SAM
https://sam.ensam.eu:443
The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Fri, 24 May 2024 19:05:00 GMT2024-05-24T19:05:00ZFlow in a weakly curved square duct: Assessment and extension of Dean's model
http://hdl.handle.net/10985/23422
Flow in a weakly curved square duct: Assessment and extension of Dean's model
RIGO, Leonardo; BIAU, Damien; GLOERFELT, Xavier
The simplified model by W. R. Dean, based on a low-curvature assumption, provided an early understanding of the laminar flow in curved ducts. However, most of the following studies relied on computer simulations of the complete curvilinear Navier-Stokes equations controlled by two nondimensional parameters, the curvature ratio and the Reynolds number. In the present article an extended version of Dean's model is used and compared to existing results. The set of equations is unsteady, parabolic in a streamwise direction, expressed in Cartesian coordinates, and contains a single control parameter, namely, the Dean number. The equations are identical to those used for the Görtler instability in boundary layer flows. Nonetheless, their extension to duct flows remains to be validated, which is the main purpose of the present article. The model satisfactorily reproduces benchmark results in the literature. In particular we retrieve the successive bifurcations between steady, unsteady, and chaotic regimes for 2D flows. The model also reproduces the development of three-dimensional flow in an elbow with a curvature radius equal to 15.1 times the square duct width. In addition, the present results confirm the Dean number as the single control parameter for laminar flows in a weakly curved ducts.
Mon, 01 Feb 2021 00:00:00 GMThttp://hdl.handle.net/10985/234222021-02-01T00:00:00ZRIGO, LeonardoBIAU, DamienGLOERFELT, XavierThe simplified model by W. R. Dean, based on a low-curvature assumption, provided an early understanding of the laminar flow in curved ducts. However, most of the following studies relied on computer simulations of the complete curvilinear Navier-Stokes equations controlled by two nondimensional parameters, the curvature ratio and the Reynolds number. In the present article an extended version of Dean's model is used and compared to existing results. The set of equations is unsteady, parabolic in a streamwise direction, expressed in Cartesian coordinates, and contains a single control parameter, namely, the Dean number. The equations are identical to those used for the Görtler instability in boundary layer flows. Nonetheless, their extension to duct flows remains to be validated, which is the main purpose of the present article. The model satisfactorily reproduces benchmark results in the literature. In particular we retrieve the successive bifurcations between steady, unsteady, and chaotic regimes for 2D flows. The model also reproduces the development of three-dimensional flow in an elbow with a curvature radius equal to 15.1 times the square duct width. In addition, the present results confirm the Dean number as the single control parameter for laminar flows in a weakly curved ducts.Sparse Bayesian Learning of Explicit Algebraic Reynolds-Stress models for turbulent separated flows
http://hdl.handle.net/10985/23747
Sparse Bayesian Learning of Explicit Algebraic Reynolds-Stress models for turbulent separated flows
CHERROUD, Soufiane; MERLE, Xavier; CINNELLA, Paola; GLOERFELT, Xavier
A novel Sparse Bayesian Learning (SBL) framework is introduced for generating parsimonious stochastic algebraic stress closures for the Reynolds-Averaged Navier–Stokes (RANS) equations from high-fidelity data. The models are formulated as physically-interpretable frame-invariant tensor polynomials and built from a library of candidate functions. By their stochastic formulation, the learned model coefficients are described by probability distributions and are therefore equipped with an intrinsic measure of uncertainty. The SBL framework is used to derive customized stochastic closure models for three separated flow configurations, characterized by different geometries but similar Reynolds number. The resulting SBL models are then propagated through a CFD solver for all three configurations. The results show significantly improved predictions of velocity profiles and friction coefficient in the separation / reattachment region in comparison with a baseline LEVM (namely, k-ω SST model), for training as well as for test cases. In all cases, the computed uncertainty intervals encompass reasonably well the reference data. Furthermore, the stochastic outputs enable a global sensitivity analysis with respect to the model terms selected by the algorithm, thus providing insights in view of further improvements of EARSM-type corrections.
