Small Amplitude Pressure Research Articles

Linear pressure waves in fogs

The modelling of small-amplitude pressure waves in dilute single- or multi-component fogs by means of averaged equations is considered. The problem is cast in a singular-perturbation framework in which the suspended droplets are the singularities. This point of view simplifies the local problem in the vicinity of the droplets. Matching in the overlap region provides the coupling with the averaged fields. Among the advantages of the method is the fact that the leading-order effects are clearly identified. In particular it is shown that, for low-amplitude waves and far below the fluid's critical point, phase change effects only start to be important when the vapour mean free path becomes comparable with the drop radius and dominate for yet smaller drops.This present method for the derivation of effective equations appears to be of general applicability to a variety of multi-phase situations and is illustrated in detail.

Turbomachinery Committee Best 1994 Paper Award: Dynamic Control of Rotating Stall in Axial Flow Compressors Using Aeromechanical Feedback

Dynamic control of rotating stall in an axial flow compressor has been implemented using aeromechanical feedback. The control strategy developed used an array of wall jets, upstream of a single-stage compressor, which were regulated by locally reacting reed valves. These reed valves responded to the small-amplitude flow-field pressure perturbations that precede rotating stall. The valve design was such that the combined system, compressor plus reed valve controller, was stable under operating conditions that had been unstable without feedback. A 10 percent decrease in the stalling flow coefficient was obtained using the control strategy, and the extension of stable flow range was achieved with no measurable change in the steady-state performance of the compression system. The experiments demonstrate the first use of aeromechanical feedback to extend the stable operating range of an axial flow compressor, and the first use of local feedback and dynamic compensation techniques to suppress rotating stall. The design of the experiment was based on a two-dimensional stall inception model, which incorporated the effect of the aeromechanical feedback. The physical mechanism for rotating stall in axial flow compressors was examined with focus on the role of dynamic feedback in stabilizing compression system instability. As predicted and experimentally demonstrated, the effectiveness of the aeromechanical control strategy depends on a set of nondimensional control parameters that determine the interaction of the control strategy and the rotating stall dynamics.

Stability of Shock Wave in Faraday-Type MHD Generator.

The response of a shock wave in a Faraday-type MHD generator to small-amplitude pressure disturbances introduced downstream of the shock wave is analyzed with the method of small perturbations. The subsequent shock wave motion is classified as a stable oscillation about the initial steady flow shock position and an unstable oscillation where the shock wave moves upstream of the MHD channel, depending on interaction parameter, channel cross section and load parameter in the upstream of the shock wave. In the case of unstable condition, the Faraday-type MHD generator has a hysteresial characteristics such as the jump behavior of shock wave position and power output.

An experimental comparison of different methods of measuring wave propagation in viscoelastic tubes

In this work the values of wave attenuation and phase velocity in a 6 × 9 latex rubber tube closed at the distal end were measured by means of different equations, and varying the distance between transducers. Three equations are based on two simultaneous pressure measurements and on the knowledge of the terminal reflection coefficient ( two-point methods). The fourth equation is based on three simultaneous pressure measurements ( three-point method). In all cases small amplitude pressure signals (20 mmHg peak-to-peak) were employed. The results of our experiments were then compared with those computed using a classic linear model of wave propagation, and with the high-frequency asymptotic values obtained experimentally using an original method recently developed by the authors. The results obtained with 40 cm between transducers demonstrate that phase velocity (about 15 m/s) and wave attenuation (about 0.003 Neper/cm at 10 Hz) are in agreement with the predictions of classic linear theories in the frequency range 1–15 Hz, provided wall tethering and viscoelasticity are taken into account. Only at certain critical frequencies, which depend on the particular equation employed, does the estimation of wave attenuation become inaccurate owing to an insufficient signal-to-noise ratio. Moreover, wave propagation measurements become inaccurate also at very low frequencies (<1 Hz). The results obtained using a small distance between transducers (10 cm) demonstrate that the two-point methods maintain greater accuracy than the three-point one. In particular, when reducing the separation between transducers, the three-point attenuation values become 3–4 times greater than the attenuation obtained using the two-point equations. This finding might explain the large differences between propagation values observed in recent in vivo experiments. Finally, asymptotic estimations of the high-frequency phase velocity and attenuation per wave-length turn out rather robust and insensitive to a reduction in the transducer distance. These estimations might, therefore, be usefully adopted during in vivo experiments performed in difficult conditions.

Etude expérimentale de l'influence d'un champ de pression fluctuant sur l'apparition de la cavitation dans un venturi

It is well known that a nucleus subject to a quasi-steady mean pressure drop can either oscillate or asymptotically grow depending the final pressure is above or blow the critical one. Recent investigations have shown that dynamically driven asymptotic growth conditions are associated to sudden mean pressure drops and to small amplitude pressure fluctuations superposed to a mean pressure larger than the quasi-steady critical pressure. In order to provide experimental support to the later results, tests were conducted to determine the effect of the modification of the upstream turbulence on the critical cavitation conditions in a venturi. The results show that cavitation is delayed when turbulence fluctuation intensities increase. A simple analysis associates this effect to the adiabatic behaviour of the gas within the cavity.

