Acoustic Mach Number Research Articles

Jet Installation Noise Modelling for Round and Chevron Jets

Wall-Modelled Large Eddy Simulations (LES) are conducted using a high-resolution CABARET method, accelerated on Graphics Processing Units (GPUs), for a canonical configuration that includes a flat plate within the linear hydrodynamic region of a single-stream jet. This configuration was previously investigated through experiments at the University of Bristol. The simulations investigate jets at acoustic Mach numbers of 0.5 and 0.9, focusing on two types of nozzle geometries: round and chevron nozzles. These nozzles are scaled-down versions (3:1 scale) of NASA’s SMC000 and SMC006 nozzles. The parameters from the LES, including flow and noise solutions, are validated by comparison with experimental data. Notably, the mean flow velocity and turbulence distribution are compared with NASA’s PIV measurements. Additionally, the near-field and far-field pressure spectra are evaluated in comparison with data from the Bristol experiments. For far-field noise predictions, a range of techniques are employed, ranging from the Ffowcs Williams–Hawkings (FW–H) method in both permeable and impermeable control surface formulations, to the trailing edge scattering model by Lyu and Dowling, which is based on the Amiet trailing edge noise theory. The permeable control surface FW–H solution, incorporating all jet mixing and installation noise sources, is within 2 dB of the experimental data across most frequencies and observer angles for all considered jet cases. Moreover, the impermeable control surface FW–H solution, accounting for some quadrupole noise contributions, proves adequate for accurate noise spectra predictions across all frequencies at larger observer angles. The implemented edge-scattering model successfully captures the mechanism of low-frequency sound amplification, dominant at low frequencies and high observer angles. Furthermore, this mechanism is shown to be effectively consistent for both M=0.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M=0.5$$\\end{document} and M=0.9\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M=0.9$$\\end{document}, and for jets from both round and chevron nozzles.

Sound attenuation performance at high sound pressure level of micro-perforated panel sound absorber with embedded resistive screen

In this paper, a composite sound absorber made of a micro-perforated panel (MPP), an air cavity with embedded resistive screen and a rigid back plate is investigated at high sound pressure level (SPL). The sound absorption coefficient predicted theoretically is compared with the experimental measurement at 150 dB and a good agreement is obtained. It is demonstrated that the incorporation of resistive screen within the air cavity improves significantly the sound absorption that presents a large frequency band and remains almost identical with respect to the SPL compared to a classical MPP absorber whose sound absorption peak varies with the SPL. The MPP absorber with the resistive screen glued on the MPP is studied and different resistive screens are compared at 150 dB and it is observed that the sound absorption coefficient increases with a large frequency band, which depends on the airflow resistivity of the screen. A sensitivity analysis shows that the resistance per unit area of the screen affects the acoustic properties of the absorber at low SPL while at high SPL, the acoustic properties are mainly controlled by the perforation ratio of the MPP and the acoustic orifice Mach number.

Acoustic characterization of an installed elliptical jet

This work demonstrates a preliminary acoustic characterization of an installed elliptical jet with an aspect ratio of 2. This configuration is compared against the nominal axisymmetric installed jet case of equivalent diameter. A baseline case for the elliptical and axisymmetric nozzle geometries are obtained in the uninstalled configuration. For all cases, the acoustic Mach number is varied between 0.4 and 1.0, the azimuthal observer angle between 0° and 90°, and the axial distance from the jet exit to the observer between 0 and 30 nozzle equivalent diameters. The latter of these is an analogue for polar angle variation by keeping the radial distance from the jet to the observer constant. A flat metal plate is used for the installed case, creating a jet–plate interaction mimicking that of an aircraft engine’s exhaust and its wing. Using the same variations as the free jet, parameters such as plate height, trailing-edge distance and, for the elliptical jet, nozzle exit rotation angle are investigated to give a broad characterization of the installed elliptical jet and enable direct comparison to the axisymmetric jet case. The key comparison metric for this work is the overall sound pressure level and polar directivity of the acoustic fields.