Thu, 01 Dec 2022 00:00:00 GMThttp://hdl.handle.net/10985/237472022-12-01T00:00:00ZCHERROUD, SoufianeMERLE, XavierCINNELLA, PaolaGLOERFELT, XavierA novel Sparse Bayesian Learning (SBL) framework is introduced for generating parsimonious stochastic algebraic stress closures for the Reynolds-Averaged Navier–Stokes (RANS) equations from high-fidelity data. The models are formulated as physically-interpretable frame-invariant tensor polynomials and built from a library of candidate functions. By their stochastic formulation, the learned model coefficients are described by probability distributions and are therefore equipped with an intrinsic measure of uncertainty. The SBL framework is used to derive customized stochastic closure models for three separated flow configurations, characterized by different geometries but similar Reynolds number. The resulting SBL models are then propagated through a CFD solver for all three configurations. The results show significantly improved predictions of velocity profiles and friction coefficient in the separation / reattachment region in comparison with a baseline LEVM (namely, k-ω SST model), for training as well as for test cases. In all cases, the computed uncertainty intervals encompass reasonably well the reference data. Furthermore, the stochastic outputs enable a global sensitivity analysis with respect to the model terms selected by the algorithm, thus providing insights in view of further improvements of EARSM-type corrections.DNS of turbulent flows of dense gases
http://hdl.handle.net/10985/23742
DNS of turbulent flows of dense gases
SCIACOVELLI, Luca; CINNELLA, Paola; GLOERFELT, Xavier; GRASSO, Francesco
The influence of dense gas effects on compressible turbulence is investigated by means of numerical simulations of the decay of compressible homogeneous isotropic turbulence (CHIT) and of supersonic turbulent flows through a plane channel (TCF). For both configurations, a parametric study on the Mach and Reynolds numbers is carried out. The dense gas considered in these parametric studies is PP11, a heavy fluorocarbon. The results are systematically compared to those obtained for a diatomic perfect gas (air). In our computations, the thermodynamic behaviour of the dense gases is modelled by means of the Martin-Hou equation of state. For CHIT cases, initial turbulent Mach numbers up to 1 are analyzed using mesh resolutions up to 5123. For TCF, bulk Mach numbers up to 3 and bulk Reynolds numbers up to 12000 are investigated. Average profiles of the thermodynamic quantities exhibit significant differences with respect to perfect-gas solutions for both of the configurations. For high-Mach CHIT, compressible structures are modified with respect to air, with weaker eddy shocklets and stronger expansions. In TCF, the velocity profiles of dense gas flows are much less sensitive to the Mach number and collapse reasonably well in the logarithmic region without any special need for compressible scalings, unlike the case of air, and the overall flow behaviour is midway between that of a variable-property liquid and that of a gas.
Sat, 01 Apr 2017 00:00:00 GMThttp://hdl.handle.net/10985/237422017-04-01T00:00:00ZSCIACOVELLI, LucaCINNELLA, PaolaGLOERFELT, XavierGRASSO, FrancescoThe influence of dense gas effects on compressible turbulence is investigated by means of numerical simulations of the decay of compressible homogeneous isotropic turbulence (CHIT) and of supersonic turbulent flows through a plane channel (TCF). For both configurations, a parametric study on the Mach and Reynolds numbers is carried out. The dense gas considered in these parametric studies is PP11, a heavy fluorocarbon. The results are systematically compared to those obtained for a diatomic perfect gas (air). In our computations, the thermodynamic behaviour of the dense gases is modelled by means of the Martin-Hou equation of state. For CHIT cases, initial turbulent Mach numbers up to 1 are analyzed using mesh resolutions up to 5123. For TCF, bulk Mach numbers up to 3 and bulk Reynolds numbers up to 12000 are investigated. Average profiles of the thermodynamic quantities exhibit significant differences with respect to perfect-gas solutions for both of the configurations. For high-Mach CHIT, compressible structures are modified with respect to air, with weaker eddy shocklets and stronger expansions. In TCF, the velocity profiles of dense gas flows are much less sensitive to the Mach number and collapse reasonably well in the logarithmic region without any special need for compressible scalings, unlike the case of air, and the overall flow behaviour is midway between that of a variable-property liquid and that of a gas.Numerical Investigation of Supersonic Dense-Gas Boundary Layers
http://hdl.handle.net/10985/23702
Numerical Investigation of Supersonic Dense-Gas Boundary Layers
SCIACOVELLI, Luca; PASSIATORE, Donatella; GLOERFELT, Xavier; CINNELLA, Paola; GRASSO, Francesco
A study of dense-gas effects on the laminar, transitional and turbulent characteristics of boundary layer flows is conducted. The laminar similarity solution shows that temperature variations are small due to the high specific heats of dense gases, leading to velocity profiles close to the incompressible ones. Nevertheless, the complex thermodynamics of the base flow has a major impact on unstable modes, which bear similarities with those obtained for a strongly cooled wall. Numerical simulations of spatially developing boundary layers yield turbulent statistics for the dense gas flow that remain closer to the incompressible regime than perfect gas ones despite the presence of strongly compressible structures.
