Jet Mean Flow Research Articles

Analysis of aeroacoustic characteristics of a supersonic jet at designed conditions based on numerical simulation

The work is devoted to the numerical simulation of aeroacoustic characteristics of a supersonic jet issuing from a Laval nozzle at the design Mach number M=2. The results of the large-eddy simulations (LES) are presented. Characteristics of mean jet flow and its fluctuations, as well as the characteristics of the far-field jet noise, including its azimuthal content, are obtained. The results of the simulation are compared with experimental data and their acceptable agreement is shown. It is concluded that there are various noise generation mechanisms in the considered jet.

Statistics of inhomogeneous turbulence in large-scale quasigeostrophic dynamics.

A remarkable feature of two-dimensional turbulence is the transfer of energy from small to large scales. This process can result in the self-organization of the flow into large, coherent structures due to energy condensation at the largest scales. We investigate the formation of this condensate in a quasigeostropic flow in the limit of small Rossby deformation radius, namely the large-scale quasigeostrophic model. In this model potential energy is transferred up-scale while kinetic energy is transferred down-scale in a direct cascade. We focus on a jet mean flow and carry out a thorough investigation of the second-order statistics for this flow, combining a quasilinear analytical approach with direct numerical simulations. We show that the quasilinear approach applies in regions where jets are strong and is able to capture all second-order correlators in that region, including those related to the kinetic energy. This is a consequence of the blocking of the direct cascade by the mean flow in jet regions, suppressing fluctuation-fluctuation interactions. The suppression of the direct cascade is demonstrated using a local coarse-graining approach allowing us to measure space dependent interscale kinetic energy fluxes, which we show are concentrated in between jets in our simulations. We comment on the possibility of a similar direct cascade arrest in other two-dimensional flows, arguing that it is a special feature of flows in which the fluid element interactions are local in space.

A data-driven Reynolds-number-dependent model for turbulent mean flow prediction in circular jets

This paper proposes a data-driven turbulence model for predicting the mean flow in turbulent circular jets over a wide range of Reynolds numbers (Re). The main formulation is adapted from the well-known k–ε model (where k is the turbulent kinetic energy, and ε is the dissipation rate) with a set Re-dependent variation of the model constants. The k–ε model with Tam–Thies correction is applied with model constants optimized using data assimilation based on the ensemble Kalman filter to minimize the deviation between the model prediction and experimental data. The model constants of converging jets at Re = 10 700, 20 100, and 95 500 are fitted using logarithmic curves with respect to Re to obtain a universal formulation for predicting the jet mean flow under various flow conditions. The model using the fitted model constants, named the k–ε–Re model, can accurately predict the mean flow in both converging and orifice jets at various Re. While the k–ε–Re model is directly applied to the pipe jets, much better prediction can be obtained at high Reynolds numbers (Re ≥ 21 000 presently) compared with the default k–ε model. However, certain discrepancy with experimental data is observed at 5 ≤ x/D ≤ 15 at Re = 6000 and 16 000. Further improvement can be achieved by assimilating the fitting coefficients based on the pipe jet data. The k–ε–Re model is adequately generalizable and can predict the mean flow in different circular jets at a moderate or high Re (≥ 21 000), while further improvement can be obtained by the data assimilation and recalibration based on the specific nozzle type at a small Re.

Noise predictions of a Mach 0.9 round jet using tailored adjoint Green’s functions

The turbulent mixing noise radiated by a Mach 0.9 jet is investigated. The focus is put on the proper calculation of acoustic propagation effects by means of adjoint Green’s function that are tailored to the jet mean flow. Tam and Auriault’s statistical mixing noise model is recast for Pierce’s wave equation that is energy preserving. An unconditionally stable formulation to compute propagation effects is thus obtained. Adjoint fields are computed from the direct problem with help of the flow reversal theorem. A finite element solver is used to solve tailored adjoint Green’s functions, and corresponding adjoint fields are displayed. Acoustic predictions are carried out for a wide range of polar angles, and compared to measurements. A particular attention is given to predictions achieved at upstream observer angles. At these angles, the present model describes the physics of upstream travelling guided jet waves. The adjoint method provides a suitable framework to split the generation of sound from its propagation. It is illustrated how tailored adjoint Green’s functions filter the radiating part of Tam and Auriault’s sound source model, by weighting with propagation effects.