Jet Flow and Noise Predictions for the Doak Laboratory Experiment

Large-eddy simulations (LESs) are performed for two isolated unheated jet flows corresponding to a Doak Laboratory experiment performed at the University of Southampton. The jet speeds studied correspond to acoustic Mach numbers of 0.6 and 0.8 as well as Reynolds numbers based on the nozzle exit diameter of about one million. The LES method is based on the compact accurately boundary-adjusting high-resolution technique (CABARET) and is implemented on graphics processing units (GPUs) to obtain 1000–1100 convective time units for statistical averaging with reasonable run times. In comparison with the previous jet LES calculations with the GPU CABARET method, the mean-flow velocity and turbulent intensity profiles are matched with the hot-wire measurements just downstream of the nozzle exit. The far-field noise spectra of the Doak jets are evaluated using two methods: the Ffowcs Williams–Hawkings approach and a reduced-order implementation of the Goldstein generalized acoustic analogy. The flow and noise results are compared with hot-wire and acoustic microphone measurements of the Doak Laboratory and critically analyzed in comparison with the NASA small hot jet acoustic rig database.

Artificial diffusion for convective and acoustic low Mach number flows I: Analysis of the modified equations, and application to Roe-type schemes

Three asymptotic limits exist for the Euler equations at low Mach number - purely convective, purely acoustic, and mixed convective-acoustic. Standard collocated density-based numerical schemes for compressible flow are known to fail at low Mach number due to the incorrect asymptotic scaling of the artificial diffusion. Previous studies of this class of schemes have shown a variety of behaviours across the different limits and proposed guidelines for the design of low-Mach schemes. However, these studies have primarily focused on specific discretisations and/or only the convective limit.In this paper, we review the low-Mach behaviour using the modified equations - the continuous Euler equations augmented with artificial diffusion terms - which are representative of a wide range of schemes in this class. By considering both convective and acoustic effects, we show that three diffusion scalings naturally arise. Single- and multiple-scale asymptotic analysis of these scalings shows that many of the important low-Mach features of this class of schemes can be reproduced in a straightforward manner in the continuous setting.As an example, we show that many existing low-Mach Roe-type finite-volume schemes match one of these three scalings. Our analysis corroborates previous analysis of these schemes, and we are able to refine previous guidelines on the design of low-Mach schemes by including both convective and acoustic effects. Discrete analysis and numerical examples demonstrate the behaviour of minimal Roe-type schemes with each of the three scalings for convective, acoustic, and mixed flows.

Quantitative criteria for designing thrust gates to mitigate jet-flap interaction noise

Thrust gates have been reported as a promising concept to reduce jet-flap interaction noise. This manuscript proposes two quantitative criteria for the design of thrust gates based on time-averaged flow parameters that can be extracted from steady-state simulations. Computations were carried out by solving the explicit, transient, compressible lattice Boltzmann equation, while the acoustic far-field was obtained via the Ffowcs-Williams and Hawkings analogy. After being validated based on the truncation error and comparisons with measurements for the far-field acoustics, the simulation model was used in a parametric analysis of thrust gates, varying the width (W/DJ = 1,2,3,4) for a fixed depth B/CF = 1, where DJ is the nozzle exit diameter and CF is the flap chord. Also, two acoustic Mach numbers (Ma = 0.5 and Ma = 0.7) and two flap deflection angles (α = 7° and α = 30°) were considered. The results show that thrust gates with W/DJ > 1 and W/DJ > 2 do not reduce significantly the far-field noise in weak (α = 7°) and strong (α = 30°) jet-flap interaction configurations for both Mach numbers. In this context, the jet-spreading angle and pressure-load are proposed as criteria for designing thrust gates that are effective for noise reduction but with minimum cutout on the flap. Thrust gates designed according to the pressure-load criterion were quieter by around 0.89 dB (α = 7°) and 4.25 dB (α = 30°) for Ma = 0.5, and 0.94 dB (α = 7°) and 3.53 dB (α = 30°) for Ma = 0.7 in comparison with those designed following the jet-spreading criterion. Additionally, the pressure-load criterion was also shown to be effective in reducing the cutout on the flap.

