Vortex Sound Theory Research Articles

A Numerical Study on the Distribution and Evolution Characteristics of an Acoustic Field in the Time Domain of a Centrifugal Pump Based on Powell Vortex Sound Theory

The acoustic field distribution and evolution characteristics in a time domain inside a centrifugal pump are studied. During the fluid motion process, the acoustic source and acoustic pressure are basically less than 0, and the minimum value of the two parameters is distributed near the tongue. Additionally, the concentration, break, extend, migration and reaggregation phenomena of the minimum acoustic source region exist. Specifically, as the blade passes through the tongue, the minimum acoustic source region concentrates on the tongue firstly, then extends and migrates downstream slightly with the blade motion, and aggregates again around the tongue, which results in the similar evolution characteristics of acoustic pressure. Moreover, the standard deviation (STD) of acoustic source mainly focuses near the pressure side of blade tail and volute tongue, and the maximum STD is located at the tongue. Compared with the source component induced by stretching of the vortex, the source component induced by non-uniformity of fluid kinetic energy is closer to the overall acoustic source. Take the tongue as an example, at various rotational speeds, the STD proportions of the two components are about 5% and 95%, respectively. This study discusses the generation, distribution and evolution characteristics of acoustic field, which lays a foundation to analyze the acoustic field propagation mechanism of centrifugal pumps.

Non-linear acoustic analysis of the pressure rise of the compression wave generated by a train entering a tunnel

Hara's formula is used to predict the pressure rise of a compression wave generated by a high-speed train entering a tunnel. The acoustic theory is used to predict its waveform. Hara's formula was derived from the shock theory. Meanwhile, the acoustic theory produces the same non-dimensional formula as Hara's formula up to order OM4, where M is the train Mach number, when the non-linear acoustic effect in the vortex sound theory is considered. However, the relationship between the shock and acoustic theories remains unclear because the closed formula produced by the vortex sound theory apparently differs from that of Hara's formula. This study shows that Hara's formula can be deductively obtained from the non-linear acoustic theory. A general equation used to predict the compression waveform with a relative error of Op/ρ0c02, where p/ρ0c02 is the non-dimensional acoustic pressure to the atmospheric density ρ0 and the sound speed c0, is shown herein using the non-linear acoustic theory.

The effect of blade outlet angle on the acoustic field distribution characteristics of a centrifugal pump based on Powell vortex sound theory

Numerical simulation method based on Powell vortex sound theory is adopted to explore the mechanisms of acoustic field distribution characteristics of a centrifugal pump with different blade outlet angles. Results reveal that with the increasing of the angle, the fluctuation range of acoustic source at the tongue in time domain extends, which causes the same fluctuation characteristics of acoustic pressure. As the angle increases from 15° to 35°, the total acoustic source intensity (TASI) and total acoustic pressure level (TAPL) at the tongue increase by 1.68% and 2.54% on average under various rotational speeds, respectively. Additionally, the TASI and TAPL show the similar directivity characteristics under different angles, and the change of the angle has slight effect on the extremum distribution characteristics. Besides, the A-weighted average acoustic pressure level (Lp) and A-weighted average acoustic source intensity level (La) are adopted to describe the overall level of TAPL and TASI. When the angle increases from 15° to 35°, the La and Lp increase gradually and increase by 1.59% and 2.21% on average under various rotational speeds, respectively. The study reveals the acoustic source and acoustic pressure distribution characteristics in time and frequency domain qualitatively and quantitatively, and manifests that the distribution and variation patterns of acoustic source lead to those of acoustic pressure. The conclusions could lay a foundation for the empirical formula proposition between acoustic pressure and acoustic source.