Assessment of Optimization Methods for Aeroacoustic Prediction of Trailing-Edge Interaction Noise in Axisymmetric Jets

Our concern in this paper is in the fine-tuning of the arbitrary parameters within the upstream turbulence structure for the acoustic spectrum of a rapid-distortion theory (RDT)-based model of trailing-edge noise. RDT models are based on an appropriate asymptotic limit of the Linearized Euler Equations and apply when the interaction time of the turbulence with the surface edge discontinuity is small compared to the eddy turnover time. When an arbitrary transversely sheared jet mean flow convects a finite region of nonhomogeneous turbulence, the acoustic spectrum of the pressure field scattered by the trailing-edge depends on (among other things) the upstream turbulence via the Fourier transform of the correlation function, R22 (where subscript 2 refers to a co-ordinate surface normal to the plate). We show that the length and time scale parameters that govern the spatial and temporal de-correlation of R22 can be found using formal optimization methods to avoid any uncertainty in their selection by hand-tuning. We assess various optimization methods that are broadly categorized into an ‘evolutionary’ and ‘non-evolutionary’ paradigm. That is, we optimize the acoustic spectrum using the Multi-Start algorithm, Particle Swarm Optimization and the Multi-Population Adaptive Inflationary Differential Evolution Algorithm. The optimization is based upon different objective functions for the acoustic spectrum and/or turbulence structure. We show that this approach, while resulting in the total modest increase in computation time (on average 2 h), gives excellent prediction over most frequencies (within 2–4 dB) where the trailing-edge noise associated amplification in sound exists.

Investigation into the turbulence statistics of installed jets using hot-wire anemometry

This work presents a detailed study of the turbulence flow statistics of a jet mounted with its axis parallel to a rigid flat plate. Hot-wire constant temperature anemometry has been used to measure the single-point and two-point statistics of the axial velocity component at several locations within the jet flow field. Results show that the jet mean flow near the plate surface is subjected to a local acceleration and redirection due to a Coandă-type effect. The propagation of these effects downstream of the plate trailing edge is strongly dependent on the plate position. Regarding the velocity fluctuations, the mean turbulence intensity levels are seen to decrease as the radial distance between the jet and surface decreases. Analysis of the single-point power spectral density data on the shear layer close to the plate shows that the reduction in magnitude of the low-frequency content of the energy spectrum is responsible for the decrease in turbulence intensity. Additionally, the characteristic time and length scales computed from two-point measurements reduce as the plate is mounted closer to the jet centre-line. The axial eddy convection velocity is seen to increase in the region of high turbulent kinetic energy in the shear layer adjacent to the surface. Empirical models for turbulence characteristic scales and eddy convection velocity are presented. These findings suggest that both the amplitude and distribution of the jet mixing noise sources are affected when closely installed next to a surface. This paper is a continuation of a recent investigation on the turbulence statistics of isolated jets presented in Proença (Exp Fluids 60(4):63, 2019).Graphic abstract

Experimental investigation of influence of sliding discharge DBD plasma on low-speed boundary layer

In this study, we investigated the effects of surface sliding discharge of a dielectric barrier discharge (SL-DBD) plasma actuator on the boundary layer flow using the time-resolved particle image velocimetry (PIV) technique. According to the PIV measurements, the peak-shaped mean jet flow is induced by the SL-DBD plasma actuator in quiescent air. Under the freestream of U∞ = 6 m/s on the flat plate, the results show that the streamwise velocity fluctuation induced by SL-DBD plasma is increased pronouncedly at the downstream of the actuator. Meanwhile, the mean flow velocity increases obviously in the downstream of the actuator. The instantaneous results show the formation of the vorticity at the bottom of the boundary layer after the plasma excitation. In addition, the vorticity has the behavior to lift up, possibly because of the induced peak-shaped jet.