Robustness of Reduced-Order Jet Noise Models

Three statistical jet noise prediction models are compared for a representative set of single-stream jet cases, which include cold and hot jets of the Strategic Investment in Low-Carbon Engine Technology experiment at an acoustic Mach number of 0.875 as well as the cold jets of the NASA small hot jet acoustic rig experiment at acoustic Mach numbers of 0.5 and 0.9. The implemented models are those proposed by Tam and Auriault (Jet Mixing Noise from Fine-Scale Turbulence,” AIAA Journal, Vol. 37, No. 2, 1999, pp. 145–153), Khavaran and Bridges (“An Empirical Temperature Variance Source Model in Heated Jets,” NASA TM 2012-217743, 2012), and the Goldstein’s “A Generalized Acoustic Analogy,” Journal of Fluid Mechanics, Vol. 488, July 2003, pp. 315–333) generalized acoustic analogy (GAA) model. By virtue of reduced-order modeling, which is based on the single-point mean flow and turbulence statistics, all of these implementations use a number of empirical dimensionless source parameters for far-field noise spectra predictions. In comparison with the Tam and Auriault model, the Khavaran and GAA model implementations use several dimensionless parameters, which are available from previous literature and assumed to be more or less universal for a class of single-stream jets. These parameters include the fluctuating enthalpy function and the dimensionless amplitudes of autocovariances of turbulent fluctuating stresses and velocities available from the literature. The comparison of the three models is aimed at not only assessing their accuracy for a range of jet conditions, observer angles, and frequencies but also to examine their robustness outside of a reference jet experiment for which their source models were calibrated. For the input to each model, the mean flow, turbulence kinetic energy, and dissipation rate extracted from Large Eddy Simulations and Reynolds-averaged Navier–Stokes solutions are considered.

Correlation analysis of flow and sound in non-isothermal subsonic jets based on large eddy simulations

The sound radiation mechanism is investigated in non-isothermal subsonic jets at acoustic Mach number 0.9 and at temperature ratios of 0.86, 1.0, and 2.7, using causality methods on the results predicted by large eddy simulations. Turbulence signals in the jet flows are rearranged according to the acoustic analogies, such as the streamwise and radial shear signals, ux′ and ur′, the self-signal, ui′uj′, the entropy fluctuation, s′, and the vortex norm, |ω|. The ray-tracing method is applied to locate the acoustically correlated regions, and the two-point correlation is employed to analyze the acoustic correlation. The results show that the cancelation between the s′ and ux′, and between the s′ and ur′, vary with temperature ratio, and, thus, may affect the radiation directionality. The density fluctuation, ρ′, suppresses the acoustic correlations of the shear- and self-signals in the cold jet, respectively, but strengthens them in the hot jet; thus, the ρ′ enhances the cancelation both in cold and in hot jets. The intense negative fluctuation of the ux′ is found to be associated with the cancelation mechanism. It induces the peaks of ρ′ and s′ by disturbing the average fields. The jet temperature changes the averaged density and entropy so as to change the cancelation mechanism. Two large-scale acoustically correlated parts of the coherent structures are visualized by the zonal correlation of the ρ′. Their acoustic correlations cancel each other in the hot jets, but enhance each other in the cold jets. The acoustically correlated regions represented by the zonal correlations of the s′ and |ω| are in small scale and gather around the end of the potential core region.

Artificial Diffusion for Convective and Acoustic Low Mach Number Flows I: Analysis of the Modified Equations, and Application to Roe-Type Schemes