Analytical model for the prediction of pulsations in a cold-gas scale-model of a Solid Rocket Motor

Cold gas scale model experiments (1/30) demonstrate that coupling of vortex shedding with acoustic standing waves can produce pressure oscillations of the same level as observed in large Solid Rocket Motors. An analytical acoustical energy balance model is proposed in which the system is described as a single mode acoustic resonator and the pulsations are assumed to be purely harmonic. The selected acoustic mode number is an input to the model. Quasi-steady linear models are used to describe losses of acoustic energy by vortex shedding at a thermal inhibitor ring, radiation at the nozzle and friction within the porous injection wall used for gas injection. The sound production is predicted by using a 2-D planar point vortex model combined with the Vortex Sound Theory. The model demonstrates that the sound production due to interaction of the vortex with the cavity surrounding the integrated nozzle is dominant, explaining previous results of cold gas and hot-gas scale models. The effect of vortex ingestion by the nozzle is negligible. Aspects of the nozzle geometry, other than the cavity volume, are not critical. The model predicts pressure pulsations within a factor 2, when the circulation of the vortices is taken one third of the maximum available circulation. This reduction factor of the circulation is assumed to be a consequence of turbulence. The Mach number corresponding to the maximum of pulsation is predicted within 20% in a range comparable to results obtained by axis-symmetrical numerical flow simulations.

Aerofoil broadband and tonal noise modelling using stochastic sound sources and incorporated large scale fluctuations

The present work discusses modifications to the stochastic Fast Random Particle Mesh (FRPM) method featuring both tonal and broadband noise sources. The technique relies on the combination of incorporated vortex-shedding resolved flow available from Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulation with the fine-scale turbulence FRPM solution generated via the stochastic velocity fluctuations in the context of vortex sound theory. In contrast to the existing literature, our method encompasses a unified treatment for broadband and tonal acoustic noise sources at the source level, thus, accounting for linear source interference as well as possible non-linear source interaction effects. When sound sources are determined, for the sound propagation, Acoustic Perturbation Equations (APE-4) are solved in the time-domain. Results of the method's application for two aerofoil benchmark cases, with both sharp and blunt trailing edges are presented. In each case, the importance of individual linear and non-linear noise sources was investigated. Several new key features related to the unsteady implementation of the method were tested and brought into the equation. Encouraging results have been obtained for benchmark test cases using the new technique which is believed to be potentially applicable to other airframe noise problems where both tonal and broadband parts are important.

Strouhal number dependency of the aero-acoustic response of wall perforations under combined grazing-bias flow

The influence of low Mach number grazing-bias flow on the linear acoustic response of slit shaped wall perforations is determined in terms of a dimensionless acoustical impedance for Strouhal numbers based on the perforation width of order unity. The influence of edge geometries is studied by experiments. In particular, slanted slits under an angle of 30° with respect to the grazing flow direction are considered. Sound production, i.e. whistling potentiality corresponding to a negative real part of the impedance, is observed for various geometries and flow conditions. Sound production restricts the largest perforation size which can be used in practice for acoustical liners. Whistling in the limit cases of purely bias and purely grazing flows can be explained qualitatively in terms of Vortex Sound Theory. For combined bias/grazing flow, most of the oscillations in the impedance as a function of the Strouhal number are related to these limit behaviours. A configuration with thin sharp edges both upstream and downstream corresponds to commonly used theoretical models assuming an infinite thin wall. This configuration displays a behaviour drastically different from a more realistic perforation geometry with sharp square edges.

Generation Mechanism and Prediction Model for Low Frequency Noise Induced by Energy Dissipating Submerged Jets during Flood Discharge from a High Dam.

As flood water is discharged from a high dam, low frequency (i.e., lower than 10 Hz) noise (LFN) associated with air pulsation is generated and propagated in the surrounding areas, causing environmental problems such as vibrations of windows and doors and discomfort of residents and construction workers. To study the generation mechanisms and key influencing factors of LFN induced by energy dissipation through submerged jets at a high dam, detailed prototype observations and analyses of LFN are conducted. The discharge flow field is simulated using a gas-liquid turbulent flow model, and the vorticity fluctuation characteristics are then analyzed. The mathematical model for the LFN intensity is developed based on vortex sound theory and a turbulent flow model, verified by prototype observations. The model results reveal that the vorticity fluctuation in strong shear layers around the high-velocity submerged jets is highly correlated with the on-site LFN, and the strong shear layers are the main regions of acoustic source for the LFN. In addition, the predicted and observed magnitudes of LFN intensity agree quite well. This is the first time that the LFN intensity has been shown to be able to be predicted quantitatively.