An experimental study of the effects of lobed nozzles on installed jet noise

Jet noise remains a significant aircraft noise contributor, and for modern high-bypass-ratio aero-engines the strong interaction between the jet and aircraft wing leads to intensified installed jet noise. An experiment is carried out in this paper to study the effects of lobed nozzles on installed jet noise. It is found that the lobed nozzles, compared to round nozzles, have similar effects on installed jet noise for all the plate positions and Mach numbers tested. On the shielded side of the plate, the use of lobed nozzles leads to a noise reduction in the intermediate- and high-frequency regimes, which is thought to be due to a combination of enhanced jet mixing and more effective shielding effects by the flat plate. On the reflected side of the plate, noise reduction is only achieved in the intermediate frequency range; the little noise reduction or a slight noise increase observed in the high-frequency regime is likely due to enhanced jet mixing. On both sides of the plates, little noise reduction is achieved for the low-frequency noise due to the scattering of jet instability waves. This is likely to be caused by the fact that lobed nozzles cause negligible change to the dominant mode 0 (axisymmetric) jet instability waves. That the jet mean flow quickly becomes axisymmetric downstream of the jet exit could also play a role.Graphic abstract

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'.

Reducing noise from twin supersonic jets using very-low-frequency control

The intense jet noise radiated by closely spaced, twin supersonic hot jets leads to sound-induced structural vibration, fatigue and personnel related operational difficulties. Experimental, theoretical, and computational investigations into the physics and control of jet noise have identified several important sound sources, including wavepackets, screech, Mach wave radiation, and broadband shock associated noise (BBSAN). Reducing the loudest sources of jet noise, without sacrificing propulsive performance, has relied on intuition, parametric survey, or optimal control techniques. With the aim of developing a more general and robust method of jet noise reduction (JNR), we present a physics-based approach that leverages very-low-frequency jet dynamics in order to achieve JNR whilst preserving propulsive performance. Our approach formulates the control problem using the very-low-frequency global modes of the compressible Navier-Stokes operator linearized about the jet mean flow to disrupt the nonmodal transient growth processes. The presentation will showcase uncontrolled and controlled single and twin supersonic hot jets issuing from biconical nozzles, with conditions and geometries motivated by tactical Naval aircraft. The predictions utilize fully resolved numerical simulations whose data inform the control development and which evaluate its performance on the jet exhaust and on its radiated noise.

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.

Prediction of fluid flow and acoustic field of a supersonic jet using vorticity confinement.

In this study, the numerical simulation of the fluid flow and acoustic field of a supersonic jet is performed by using high-order discretization and the vorticity confinement (VC) method on coarse grids. The three-dimensional Navier-Stokes equations are considered in the generalized curvilinear coordinate system and the high-order compact finite-difference scheme is applied for the space discretization, and the time integration is performed by the fourth-order Runge-Kutta scheme. A low-pass high-order filter is applied to stabilize the numerical solution. The non-reflecting boundary conditions are adopted for all the free boundaries, and the Kirchhoff surface integration is utilized to obtain the far-field sound pressure levels in a number of observer locations. Comparisons of the jet mean flow and jet aeroacoustics results with the other numerical and experimental data at similar flow conditions are made and show a reasonable agreement. The study shows that the proposed solution methodology based on the high-order compact finite-difference scheme in conjunction with the VC method can reasonably predict the near-field flow and the far-field noise of high Reynolds number jets with a fairly coarser grid than that used in the large eddy simulations and, thus, the computational cost can be significantly decreased.

Numerical modelling of horizontal sediment-laden jets

Sediment-laden turbulent flows are commonly encountered in natural and engineered environments. It is well known that turbulence generates fluctuations to the particle motion, resulting in modulation of the particle settling velocity. A novel stochastic particle tracking model is developed to predict the particle settling out and deposition from a sediment-laden jet. Particle velocity fluctuations in the jet flow are modelled from a Lagrangian velocity autocorrelation function that incorporates the physical mechanism leading to a reduction of settling velocity. The model is first applied to study the settling velocity modulation in a homogeneous turbulence field. Consistent with basic experiments using grid-generated turbulence and computational fluid dynamics (CFD) calculations, the model predicts that the apparent settling velocity can be reduced by as much as 30 % of the stillwater settling velocity. Using analytical solution for the jet mean flow and semi-empirical RMS turbulent velocity fluctuation and dissipation rate profiles derived from CFD predictions, model predictions of the sediment deposition and cross-sectional concentration profiles of horizontal sediment-laden jets are in excellent agreement with data. Unlike CFD calculations of sediment fall out and deposition from a jet flow, the present method does not require any a priori adjustment of particle settling velocity.