Three asymptotic limits exist for the Euler equations at low Mach number - purely convective, purely acoustic, and mixed convective-acoustic. Standard collocated density-based numerical schemes for compressible flow are known to fail at low Mach number due to the incorrect asymptotic scaling of the artificial diffusion. Previous studies of this class of schemes have shown a variety of behaviours across the different limits and proposed guidelines for the design of low-Mach schemes. However, these studies have primarily focused on specific discretisations and/or only the convective limit. In this paper, we review the low-Mach behaviour using the modified equations - the continuous Euler equations augmented with artificial diffusion terms - which are representative of a wide range of schemes in this class. By considering both convective and acoustic effects, we show that three diffusion scalings naturally arise. Single- and multiple-scale asymptotic analysis of these scalings shows that many of the important low-Mach features of this class of schemes can be reproduced in a straightforward manner in the continuous setting. As an example, we show that many existing low-Mach Roe-type finite-volume schemes match one of these three scalings. Our analysis corroborates previous analysis of these schemes, and we are able to refine previous guidelines on the design of low-Mach schemes by including both convective and acoustic effects. Discrete analysis and numerical examples demonstrate the behaviour of minimal Roe-type schemes with each of the three scalings for convective, acoustic, and mixed flows.

Generalized Acoustic Analogy Modeling of Hot Jet Noise

A generalized acoustic analogy model is implemented for the hot and cold static high-speed jet cases corresponding to conditions of the Strategic Investment in Low-carbon Engine Technology (SILOET) experiment performed by QinetiQ. The model is statistical and based on the covariance of fluctuating Reynolds stresses and enthalpy source terms in accordance with Goldstein’s theory. These quantities are obtained from a solution of the validated large-eddy simulation accelerated on graphics processing units. The covariance of fluctuating enthalpy terms is represented by the Khavaran and Bridges model, which involves the velocity autocorrelation function and temperature gradient in the jet. The velocity autocorrelation function and the covariance of fluctuating Reynolds stresses are approximated by an analytical Gaussian-exponential function. The input parameters of the acoustic model include single-point quantities such as the time-averaged local streamwise velocity, sound speed, temperature, vorticity magnitude, turbulent kinetic energy, and dissipation rate. Modeling choices for the acoustic length and time scales based on either the turbulent kinetic energy dissipation rate or mean flow vorticity are discussed. In each case, the model involves two dimensionless parameters associated with the acoustic correlation length and time scale. These two parameters are calibrated based on the far-field noise data at 90° observer angle. The sensitivity of the calibration coefficients to the jet type, cold versus hot, is investigated. Furthermore, the same acoustic model without recalibration is applied for far-field noise predictions of two NASA Small Hot Jet Acoustic Rig jets for acoustic Mach numbers 0.5 and 0.9. To probe the sensitivity of the acoustic model to the input flow data, Reynolds-averaged Navier–Stokes solutions of the same jet cases are considered along with the large-eddy-simulation solutions. The comparison of the predicted far-field noise spectra with the experiment is discussed in each case.

A proper framework for studying noise from jets with non-compact sources

A quantitative assessment of the acoustic source field produced by a laboratory-scale heated jet with a gas dynamic Mach number of 1.55 and an acoustic Mach number of 2.41 is performed using arrays of microphones that are traversed across the axial and radial plane of the jet's acoustic field. The nozzle contour comprises a method of characteristics shape so that shock-related noise is minimal and the dominant sound production mechanism is from Mach waves. The spatial topography of the overall sound pressure level is shown to be dominated by a distinct lobe residing on the principal acoustic emission path, which is expected from flows of this kind with supersonic convective acoustic Mach numbers. The sound field is then analysed on a per-frequency basis in order to identify the location, strength, convection velocity and propagation angle of the various axially distributed noise sources. The analysis reveals a collection of unique data-informed polar patterns of the sound intensity for each frequency. It is shown how these polar patterns can be propagated to any point in the far field with extreme accuracy using the inverse square law. Doing so allows one to gauge the kinds of errors that are encountered using a nozzle-centred source to calculate sound pressure spectrum levels and acoustic power. It is proposed that the measurement strategy described here be used for situations where measurements are being used to compare different facilities, for extrapolating measurements to different geometric scales, for model validation or for developing noise control strategies.