A Numerical Model to Predict the Nonlinear Response of External Flow Over Vibrating Bodies (Planar Flow)

A model is developed to simulate two-dimensional laminar flow over an arbitrarily shaped body, a portion of which is subjected to time varying harmonic motion. The model is tested by comparison to previous numerical simulations for flow over a square cavity, oscillatory flow through a wavy channel and boundary layer flow along a flat plate. The model is applied to predict the flow over a flat plate with a section forced in simple sinusoidal motion. The dimensionless vibration amplitude, H0, and the Reynolds number, Re are maintained at 0.1 and 1000, respectively. The Strouhal number, St, defined as the ratio of the flow advective time scale to the plate oscillation period, is varied in the range 0.0 ≦ St ≦ 1.0. The friction and pressure coefficients over the vibrating portion of the body are analyzed using Fast Fourier Transform techniques. For low frequency vibrations (low Strouhal number) the pressure and friction coefficients match the steady state results for flow over a fixed sinusoidal bump. A small amplitude pressure wave generated by the oscillating plate propagates downstream with the flow. For high frequency vibrations (high Strouhal number) the pressure and friction coefficients over the vibrating portion of the body deviate from the steady state results and a high amplitude pressure wave propagates downstream. The pressure at one chord length upstream is also affected. As St increases the flow becomes highly nonlinear and harmonics appear in the downstream velocity and pressure fields. The nonlinearity is controlled by the convective acceleration term near the vibrating plate surface.

Numerical Simulation of Unsteady Laminar Flow Over Vibrating Bodies (Planar Flow)

A model is developed to simulate two-dimensional laminar flow over an arbitrarily shaped body, a part of which is subjected to simple harmonic motion. The vibration amplitude ratio, Ho, and the Reynolds number, Re, are maintained at 0.1 and 1000, respectively. The Strouhal number, St, is varied in the range 0.0 ≤ St ≤ 1.0. The computer code is tested for the flow in a square cavity and also over a flat plate. The friction and pressure coefficients over the vibrating portion of the body are determined. Fast Fourier Transforms are performed on the time series data of these coefficients. For low-frequency vibrations (low Strouhal number) the pressure and friction coefficients match the steady-state results for flow over a sinusoidal bump. A small-amplitude pressure wave generated by the oscillating plate propagates downstream with the flow. For high-frequency vibrations (high Strouhal number) the pressure and friction coefficients over the vibrating portion of the body deviate from the steady-state results and a high-amplitude pressure wave propagates downstream. The pressure at one chord length upstream is also affected. As St increases, the flow becomes highly nonlinear and higher harmonics appear in the downstream flow. Subsequent analysis indicates that the nonlinearity is controlled by the term v(Əu/Əy).

Pulsatile Pressure and Flow in the Skeletal Muscle Microcirculation

Although blood flow in the microcirculation of the rat skeletal muscle has negligible inertia forces with very low Reynolds number and Womersley parameter, time-dependent pressure and flow variations can be observed. Such phenomena include, for example, arterial flow overshoot following a step arterial pressure, a gradual arterial pressure reduction for a step flow, or hysteresis between pressure and flow when a pulsatile pressure is applied. Arterial and venous flows do not follow the same time course during such transients. A theoretical analysis is presented for these phenomena using a microvessel with distensible viscoelastic walls and purely viscous flow subject to time variant arterial pressures. The results indicate that the vessel distensibility plays an important role in such time-dependent microvascular flow and the effects are of central physiological importance during normal muscle perfusion. In-vivo whole organ pressure-flow data in the dilated rat gracilis muscle agree in the time course with the theoretical predictions. Hemodynamic impedances of the skeletal muscle microcirculation are investigated for small arterial and venous pressure amplitudes superimposed on an initial steady flow and pressure drop along the vessel.

Mechanical impedance of the canine diaphragm

A technique which does not require the measurement of strain has been developed for the investigation of the incremental dynamic properties of soft tissue sheets. Radially prestressed and circularly clamped canine diaphragm samples were exposed to small-amplitude pseudorandom pressure variations. From the measurement of these pressure variations and the volume flow caused by the vibration of the membrane the incremental mechanical impedance spectrum was computed in the 0.25-5 Hz frequency range at three different levels of initial stress. The diaphragm tissue was found to be basically elastic. However, the small viscous component showed a sharp negative frequency dependence between 0.25 and 2 Hz. The quasistatic elastances of the samples were in good agreement with the elastance values derived from the impedance data. The relationship between the elastance and the initial stress was close to linear. It was concluded that the method is applicable to the study of the incremental dynamic properties of planar soft tissue samples.