Wed, 01 Jul 2020 00:00:00 GMThttp://hdl.handle.net/10985/237022020-07-01T00:00:00ZSCIACOVELLI, LucaPASSIATORE, DonatellaGLOERFELT, XavierCINNELLA, PaolaGRASSO, FrancescoA study of dense-gas effects on the laminar, transitional and turbulent characteristics of boundary layer flows is conducted. The laminar similarity solution shows that temperature variations are small due to the high specific heats of dense gases, leading to velocity profiles close to the incompressible ones. Nevertheless, the complex thermodynamics of the base flow has a major impact on unstable modes, which bear similarities with those obtained for a strongly cooled wall. Numerical simulations of spatially developing boundary layers yield turbulent statistics for the dense gas flow that remain closer to the incompressible regime than perfect gas ones despite the presence of strongly compressible structures.Analysis of Dense Gas Effects in Compressible Turbulent Channel Flows
http://hdl.handle.net/10985/23741
Analysis of Dense Gas Effects in Compressible Turbulent Channel Flows
SCIACOVELLI, Luca; CINNELLA, Paola; GLOERFELT, Xavier
In this work we investigate the influence of dense gas effects on compressible wall-bounded turbulence. Turbulent flows of dense gases represent a research field of great importance for a wide range of applications in engineering. Dense gases are single-phase fluids with a molecular complexity such that the fundamental derivative of gas dynamics [1], which measures the rate of change of the sound speed in isentropic transformations, is less than one in a range of thermodynamic conditions close to the saturation curve. In such conditions, the speed of sound increases in isentropic expansions and decreases in isentropic compressions, unlike the case of perfect gases. For dense gases, the perfect gas model is no longer valid, and more complex equations of state must be used to account for their peculiar thermodynamic behavior. Moreover, in the dense gas regime, the dynamic viscosity μ and the thermal conductivity λ depend on temperature and pressure through complex relationships. Similarly, the approximation of nearly constant Prandtl number Pr= μ c p / λ is no longer valid. Numerical simulations of turbulent dense gas flows of engineering interest are based on the (Reynolds-Averaged Navier–Stokes) RANS equations, which need to be supplemented by a model for the Reynolds stress tensor and turbulent heat flux. The accuracy of RANS models for dense-gas flows has not been properly assessed up to date, due to the lack of both experimental and numerical reference data. DNS databases [2, 3] are then needed to quantify the deficiencies of existing turbulence models and to develop and calibrate improved ones. In this work we first summarize some recent direct numerical simulation (DNS) results [4] for supersonic turbulent channel flows (TCF) of PP11, a heavy fluorocarbon representative of dense gases, at various bulk Mach and Reynolds numbers. The most relevant effects are represented by non-conventional variations of the fluctuating thermodynamic quantities, compared to perfect gases and a strong decoupling between thermal and dynamic effects almost everywhere in the flow, except in the immediate vicinity of the solid wall. Preliminary considerations about the validity of some currently-used models for the turbulent stresses and heat flux are carried out based on a priori comparisons between the exact terms computed from the DNS and their modeled counterparts.