Computation of vortical flow and flow induced noise by large eddy simulation with FW-H acoustic analogy and Powell vortex sound theory

The sound generated by a NACA0012 airfoil in the wake of a rod is numerically simulated by two approaches, one is the large eddy simulation (LES) with the FW-H acoustic analogy and the other is the LES with the Powell vortex sound theory, in order to compare the accuracies of their predictions. The vortical structures around the rod-airfoil are computed by the LES and captured by the vortex identification (Q). The acoustic predictions are verified by the measurements. It is shown that the computed results by the two hybrid approa- ches (LES and FW-H, LES and Powell) are very similar. Both are shown to be satisfactory in the prediction of the noise generated by an unsteady flow. Subsequently, the numerical simulations of the wall pressure fluctuations and the flow-induced noise of a NACA0015 airfoil are made by the two hybrid approaches. At two angles of attack (0° and 8°), the wall pressure fluctuations of the NACA0015 airfoil are computed. The obtained power spectra of the wall pressure fluctuations are analyzed and compared with the measured data. And the vortical structures around the airfoil at two angles of attack are simulated and analyzed. After that, the flow induced noises of the NACA0015 airfoil at two angles of attack are predicted by the two hybrid approaches (LES and FW-H, LES and Powell). The radiated sound spectra are analyzed and compared with the experimental data. Comparisons show that both are robust, credible and satisfactory in the numerical prediction of the flow induced noise. All numerical simulations are carried out by parallel processing in the Wuxi supercomputing center.

Sound Source Measurement of a Semi-Circular Cylinder in a Uniform Flow by Particle Image Velocimetry

In this paper, the measurement of an aerodynamic sound source for a semi-circular cylinder in a uniform flow is described using Particle Image Velocimetry (PIV). This experimental technique is based on vortex sound theory, where the time derivative of vorticity is evaluated with the aid of two sets of standard PIV systems. The experimental results indicate that the sound source for the semi-circular cylinder is located around the shear layer near the edge of the semi-circular cylinder. The sound source intensity and the area are reduced in the semi-circular cylinder compared with those of a circular cylinder. This result indicates that the aerodynamic sound of the semi- circular cylinder is smaller than that of the circular cylinder, which supports the microphone measurement result.

The Cooling Module Aerodynamic Noise Prediction Considering Porous Media

The influence of the radiator and other components in the noise prediction process of cooling module is difficult to calculate. Firstly, the model including porous media is established. And the large eddy simulation (LES) is used to analyze its impact on the inflow instability and calculate the urbulent kinetic energy and vorticity around the fan. Then the main noise sources are identified by vortex sound theory. The acoustic BEM model is established for discrete and broadband aerodynamic noise prediction of cooling module. And the sound field sound pressure spectrum is analyzed. Finally, the noise test is made to verify the prediction. The results show that the radiator and other components have a huge influence in the flow field and noise prediction and they can not be ignored in the aerodynamic noise calculation process.

Comments on the low frequency radiation impedance of a duct exhausting a hot gas.

The influence of convection and temperature on the radiation impedance of an open duct termination exhausting a hot gas is commonly described by a complex theory. A simplified analytical expression is proposed for low frequencies. Both models assume a free jet with uniform velocity bounded by infinitely thin shear layers. The convective velocity that should be assumed when applying these models to a non-uniform outflow is uncertain. A simplified version of the so-called Vortex Sound Theory demonstrates that the convective velocity one should assume is lower than the jet centerline velocity.

F091003 渦音理論に基づく空力音の分離解法([F09100]環境工学企画,数値空力音響の最前線と課題)

F091003 渦音理論に基づく空力音の分離解法([F09100]環境工学企画,数値空力音響の最前線と課題)

Flow-acoustic coupling in coaxial side branch resonators with rectangular splitter plates

Flow past symmetrically located side branches mounted in a duct can give rise to pronounced flow oscillations due to coupling between separated shear layers and standing acoustic waves. The acoustically-coupled flows were investigated using digital particle image velocimetry (PIV) in conjunction with unsteady pressure measurements. Global instantaneous, phase- and time-averaged flow images were evaluated to provide insight into the flow physics during flow tone generation. Onset of the locked-on resonant states was characterized in terms of the acoustic pressure amplitude and frequency of the resonant pressure peak. Structure of the acoustic noise source was discussed in terms of patterns of generated acoustic power, which was evaluated by applying the vortex sound theory in conjunction with global quantitative flow imaging and numerical simulation of the acoustic field. In addition to the basic side branch configuration, the effect of bluff rectangular splitter plates located along the centerline of the main duct was investigated. The first mode of the shear layer oscillation was inhibited by the presence of the plates, which resulted in substantial reduction of the amplitude of acoustic pulsations and the strength of the acoustic source.