The Relationship Between Standing Waves, Pressure Pulse Propagation, and Critical Flow Rate in Two-Phase Mixtures

A two-fluid model is presented that can be used to predict the celerity and attenuation of small-amplitude harmonic disturbances in bubbly two-phase flow. This frequency-dependent relationship is then used to predict the propagation of small-amplitude pressure perturbations through the use of Fourier decomposition techniques. Predictions of both standing waves and propagating pressure perturbations agree well with existing data. The low and high-frequency limits of the celerities predicted by the model are examined and their relationship to critical flow rate is demonstrated. Some limitations of the interfacial pressure model employed in conventional critical flow analysis are exposed and the implications to the prediction of critical flow rate are discussed.

A Viscous-Flow Approach to the Computation of Propeller-Hull Interaction

A model is developed to simulate two-dimensional laminar flow over an arbitrarily shaped body, a part of which is subjected to simple harmonic motion. The vibration amplitude ratio, Ho, and the Reynolds number, Re, are maintained at 0.1 and 1000, respectively. The Strouhal number, St, is varied in the range 0.0 ≤ St ≤ 1.0. The computer code is tested for the flow in a square cavity and also over a flat plate. The friction and pressure coefficients over the vibrating portion of the body are determined. Fast Fourier Transforms are performed on the time series data of these coefficients. For low-frequency vibrations (low Strouhal number) the pressure and friction coefficients match the steady-state results for flow over a sinusoidal bump. A small-amplitude pressure wave generated by the oscillating plate propagates downstream with the flow. For high-frequency vibrations (high Strouhal number) the pressure and friction coefficients over the vibrating portion of the body deviate from the steady-state results and a high-amplitude pressure wave propagates downstream. The pressure at one chord length upstream is also affected. As St increases, the flow becomes highly nonlinear and higher harmonics appear in the downstream flow. Subsequent analysis indicates that the nonlinearity is controlled by the term v(Əu/Əy).

Investigations of transonic diffusers. 2nd report Theoretical study on stability of a shock wave.

The response of a normal shock wave in a transonic diffuser to small-amplitude pressure disturbances introduced downstream of the shock wave is analyzed with the method of small perturbations. The subsequent shock wave motion is classified into a stable oscillation about the initial steady flow shock position and an unstable case where the shock wave moves upstream of the throat, depending on the initial shock position and the pressure recovery in the subsonic region downstream of the shock wave. The stability criterion of the shock wave is presented as a function of the Mach number where the shock is initially located and the diffuser efficiency of the subsonic region downstream of the shock, and it is shown that the criterion agrees well with the previous experimental results.

High amplitude wave propagation in collapsible tube. I. — Relation between rheological properties and wave propagation

The mechanical behaviour of collapsible tubes is theoretically and experimentally studied when the viscoelastic wall is longitudinally stretched. The dynamic rheological law is deduced from the static law by introducing the dynamic Young's modulus as experimentally obtained. It is then shown that the speed of small amplitude pressure waves is well predicted using this dynamic rheological law.

Experiments on flow limitation during forced expiration in a monoalveolar lung model.

To understand the mechanism of flow limitation during forced expiration, flow properties were studied using a rubber model made up of two elements in series: a balloon and a thin-walled collapsible tube. This elastic model was inserted into a rigid box and flow was provided by pressure ramps in the box. Flow rate and transmural pressures were then measured; wave speed and fluid velocity were calculated from the area-pressure law. For a sufficiently high flow rate, a flow-limiting segment was observed. The flow became supercritical relative to the small amplitude pressure wave speed and a choke flow occurred. Then the tube collapsed. Consequently, the fluid velocity decreased and the flow became subcritical throughout the entire tube. Thus the flow rate appeared to be limited by viscous effects.

Small amplitude pressure wave in subsonic and supersonic bubble flows in convergent-divergent nozzles

This paper makes a theoretical analysis of the propagation phenomena of the small amplitude pressure wave in the subsonic and supersonic bubble flow with a velocity slip between bubble and liquid in the convergent-divergent nozzle. From an analysis of the time-mean flow, the nondimensional parameter m = {u 2 G ·α(1 − α)ρ lβ(2 − 1/S)/P·[αβS + (1 − α)βS 2 + α(1 − α)]} 1 2 corresponds to Mach number is gasdynamics where u G is the gas velocity, α: the void fraction, ρ L: the liquid density, P: the pressure, S: the velocity ratio of the gas and liquid flows and β: the proportional constant for the virtual mass. From a theoretical analysis of the small disturbance field, it is clarified that the parameter m also plays an essential and important role as Mach number, although the propagation performance of the disturbance is very complicated compared with that in gasdynamics. It is also shown that the pressure waves are divided into four groups depending on the velocity ratio S. Two of them are rather realistic, but the other two are required of a further investigation in future.