Sat, 02 Feb 2019 00:00:00 GMThttp://hdl.handle.net/10985/237412019-02-02T00:00:00ZSCIACOVELLI, LucaCINNELLA, PaolaGLOERFELT, XavierIn this work we investigate the influence of dense gas effects on compressible wall-bounded turbulence. Turbulent flows of dense gases represent a research field of great importance for a wide range of applications in engineering. Dense gases are single-phase fluids with a molecular complexity such that the fundamental derivative of gas dynamics [1], which measures the rate of change of the sound speed in isentropic transformations, is less than one in a range of thermodynamic conditions close to the saturation curve. In such conditions, the speed of sound increases in isentropic expansions and decreases in isentropic compressions, unlike the case of perfect gases. For dense gases, the perfect gas model is no longer valid, and more complex equations of state must be used to account for their peculiar thermodynamic behavior. Moreover, in the dense gas regime, the dynamic viscosity μ and the thermal conductivity λ depend on temperature and pressure through complex relationships. Similarly, the approximation of nearly constant Prandtl number Pr= μ c p / λ is no longer valid. Numerical simulations of turbulent dense gas flows of engineering interest are based on the (Reynolds-Averaged Navier–Stokes) RANS equations, which need to be supplemented by a model for the Reynolds stress tensor and turbulent heat flux. The accuracy of RANS models for dense-gas flows has not been properly assessed up to date, due to the lack of both experimental and numerical reference data. DNS databases [2, 3] are then needed to quantify the deficiencies of existing turbulence models and to develop and calibrate improved ones. In this work we first summarize some recent direct numerical simulation (DNS) results [4] for supersonic turbulent channel flows (TCF) of PP11, a heavy fluorocarbon representative of dense gases, at various bulk Mach and Reynolds numbers. The most relevant effects are represented by non-conventional variations of the fluctuating thermodynamic quantities, compared to perfect gases and a strong decoupling between thermal and dynamic effects almost everywhere in the flow, except in the immediate vicinity of the solid wall. Preliminary considerations about the validity of some currently-used models for the turbulent stresses and heat flux are carried out based on a priori comparisons between the exact terms computed from the DNS and their modeled counterparts.Numerical Investigation of Hypersonic Boundary Layers of Perfect and Dense Gases
http://hdl.handle.net/10985/23691
Numerical Investigation of Hypersonic Boundary Layers of Perfect and Dense Gases
SCIACOVELLI, Luca; GLOERFELT, Xavier; CINNELLA, Paola; GRASSO, Francesco
Hypersonic turbulent boundary layers (HTBL) at Mach number M =6 of a dense gas (PP11) and a perfect gas (air) are investigated by means of Direct Numerical Simulations (DNS), from the laminar to fully turbulent state. The operating conditions are chosen in such a way to highlight dense gas effects, which profoundly alter the transition mechanisms and affect the turbulent flow properties significantly.
Fri, 01 May 2020 00:00:00 GMThttp://hdl.handle.net/10985/236912020-05-01T00:00:00ZSCIACOVELLI, LucaGLOERFELT, XavierCINNELLA, PaolaGRASSO, FrancescoHypersonic turbulent boundary layers (HTBL) at Mach number M =6 of a dense gas (PP11) and a perfect gas (air) are investigated by means of Direct Numerical Simulations (DNS), from the laminar to fully turbulent state. The operating conditions are chosen in such a way to highlight dense gas effects, which profoundly alter the transition mechanisms and affect the turbulent flow properties significantly.A domain decomposition matrix-free method for global linear stability
http://hdl.handle.net/10985/8644
A domain decomposition matrix-free method for global linear stability
ALIZARD, Frédéric; ROBINET, Jean-Christophe; GLOERFELT, Xavier
This work is dedicated to the presentation of a matrix-free method for global linear stability analysis in geometries composed of multi-connected rectangular subdomains. An Arnoldi technique using snapshots in subdomains of the entire geometry combined with a multidomain linearized Direct Numerical Finite difference simulations based on an influence matrix for partitioning are adopted. The method is illustrated by three benchmark problems: the lid-driven cavity, the square cylinder and the open cavity flow. The efficiency of the method to extract large-scale structures in a multidomain framework is emphasized. The possibility to use subset of the full domain to recover the perturbation associated with the entire flow field is also highlighted. Such a method appears thus a promising tool to deal with large computational domains and three-dimensionality within a parallel architecture.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/86442012-01-01T00:00:00ZALIZARD, FrédéricROBINET, Jean-ChristopheGLOERFELT, XavierThis work is dedicated to the presentation of a matrix-free method for global linear stability analysis in geometries composed of multi-connected rectangular subdomains. An Arnoldi technique using snapshots in subdomains of the entire geometry combined with a multidomain linearized Direct Numerical Finite difference simulations based on an influence matrix for partitioning are adopted. The method is illustrated by three benchmark problems: the lid-driven cavity, the square cylinder and the open cavity flow. The efficiency of the method to extract large-scale structures in a multidomain framework is emphasized. The possibility to use subset of the full domain to recover the perturbation associated with the entire flow field is also highlighted. Such a method appears thus a promising tool to deal with large computational domains and three-dimensionality within a parallel architecture.Turbulent boundary layer noise : direct radiation at Mach number 0.5