Jet-installation noise reduction with flow-permeable materials

This paper investigates the application of flow-permeable materials as a solution for reducing jet-installation noise. Experiments are carried out with a flat plate placed in the near field of a single-stream subsonic jet. The flat plate is modular and the solid surface near the trailing edge can be replaced with different flow-permeable inserts, such as a metal foam and a perforated plate structure. The time-averaged jet flow field is characterized through planar PIV measurements at three different velocities (Ma=0.3,Ma=0.5 and Ma=0.8, where Ma is the acoustic Mach number), whereas the acoustic far-field is measured with a microphone arc-array. Acoustic measurements confirm that installation effects cause significant noise increase, up to 17 dB for the lowest jet velocity, particularly at low and mid frequencies (i.e. St<0.7, with the Strouhal number based on the jet diameter and velocity), and mostly in the upstream direction of the jet. By replacing the solid trailing edge with the metal foam, noise abatement of up to 9 dB is achieved at the spectral peak for Ma=0.3 and a polar angle θ=40∘, with an overall reduction in the entire frequency range where jet-installation noise is dominant. The perforated plate provides lower noise reduction than the metal foam (7 dB at the spectral peak for Ma=0.3 and θ=40∘), and it is less effective at low frequencies. This is related to the values of permeability and form coefficient of the materials, which are the major parameters controlling the pressure balance across the trailing edge and, consequently, the noise generated by the plate. However, despite having a high permeability, the plate with the metal-foam trailing edge still has a distinct noise production at mid frequencies (St≈0.43 for Ma=0.3). Based on the analyses of different treated surface lengths, it is conjectured that the solid-permeable junction in the plate acts as a new scattering region, and thus its position also affects the far-field noise, which is in line with analytical predictions in the literature. Nonetheless, both types of inserts provide significant noise reduction and are potential solutions for the problem of jet-installation noise.

Acoustic streaming in second-order fluids

In this article, inner acoustic streaming for second-order fluids has been studied analytically by employing asymptotic expansions for a thin Stokes layer and low acoustic Mach number. In addition, a multiple-timescale approach has been adopted to separate the primary oscillatory flow and the steady acoustic streaming. The study considers two sample cases: (i) motionless boundary and (ii) vibrating boundary and compares the characteristics associated with their streaming. It is observed that both the primary oscillatory flow and acoustic streaming flow fields are suppressed in second-order fluids due to the extra stress components present in the fluids. This study considers both compressible and incompressible Stokes layers to bring out the acoustic streaming characteristics associated with fluid compressibility. For the compressible Stokes layer, stronger acoustic streaming flow results for the motionless boundary, leveraging the deeper interaction between the primary oscillatory pressure field and the steady streaming. In the case of a vibrating boundary, the primary oscillatory pressure field is independent of the Stokes layer compressibility, and hence, the acoustic streaming flow remains unaltered. The extra stresses in second-order fluids reduce the acoustic body force density, and the maximum reduction has been observed for the vibrating boundary. In order to understand Lagrangian streaming, Stokes drift has also been calculated and compared for all the scenarios. The theoretical analysis and fundamental insights derived from this study have potential for applications in diverse fields such as particle manipulation, biosensing, cell sorting, and removal of loosely bound material such as non-specifically bound proteins.

Spatiotemporal differential partitioning for one-dimensional fast acoustic streaming

Historically, acoustofluidics modeling of streaming behaviors has relied heavily and almost exclusively upon formal asymptotic expansions in a relevant small parameter (e.g., the acoustic Mach number) in order to render tractable the highly nonlinear governing equations. However, the direction of modern acoustofluidics research dictates that no such order of magnitude separation between the acoustic and streaming fields can be generally relied upon—in extremal systems, formal asymptotic methods fail to properly extract the dynamics of interest. We outline progress toward the development of a theoretical approach that affords greater generality through its direct, explicit consideration and exploitation of all spatiotemporal scale disparities by partitioning differential operations. The method is applied to a one-dimensional problem of semiinfinite extent that, by convention, is classified as “fast streaming.” The compressible Navier-Stokes equations are solved in an approximate successive manner in order to obtain the acoustic and streaming fields. We show that the steady multi-temporal behavior of this result is characterized by a conservation of energy across acoustic and streaming scales.