Aeroacoustic power generated by a compact axisymmetric cavity: prediction of self-sustained oscillation and influence of the depth

AbstractAeroacoustic power generation due to a self-sustained oscillation by an axisymmetric compact cavity exposed to a low-Mach-number grazing flow is studied both experimentally and numerically. The feedback effect is produced by the velocity fluctuations resulting from a coupling with acoustic standing waves in a coaxial pipe. A numerical methodology that combines incompressible flow simulations with vortex sound theory is used to predict the time-averaged acoustic source power generated by the cavity. The effect of cavity depth on the whistling is addressed. It is observed that the whistling occurs around a peak-whistling Strouhal number which depends on the cavity depth to width ratio. The proposed numerical method provides excellent predictions of the peak-whistling Strouhal number as a function of cavity depth. Given the oscillation amplitude, the numerical method predicts the time-averaged acoustic source power within a factor of two for moderate fluctuation amplitudes. For deep cavities the time-averaged acoustic source power appears to be independent of the cavity depth.

Experimental examination of vortex-sound generation in an organ pipe: A proposal of jet vortex-layer formation model

Aero-dynamical models of sound generation in an organ pipe driven by a thin jet are investigated through an experimental examination of the vortex-sound theory. An important measurement requirement (acoustic cross-flow as an irrotational potential flow reciprocating sinusoidally) from the vortex-sound theory is carefully realized when the pipe is driven with low blowing pressures of about 60Pa (jet velocities of about 10m/s). Particle image velocimetry (PIV) is applied to measure the jet velocity and the acoustic cross-flow velocity over the mouth area at the same phase by quickly switching the jet drive and the loudspeaker-horn drive. The vorticity of the jet flow field and the associated acoustic generation term are evaluated from the measurement data. It is recognized that the model of the “jet vortex-layer formation” is more relevant to the sound production than the vortex-shedding model. The acoustic power is dominantly generated by the flow–acoustic interaction near the edge, where the acoustic cross-flow velocity takes larger magnitudes. The acoustic generation formula on the vortex sound cannot deny the conventional acoustical volume-flow model because of the in-phase relation satisfied between the acoustic pressure at the mouth and the acoustic volume flow into the pipe. The vortex layers formed along both sides of the jet act as the source of an accelerating force (through the “acceleration unbalance”) with periodically alternating direction to oscillate the jet flow and to reinforce the acoustic cross-flow at the pipe mouth.

Aeroacoustics of the swinging corrugated tube: Voice of the Dragon

When one swings a short corrugated pipe segment around one's head, it produces a musically interesting whistling sound. As a musical toy it is called a "Hummer" and as a musical instrument, the "Voice of the Dragon." The fluid dynamics aspects of the instrument are addressed, corresponding to the sound generation mechanism. Velocity profile measurements reveal that the turbulent velocity profile developed in a corrugated pipe differs notably from the one of a smooth pipe. This velocity profile appears to have a crucial effect both on the non-dimensional whistling frequency (Strouhal number) and on the amplitude of the pressure fluctuations. Using a numerical model based on incompressible flow simulations and vortex sound theory, excellent predictions of the whistling Strouhal numbers are achieved. The model does not provide an accurate prediction of the amplitude. In the second part of the paper the sound radiation from a Hummer is discussed. The acoustic measurements obtained in a semi-anechoic chamber are compared with a theoretical radiation model. Globally the instrument behaves as a rotating (Leslie) horn. The effects of Doppler shift, wall reflections, bending of the tube, non-constant rotational speed on the observed frequency, and amplitude are discussed.