Metastable effects associated with the reflection of a pressure pulse at the free surface of water

Evidence is now brought forward to show that the reflection of evan a small amplitude pressure pulse at a free surface is accompanied by considerable distortion. An explanation of this fact, and of the low values of tensile strength of water inferred from underwater explosion and similar 'once only' pulses, is suggested in the light of existing ideas about the structure of a liquid surface. It is concluded that there is now no real disagreement between experiment and theory on tensile strength as there are now acceptable explanations of the low values found from ultrasonic and 'once only' pulse methods.

The Effect of Mass Flow Rate on the Reflection Behaviour of Small-Amplitude Pressure Waves from Duct Terminations

This paper describes an investigation of the reflection characteristics of small-amplitude pressure waves in the presence of steady flow in a duct. A correlation technique employing pseudo-random binary-sequence (p.r.b.s.) pulses is introduced. A theoretical model of the process is presented together with considerations of correlation analysis. The results show agreement between the experimental results and the model; they further indicate that, in the presence of a steady flow component, there is a significant effect on the reflection behaviour of plane pressure waves for a reduction in the area terminating a duct. The experimental technique is effective at very low flow velocities (Mach number = 0·02, Reynolds number = 30 times 103) and establishes a linear relationship between a reflection coefficient and a non-dimensional mass flow number. A reflection coefficient of flow is introduced as an appropriate parameter for such conditions. The procedure could be applied to a wide range of industrial processes to determine flow coefficients of duct elements in situ, to optimize flow processes and to locate leakage flows.

The effect of variation of longitudinal stretch on the dynamic elastic properties of isolated segments of canine carotid arteries

Isolated canine carotid arterial segments were subjected to small constant amplitude pressure fluctuations, and the frequency responses of the radial displacements were obtained. These frequency responses, which exhibited a flat low-frequency portion followed by at least two resonance peaks, were measured at several elongations and transmural pressures. Static and dynamic circumferential elastic moduli were calculated and showed a direct dependence on increasing transmural pressure, whereas the dependence on longitudinal elongation was absent. At elongations greater than natural, the frequencies at which resonance occurred increased with increased transmural pressure; however, measurements of longitudinal tensions at varying elongations and transmural pressures suggests a closer relationship between longitudinal tension and the frequencies at which resonance occurs. This implies that the mode of vibration at resonance is similar to the transverse vibration of a string. This idea was supported by calculation of the frequency response of arterial segments using the vibrating string mode. This gave close agreement to the experimental results, whereas there was no such agreement between calculated curves based on the dilatational mode and the experimental results.

Combustion Response Function Measurements by the Rotating Valve Method

A study has been conducted to evaluate the rotating valve method of measuring the combustion response of solid propellants to small amplitude pressure oscillations. The method is based on producing pressure oscillations in a small rocket motor by varying the area of a secondary exhaust nozzle in a periodic manner. This is accomplished by using a rotating valve as the secondary orifice. The valve apparatus operates concurrently with a primary nozzle which controls the steady-state pressure. The frequency of the oscillations is determined by the rotational speed of the valve. A theoretical analysis was conducted to relate the combustion response function to measurable ballistic properties of the combustion chamber. Assuming that the combustion chamber is small in comparison to the acoustic wavelength, the combustion response function can be calculated from the amplitude of the oscillating pressure and the phase angle between the oscillating pressure and oscillating nozzle area. Cold flow tests were conducted using nitrogen and helium to test the validity of the analysis. Excellent agreement was found between the measured and predicted amplitudes and phase angles. Combustion tests then were conducted using two aluminized propellant formulations and three nonaluminized formulations. There was excellent agreement between the T-burner and rotating valve tests conducted on the same batch of propellant. For two nonaluminized propellants, the comparisons were based on different batches of propellant. Differences in combustion response and variations in burning rate and characteristic exhaust velocity were observed for these two formulations. It was concluded that the rotating valve method is a valid substitute for the T-burner. Substantial reductions in the cost of characterizing propellants also were obtained using this new approach.

Investigation of non-reflecting end conditions within a duct by means of pseudo-random binary pressure pulses

A newly developed experimental technique is described for detecting in-duct pressure waves reflected from a termination. An application of the technique to making the end of a partially closed pipe non-reflecting is also described. The method is potentially applicable to a wide range of pressure wave action problems. In cases such as in two-phase flow work it may well be the only practical approach. Measuring times are short, less than one second, and readings are easy to take. The technique adopted is to inject small amplitude pressure pulses in the form of a pseudo-random binary sequence which allows on-line and easily interpreted correlograms of incident and reflected waves to be obtained.