Numerical Investigation of 3-D Supersonic Jet Flows Using Large-Eddy Simulation

The farfield noise generated by supersonic jets is investigated by a computational aeroacoustics methodology that couples 3-D large-eddy simulation (LES) near field data with the Ffowcs Williams- Hawkings method for farfield noise prediction. In order to accurately simulate jets at off-design supersonic conditions, we employ LES with characteristic filters for shock-capturing. This approach limits the dissipation of noise-producing turbulent fluctuations, and is suitable for incorporation into existing solvers. To further limit dissipation, a shock detector is used to determine shock locations and characteristic filters are applied locally. In this study, both perfectly-expanded and under-expanded unheated jets are investigated, with and without using characteristic filters. Comparisons with similar numerical and experimental data show reasonable agreement of the jet mean flow, turbulent statistics, and acoustics results. Preliminary grid-refinement shows improvement in these results.

Instability wave models for the near-field fluctuations of turbulent jets

AbstractPrevious work has shown that aspects of the evolution of large-scale structures, particularly in forced and transitional mixing layers and jets, can be described by linear and nonlinear stability theories. However, questions persist as to the choice of the basic (steady) flow field to perturb, and the extent to which disturbances in natural (unforced), initially turbulent jets may be modelled with the theory. For unforced jets, identification is made difficult by the lack of a phase reference that would permit a portion of the signal associated with the instability wave to be isolated from other, uncorrelated fluctuations. In this paper, we investigate the extent to which pressure and velocity fluctuations in subsonic, turbulent round jets can be described aslinearperturbations to the mean flow field. The disturbances are expanded about the experimentally measured jet mean flow field, and evolved using linear parabolized stability equations (PSE) that account, in an approximate way, for the weakly non-parallel jet mean flow field. We utilize data from an extensive microphone array that measures pressure fluctuations just outside the jet shear layer to show that, up to an unknown initial disturbance spectrum, the phase, wavelength, and amplitude envelope of convecting wavepackets agree well with PSE solutions at frequencies and azimuthal wavenumbers that can be accurately measured with the array. We next apply the proper orthogonal decomposition to near-field velocity fluctuations measured with particle image velocimetry, and show that the structure of the most energetic modes is also similar to eigenfunctions from the linear theory. Importantly, the amplitudes of the modes inferred from the velocity fluctuations are in reasonable agreement with those identified from the microphone array. The results therefore suggest that, to predict, with reasonable accuracy, the evolution of the largest-scale structures that comprise the most energetic portion of the turbulent spectrum of natural jets, nonlinear effects need only be indirectly accounted for by considering perturbations to the mean turbulent flow field, while neglecting any non-zero frequency disturbance interactions.

Jet Noise: Acoustic Analogy informed by Large Eddy Simulation

A novel approach to the development of a hybrid prediction methodology for jet noise is described. Modeling details and numerical techniques are optimized for each of the three components of the model. Far-field propagation is modeled by solution of a system of adjoint linear Euler equations, capturing convective and refraction effects using a spatially developing jet mean flow provided by a Reynolds-averaged Navier―Stokes computational fluid dynamics solution. Sound generation is modeled following Goldstein's acoustic analogy, including a Gaussian function model for the two-point cross correlation of the fourth-order velocity fluctuations in the acoustic source. Parameters in this model describing turbulent length and time scales are assumed to be proportional to turbulence information also taken from the Reynolds-averaged Navier―Stokes computational fluid dynamics prediction. The constants of proportionality are, however, not determined empirically, but extracted by comparison with turbulence length and time scales obtained from a large eddy simulation prediction. The large eddy simulation results are shown to be in good agreement with experimental data for the fourth-order two-point cross-correlation functions. The large eddy simulation solution is then used to determine the amplitude parameter and also to examine which components of the cross correlation are largest, enabling inclusion of all identified dominant terms in the Gaussian source model. The acoustic source description in the present approach is therefore determined with no direct input from experimental data. This model is applied to the prediction of sound to the experimental configuration of the European Union JEAN project, and gives encouraging agreement with experimental data across a wide spectral range and for both sideline and peak noise angles. This paper also examines the accuracy of various commonly made simplifications, for example: a locally parallel mean flow approximation rather than consideration of the spatially evolving mean jet flow and scattering from the nozzle; the assumption of small radial variation in Green function over the turbulence correlation length; the application of the far-field approximation in the Green function; and the impact of isotropic assumptions made in previous acoustic source models.

