air flow in a pipe by 90° radiused bends, 45° and 90° mitred bends, and butterfly and gate valves are presented. The measurements were made at sufficient distances downstream of the disturbance for an undisturbed hydrodynamic regime to be re-established, and for the only remaining disturbance to be a superimposed internal acoustic field radiated from the disturbance. This internal acoustic field, which can be responsible for extending the influence of the disturbance throughout a piping system, comprises, in general, both plane wave and higher order acoustic modes, although its detailed character depends on the particular characteristics of the individual fittings. It gives rise to increases in pipe wall vibration and external radiation, by large amounts in the cases of the more severe disturbances, over those due to undisturbed turbulent pipe flow. The background theory of pipe wall response and radiation which provides the framework for interpretation of the experimental results and identification of sound generation mechanisms is also presented. At frequencies at which only plane acoustic waves can propagate in the pipe, both forced peristaltic motion and resonant modes of the pipe wall contribute to the acceleration response of the wall. For a circular pipe with uniform wall thickness, theory predicts no coupling between plane waves and resonant wall modes of circumferential order m>0; but departures from the ideal state result in excitation of apparently all pipe modes with resonance frequencies in this range. High subsonic and supersonic structural modes and the peristaltic motion (which, because of augmentation of acoustic velocity by the flow, is supersonic with respect to the external fluid) all have high radiation ratios and make the dominant contributions to the external sound radiation. Increases in pipe wall response and external radiation are largest at frequencies at which higher order acoustic modes can propagate, in which case coincidence effects lead to strong excitation of supersonic pipe modes. A previous conclusion that coincidence occurs at a frequency close to the cut-off frequency of the acoustic mode involved is confirmed. The results show the effect of the combination of the set of discrete resonance frequencies of the pipe wall and the influence of the flow on the wavenumber-frequency relation for the acoustic modes in producing four different principal wavenumber coincidences for each acoustic mode, in agreement with theoretical predictions.

Coherent modes and boundary waves in a rough-walled acoustic waveguide

The theory of Biot scatter was generalized to acoustically rough interfaces between fluids of differing densities and sound velocities by Tolstoy [J. Acoust. Soc. Am. 72, 960–972 (1982)] for the case kh≤1, k being the wavenumber and h the mean spacing between roughness elements. The present paper applies this approach to a harmonic point acoustic source in a fluid layer of thickness H and sound velocity c1, with: (1) a rigid floor with hard pebbles and (2) a soft floor of sound velocity c2≥c1 (Pekeris waveguide) with a monolayer of hard pebbles at the interface. For a ratio H/h=102 it is shown that: (a) pebbles have a marked influence on the usual coherent acoustic waveguide modes. This effect is best understood in terms of an alteration of the smooth-walled phase shift suffered by sound totally reflected from the bottom. This is particularly obvious for the Pekeris waveguide, for which the net effect on individual modes, for tightly packed spherical pebbles and for typical bottom acoustic parameters, is to increase their excitation amplitudes by factors approaching 2 near the limit of validity of the scatter theory (kh=1). (b) Pebbles may bring about the existence of a subsonic branch of the lowest mode, corresponding to a wall roughness boundary mode carried by the rough boundary. In the hard-bottomed model this branch always exists for k≥(εH)−1/2, where ε is a scattering parameter determined by the shape and volume per unit area of the scatterers. When combined with the criterion kh≤1 this condition yields a definite boundary wave passband. In the case of the Pekeris waveguide the passband is quite restrictive, being very sensitive to the ratio c2/c1; the boundary mode exists only for c2/c1≂1+δ, where δ≲0.008. For the special case c2=c1 the boundary wave is strongest and allows for an entirely subsonic mode having no analog in the smooth-walled model. The c2/c1 restriction being fairly stringent one must expect the chief practical effect of this kind of bottom roughness to be of the type (a).

Heat exchange between subsonic and supersonic plasma jets and a plane surface

The thermal and gasdynamic parameters of subsonic and supersonic plasma streams are investigated. The permissible size of test models for the subsonic mode is determined.

A study of air breathing rockets—Subsonic mode combustion

Subsonic mode combustion in cylindrical secondary combustors of Air Breathing Rockets (ABR) was investigated. Experiments determined the influence of oxidizer-fuel ratio of the primary rocket, mass flow ratio of secondary air to the primary rocket propellants, and length of secondary combustors on the performance of ABR. Gaseous hydrogen and gaseous oxygen were used as the primary rocket propellants and compressed air at room temperature was used as secondary air. Experimental results were compared with ideal conditions calculated on the assumption of complete mixing and burning. A one-dimensional analysis made it possible to calculate axial distribution of flow properties. From the calculated stagnation temperature distribution, we determined “effective flame length” l f . The performance of the secondary combustors correlated well to the non-dimensional combustor length L l f . Cross sectional distribution of flow properties were obtained from gas sample and Pitot pressure data. Combustion efficiency was also obtained by integrating heat release flux over an exit cross sectional plane. Using a model assuming incomplete mixing and burning, combustion efficiency and other properties were related to the ratio of the exit pressure to the theoretical projection based on the complete burning model. These results agreed well with the experiments.