Temperature effects on the noise source mechanisms in a realistic subsonic dual-stream jet

A detailed numerical investigation of temperature effects on both aerodynamics and acoustics of a dual-stream jet including a central plug is carried out. The geometry is representative of a realistic turbofan with a high by-pass-ratio (BPR) close to 9. Two take-off high-subsonic operating points are investigated numerically by compressible large-eddy simulation. For these two selected points, the secondary stream is exactly the same in terms of static temperature and velocity. Both jets have also the same primary velocity. The only difference lies in the static temperature of the primary jet. There is a ratio of two between the two jets considered in this study, namely Tj=400 K and Tj=800 K. More precisely, the primary jet temperature is reduced while keeping the acoustic Mach number constant, leading to an increase of the primary jet Mach number from Mj=0.65 in the heated case to Mj=0.89 in the cold case. Some experimental data are available for the hot jet while the cold jet is introduced for academic reasons. The heated jet compares reasonably well with the experimental data, taking into account the complexity of the geometry. Temperature effects have a limited impact on aerodynamic development and acoustic radiation. The influence of the core flow is found to be weak due to the high BPR considered and the radiated acoustic is mainly driven by the secondary flow. Further investigations are carried out in order to highlight the differences between the two cases. The acoustic production area are identified by the way of axial velocity skewness coefficient maps. Finally, a decrease of the primary stream temperature leads to the development of trapped acoustic waves inside the jet core. An increase of the overall sound spectrum level about 5 dB is thus observed in the upstream direction for the cold jet, in agreement with the vortex sheet theory.

Modelling and prediction of the peak-radiated sound in subsonic axisymmetric air jets using acoustic analogy-based asymptotic analysis.

This paper uses asymptotic analysis within the generalized acoustic analogy formulation (Goldstein 2003 JFM 488, 315-333. (doi:10.1017/S0022112003004890)) to develop a noise prediction model for the peak sound of axisymmetric round jets at subsonic acoustic Mach numbers (Ma). The analogy shows that the exact formula for the acoustic pressure is given by a convolution product of a propagator tensor (determined by the vector Green's function of the adjoint linearized Euler equations for a given jet mean flow) and a generalized source term representing the jet turbulence field. Using a low-frequency/small spread rate asymptotic expansion of the propagator, mean flow non-parallelism enters the lowest order Green's function solution via the streamwise component of the mean flow advection vector in a hyperbolic partial differential equation. We then address the predictive capability of the solution to this partial differential equation when used in the analogy through first-of-its-kind numerical calculations when an experimentally verified model of the turbulence source structure is used together with Reynolds-averaged Navier-Stokes solutions for the jet mean flow. Our noise predictions show a reasonable level of accuracy in the peak noise direction at Ma = 0.9, for Strouhal numbers up to about 0.6, and at Ma = 0.5 using modified source coefficients. Possible reasons for this are discussed. Moreover, the prediction range can be extended beyond unity Strouhal number by using an approximate composite asymptotic formula for the vector Green's function that reduces to the locally parallel flow limit at high frequencies. This article is part of the theme issue 'Frontiers of aeroacoustics research: theory, computation and experiment'.

Effect of non-parallel mean flow on the acoustic spectrum of heated supersonic jets: Explanation of “jet quietening”

Noise measurements of heated axisymmetric jets at a fixed supersonic acoustic Mach number indicate that the acoustic spectrum reduces when the temperature ratio increases. The “spectral quietening” effect has been observed both experimentally and computationally using large Eddy simulations. It was explained by Afsar, Goldstein, and Fagan [AIAA J. 49, 2522 (2011)] through the cancellation introduced by the enthalpy flux/momentum flux coupling term using the generalized acoustic analogy formulation. But the parallel flow assumption is known to give inaccurate predictions at high jet speeds. In this paper, we therefore extend the nonparallel flow asymptotic theory of Goldstein, Sescu, and Afsar [J. Fluid Mech. 695, 199 (2012)] for the vector Green’s function of the adjoint linearized Euler equations in the analogy. Using the steady Reynolds averaged Navier Stokes calculation for the jet mean flow, we find that the coupling term propagator is positive-definite and asymptotically subdominant at low frequencies corresponding to the peak jet noise when nonparallel flow effects are taken into account and self-consistent approximations for the turbulence structure are made. We then assess the validity of the non-parallel flow-based acoustic analogy model by computing the overall sound pressure level (OASPL) at various observation angles. Interpretation of the latter allows a more rational explanation of the quietening effect. In general, our noise predictions are in very good agreement with acoustic data beyond the peak frequency.