A study on the application of two different acoustic analogies to experimental PIV data

The aim of the present study is to compare two different acoustic analogies applied to time-resolved particle image velocimetry (PIV) data for the prediction of the acoustic far-field generated by the flow over a rectangular cavity. We consider the model problem of sound radiating from an open, two-dimensional, shallow cavity with an aspect ratio of 2 at a Reynolds number of 3.0 × 104 (based on the cavity length). The study is carried out by simultaneous high-speed two-dimensional PIV and sound measurements. The instantaneous flow field is obtained from the PIV measurements. The emitted sound is then calculated using Curle’s analogy and Vortex Sound Theory. To our knowledge, Vortex Sound Theory is used here for the first time in combination with time-resolved PIV data. The acoustic analogies are derived through rather different pathways, and the mathematical schemes used to solve the equations are sensitive in a different way to factors such as data resolution, noise level, and complexity of the geometry. Both methods indicate that the trailing edge of the cavity is the main sound source. The predictions of the acoustic field obtained by applying the two methods are analyzed and compared with the measured sound. For the presented case, the results show that both analogies estimate the overall sound pressure level quite well and that they give very similar results, both in total intensity and in the spectral distribution of the emitted sound.

On the whistling of corrugated pipes: effect of pipe length and flow profile

Whistling behaviour of two geometrically periodic systems, namely corrugated pipes and multiple side branch systems, is investigated both experimentally and numerically. Tests are performed on corrugated pipes with various lengths and cavity geometries. Experiments show that the peak-whistling Strouhal number, where the maximum amplitude in pressure fluctuations is registered, is independent of the pipe length. Experimentally, a decrease of the peak-whistling Strouhal number by a factor of two is observed with increasing confinement ratio, i.e. the ratio of pipe diameter to cavity width. A numerical methodology that combines incompressible flow simulations with vortex sound theory is proposed to estimate the acoustic source power in periodic systems. The methodology successfully predicts the Strouhal number ranges of acoustic energy production/absorption and the nonlinear saturation mechanism responsible for the stabilization of the limit cycle oscillation. The methodology predicts peak-whistling Strouhal numbers in agreement with experiments and explains the dependence of the peak-whistling Strouhal number on the confinement ratio. Combined with an energy balance, the proposed methodology is used to estimate the acoustic fluctuation amplitudes.

Effect of skewed blades on tip-clearance for different flow rates in axial fans

Tip-clearance noise induced by tip-leakage flow in axial flow fans, with the blades skewed circumferentially at angles of ±8.3°, has been investigated under off-design conditions by numerical simulation and experiments. Aerodynamic and aeroacoustic performances have been measured. Tip-leakage flow has been investigated by Navier-Stokes flow simulations at off-design conditions. The characteristics of noise sources in the tip-clearance region, obtained numerically, have been analyzed using vortex sound theory. Synergy between the tip-leakage vortex and the noise source in the tip region is discussed. Moreover, the noise source in the tip region has been measured by dynamic pressure sensors mounted in the casing wall near the blade tip and the acoustic far field has been obtained simultaneously as a function of flow rate. The frequency characteristic of the tip noise component is analyzed by measured results. The characteristics of noise source reveal that tip-clearance noise is associated with skewed blades, which are found to be effective in controlling tip-leakage flow and in eliminating the noise source in the tip-clearance region at off-design conditions. Forward-skewed blade are more effective than backward-skewed blades in reducing noise

Experimental Evaluation Methods of Aeroacoustic Noise Based on Time Series Analysis of Flow Field

In this study, we propose an experimental method for evaluating dipole sound on the basis of the vortex sound theory. By using time-resolved particle image velocimetry (PIV) in a wind tunnel test, we measured time series data of unsteady two-dimensional flow around a circular cylinder which is suitable for applying the vortex sound theory and validating our proposed methods. The sound pressure in the far field experimentally estimated from PIV measurements is validated by a correlation analysis with a measured sound pressure. Furthermore, we performed a correlation analysis between the source intensity defined as the integrand in the equation of the vortex sound theory and the measured sound pressure to determine the relationship between the estimated dipole sound and the measured flow field. The results show that the estimated sound pressure can detect the Aeolian tone due to Karman vortex shedding. Periodic fluctuation around the shear layer separation regions and the vortex formation region in the wake region causes the estimated dipole sound.