PIV measurement of the attached plane jet velocity field at a high turbulence intensity level in a room

The behaviour of an attached plane jet at high turbulence intensity (>20%) is not completely understood, especially at relatively low Reynolds numbers (<2000) in a room. This study focuses on the detailed mean and instantaneous jet flow field using the particle image velocimetry (PIV) measurement technique in a full-scale climate chamber. Three isothermal conditions at different Reynolds numbers based on the jet slot height and slot average velocity, 960, 1320 and 1680, were measured, having a turbulence intensity of 44%, 30% and 22%, respectively. The results show that the measured jet velocity was able to match the earlier empirical turbulent jet results when the turbulence intensity was of the order of 40%. Incomplete self-similarity occurs when the turbulence intensity is less than 30%. After a few slot heights downstream from the jet slot, most of the data of the jet at the Reynolds number 960 present self-similarity characteristics.

Reprint of: Sources of high-speed jet noise: analysis of LES data and modeling

Results from recent LES studies of high-speed jet flows and its near and far-field noise (Mendez et al. AIAA-2010-271) are reviewed with an emphasis on validation of the LES results. Far-field noise is predicted using data collected on a conical FW-H surface. Very good agreement with the measurement reported by Bridges & Wernet (AIAA-2008-2834) is observed. Data analysis of the flow disturbances within the jet and in the near-field is used to better characterize the sound source processes. We analyze LES data of Bodony and Lele (Phys. Fluids, vol. 46, 2005) using a filter in the wavenumber-frequency domain. The supersonic components of pressure and radial velocity fluctuation show peaks within the jet and show the U8j scaling behavior consistent with the far-field radiated noise levels. The observed scaling is also consistent with a perturbation expansion of nearly incompressible turbulent fluctuations within the jet flow. Linear global mode analysis of the non-parallel jet mean flow is performed. Features of Mach wave radiation are evident in the global modes for supersonic convection. Large transient growth is found due to convective non-normality. Some implications of this analysis for jet noise modeling are discussed.

Sources of high-speed jet noise: Analysis of LES data and modeling

Results from recent LES studies of high-speed jet flows and its near and far-field noise (Mendez et al. AIAA2010-271) are reviewed with an emphasis on validation of the LES results. Far-field noise is predicted using data collected on a conical FW-H surface. Very good agreement with the measurement reported by Bridges & Wernet (AIAA-2008-2834) is observed. Data analysis of the flow disturbances within the jet and in the near-field is used to better characterize the sound source processes. We analyze LES data of Bodony and Lele (Phys. Fluids, vol. 46, 2005) using a filter in the wavenumber-frequency domain. The supersonic components of pressure and radial velocity fluctuation show peaks within the jet and show the Uj8 scaling behavior consistent with the far-field radiated j noise levels. The observed scaling is also consistent with a perturbation expansion of nearly incompressible turbulent fluctuations within the jet flow. Linear global mode analysis of the non-parallel jet mean flow is performed. Features of Mach wave radiation are evident in the global modes for supersonic convection. Large transient growth is found due to convective non-normality. Some implications of this analysis for jet noise modeling are discussed.

A model for the symmetry breaking of the reverse Bénard–von Kármán vortex street produced by a flapping foil

The vortex streets produced by a flapping foil of span to chord aspect ratio of 4:1 are studied in a hydrodynamic tunnel experiment. In particular, the mechanisms giving rise to the symmetry breaking of the reverse Bénard–von Kármán (BvK) vortex street that characterizes fishlike swimming and forward flapping flight are examined. Two-dimensional particle image velocimetry (PIV) measurements in the midplane perpendicular to the span axis of the foil are used to characterize the different flow regimes. The deflection angle of the mean jet flow with respect to the horizontal observed in the average velocity field is used as a measure of the asymmetry of the vortex street. Time series of the vorticity field are used to calculate the advection velocity of the vortices with respect to the free stream, defined as the phase velocity Uphase, as well as the circulation Γ of each vortex and the spacing ξ between consecutive vortices in the near wake. The observation that the symmetry-breaking results from the formation of a dipolar structure from each couple of counter-rotating vortices shed on each flapping period serves as the starting point to build a model for the symmetry-breaking threshold. A symmetry-breaking criterion based on the relation between the phase velocity of the vortex street and an idealized self-advection velocity of two consecutive counter-rotating vortices in the near wake is established. The predicted threshold for symmetry breaking accounts well for the deflected wake regimes observed in the present experiments and may be useful to explain other experimental and numerical observations of similar deflected propulsive vortex streets reported in the literature.