High Performance Dash-on-Warning Air Mobile Missile System

On receipt of warning, the air mobile aircraft-missile system performs a high acceleration takeoff followed by a supersonic dash to a safe distance from the launch site. At that time a subsonic long endurance mode is entered. The study objectives were to 1) determine technological aircraft and boost trajectory requirements, 2) provide initial definition of the aircraft and boost trajectory requirements, and 3) provide partial cost estimates for a fleet of aircraft which provides 200 missile on airborne alert. Three aircraft boost propulsion systems were studied: an unstaged cryogenic rocket, an unstaged storable liquid, and a solid rocket staged system. Aircraftgross weight was minimized for the combined dash and endurance mission profile. Using existing technologies, the resulting vehicles could accomplish the mission for gross weights of approximately one million Ib.

Aspects of the reflexion and free wave properties of a composite panel under fluid loading

The response of a composite panel to external forcing, with inclusion of fluid loading effects, is considered. Of the two strata comprising the composite panel one, backed by a vacuum, is of the conventional thin elastic plate or membrane kind, while the other, in contact with the fluid, is more like an elastic solid and may suffer significant compression. The behaviour of the acoustic field close to grazing incidence is examined, this behaviour being determined by that of the plane wave reflexion coefficient. In the absence of the upper stratum it is well known that the reflexion coefficient has the value −1 around grazing incidence, so that direct and reflected fields from an external source cancel and preclude the propagation of a genuine acoustic field over the surface (a situation known in optics as the “Lloyd's mirror” effect). It is shown that, at any given frequency, an impedance for the upper stratum can be prescribed which will lead to the value +1 for the grazing incidence reflexion coefficient, and will thus obviate the severe power loss which would otherwise occur in directions close to the surface. Next the free subsonic surface waves which can exist in the coupled three-part (two-layer panel plus fluid) system are examined. It is shown analytically that, if the upper layer has low impedance controlled by stiffness forces, a new surface wave can exist in the system. This wave essentially involves the stiffness of the upper layer and the mass of the fluid, and has a wavenumber much higher than that of the surface wave in a single conventional panel. It is also shown from numerical studies that two subsonic surface waves will exist over quite a wide range of parameters, though not necessarily with the wide wavenumber separation of the low impedance case. A discussion is given of the possible importance of the high wavenumber mode in the case of excitation by high wavenumber boundary layer turbulence, and of the significance of two free subsonic surface wave modes in calculations of energy transmission over composite panels of the kind modelled here.

Edge scattering of aerodynamic sound by a lightly loaded elastic half-plane

We investigate the acoustic field radiated when a compact turbulent eddy lies close to a semi-infinite wave-bearing surface, but many acoustic wavelengths from its edge. The Lighthill acoustic analogy is used to reduce the problem to the simpler one of the diffraction of a plane sound wave by a semi-infinite elastic plate. This is solved exactly in terms of a contour integral by means of the Wiener-Hopf technique. An explicit solution for the far sound field is then developed for the limiting case when a non-dimensional fluid loading parameter ϵ tends to zero. Particular attention is paid to the subsonic surface wave modes which couple the fluid and plate vibrations. At low frequencies the bulk of the elastic wave energy induced in the plate by the adjacent turbulent eddy propagates without attenuation in a subsonic surface wave mode. Interaction with the edge of the plate induces an indirect scattered field whose intensity exhibits the dependence on cos 2 ½ θ (the line θ = 0 defines the semi-infinite surface) typical of the acoustic field of an edge scattering half-plane. The acoustic power of the eddy is increased over its free space value by a factor ϵ 2 ( Ma s ) -1 , where Ma s = c p/ c represents the ratio of the natural speed of plate waves in vacuo to the speed of sound. In typical aeronautical applications e can be as large as 18 dB at characteristic eddy frequencies of 100 Hz.

A Mott-Smith Distribution to Describe the Structure of a Plane Shock Wave in a Binary Mixture

The problem of the shock wave structure in a binary mixture is restudied in view of an inconsistency in the postulates of an earlier paper. Assuming a bimodal distribution—a supersonic and a subsonic mode—for each component gas, it is observed that, for consistency, the flow velocity and temperature of the subsonic mode must be postulated as functions of position. Explicit calculations are given for the case when the initial mixture contains only a small fraction of the second gas. The results for this case are found not to differ much from earlier results.