Incompressible flow assumption in hydroacoustic predictions of marine propellers

Incompressible flow assumption is an essential step that simplifies numerical simulations for objects inside flowing water. However, incompressibility assumption creates a conflicting situation for sound propagation as the propagation speed is given by c0=dp/dρ where p denotes the pressure and ρ denotes the density. When dρ=0 is assumed to relieve simulations, speed of sound theoretically becomes infinite and therefore, induced pressures should be corrected with the acoustic analogy. This approach is called the “hybrid method” that combines hydrodynamic solver with hydroacoustic solver. Hydroacoustic solver adds compressibility effects to the incompressible hydrodynamic solver and uses hydrodynamic pressure to calculate acoustic pressure. Time step size is an important parameter to calculate acoustic pressure field in the fluid domain and an approach to determine the minimum value (for at least capturing the first blade passage frequency) is presented in this study. Another purpose of this paper is to investigate the effect of incompressibility on hydroacoustics and to analyze the necessity of utilising the famous Ffowcs Williams-Hawkings (FWH) equation for predicting marine propeller noise; both for cavitating and non-cavitating cases. Our results are in line with other researchers; hydrodynamic pressure is sufficient to assess the hydroacoustic performance of marine propellers in the near-field due to having very low acoustic Mach numbers. Near-field results from the hydrodynamic solver are then extrapolated to the far-field by adopting ITTC distance normalization equation. However; this equation, which is actually the inverse distance law, is only valid for point noise sources in stationary flow. It is found out that eliminating FWH equation by coupling the incompressible hydrodynamic solver with ITTC distance normalization equation fails to produce satisfactory results. For cavitating cases, numerical results in this study show that implementation of FWH is required even in the near-field.

A combined momentum-interpolation and advection upstream splitting pressure-correction algorithm for simulation of convective and acoustic transport at all levels of Mach number

A pressure-correction algorithm is presented for compressible fluid flow regimes. It is well-suited to simulate flows at all levels of Mach number with smooth and discontinuous flow field changes, by providing a precise representation of convective transport and acoustic propagation. The co-located finite volume space discretization is used with the AUSM flux splitting. It is demonstrated that two ingredients are essential for obtaining good quality solutions: the presence of an inertia term in the face velocity expression; a velocity difference diffusive term in the face pressure expression, with a correct Mach number scaling to recover the hydrodynamic and acoustic low Mach number limits. To meet these two requirements, a new flux scheme, named MIAU, for Momentum Interpolation with Advection Upstream splitting is proposed.

Investigation of the effect of turbulence intensity and nozzle exit boundary layer thickness on stability pattern of subsonic jet

In this study, factors affecting the noise generation by instability waves in a subsonic jet with acoustic Mach number of 0.5 are investigated using linear stability analysis. The base flow required for instability analysis is obtained by modeling the jet stream based on the k-ε turbulence model and using the empirical coefficients suggested by Thies and Tam [1]. The resulting base flow profiles are used to solve the linear instability equation, which governs the pressure perturbation for obtaining the eigenvalues and eigenfunctions. The results of linear instability analysis for phase and amplitude of pressure fluctuations are compared against the existing experimental data, which demonstrated the validity of the conducted instability analysis. The effects of turbulence intensity and thickness of the boundary layer at the jet nozzle exit on the results of the linear instability analysis are investigated. The results show that as the turbulence intensity at nozzle exit increases, the frequency range for which the spatial growth rates are positive grows smaller, and except for very low frequencies, this leads to decreased growth rates in both axisymmetric and first azimuthal modes. Also, in both of these modes, an increase in the thickness of the boundary layer at nozzle exit leads to a decrease in perturbation's growth rates in the surveyed frequency ranges.