http://hdl.handle.net/10985/8636
Turbulent boundary layer noise : direct radiation at Mach number 0.5
BERLAND, Julien; GLOERFELT, Xavier
Boundary layers constitute a fundamental source of aerodynamic noise. A turbulent boundary layer over a plane wall can provide an indirect contribution to the noise by exciting the structure, and a direct noise contribution. The latter part can play a significant role even if its intensity is very low, explaining why it is hardly measured unambiguously. In the present study, the aerodynamic noise generated by a spatially developing turbulent boundary layer is computed directly by solving the compressible Navier-Stokes equations. This numerical experiment aims at giving some insight into the noise radiation characteristics. The acoustic wavefronts have a large wavelength and are oriented in the direction opposite to the flow. Their amplitude is only 0.7 % of the aerodynamic pressure for a flat-plate flow at Mach 0.5. The particular directivity is mainly explained by convection effects by the mean flow, giving an indication about the compactness of the sources. These vortical events correspond to low-frequencies, and have thus a large life time. They cannot be directly associated with the main structures populating the boundary layer such as hairpin or horseshoe vortices. The analysis of the wall pressure can provide a picture of the flow in the frequency-wavenumber space. The main features of wall pressure beneath a turbulent boundary layer as described in the literature are well reproduced. The acoustic domain, corresponding to supersonic wavenumbers, is detectable but can hardly be separated from the convective ridge at this relatively high speed. This is also due to the low frequencies of sound emission as noted previously.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/86362013-01-01T00:00:00ZBERLAND, JulienGLOERFELT, XavierBoundary layers constitute a fundamental source of aerodynamic noise. A turbulent boundary layer over a plane wall can provide an indirect contribution to the noise by exciting the structure, and a direct noise contribution. The latter part can play a significant role even if its intensity is very low, explaining why it is hardly measured unambiguously. In the present study, the aerodynamic noise generated by a spatially developing turbulent boundary layer is computed directly by solving the compressible Navier-Stokes equations. This numerical experiment aims at giving some insight into the noise radiation characteristics. The acoustic wavefronts have a large wavelength and are oriented in the direction opposite to the flow. Their amplitude is only 0.7 % of the aerodynamic pressure for a flat-plate flow at Mach 0.5. The particular directivity is mainly explained by convection effects by the mean flow, giving an indication about the compactness of the sources. These vortical events correspond to low-frequencies, and have thus a large life time. They cannot be directly associated with the main structures populating the boundary layer such as hairpin or horseshoe vortices. The analysis of the wall pressure can provide a picture of the flow in the frequency-wavenumber space. The main features of wall pressure beneath a turbulent boundary layer as described in the literature are well reproduced. The acoustic domain, corresponding to supersonic wavenumbers, is detectable but can hardly be separated from the convective ridge at this relatively high speed. This is also due to the low frequencies of sound emission as noted previously.Numerical Investigation of High‑Speed Turbulent Boundary Layers of Dense Gases
http://hdl.handle.net/10985/21896
Numerical Investigation of High‑Speed Turbulent Boundary Layers of Dense Gases
PASSIATORE, Donatella; CINNELLA, Paola; GRASSO, Francesco; SCIACOVELLI, Luca; GLOERFELT, Xavier
High-speed turbulent boundary layers of a dense gas (PP11) and a perfect gas (air) over flat plates are investigated by means of direct numerical simulations and large eddy simulations. The thermodynamic conditions of the incoming flow are chosen to highlight dense gas effects, and laminar-to-turbulent transition is triggered by suction and blowing. In the paper, the behavior of the fully developed turbulent flow region is investigated. Due to the low characteristic Eckert number of dense gas flows ( Ec = U2
∞∕cp,∞T∞ ), the mean velocity profiles are largely insensitive to the Mach number and very close to the incompressible
case even at high speeds. Second-order velocity statistics are also weakly affected by the flow Mach number and the velocity spectra are characterized by a secondary peak in the outer region of the boundary layer because of the higher local friction Reynolds number. Despite the incompressible-like velocity and Reynolds-stress profiles, the strongly nonideal
thermodynamic and transport-property behavior of the dense gas results in unconventional distributions of the fluctuating thermo-physical quantities. Specifically, density and viscosity fluctuations reach a peak close to the wall, instead of vanishing as in perfect
gas flows. Additionally, dense gas boundary layers exhibit higher values of the fluctuating Mach number and velocity divergence and a larger dilatational-to-solenoidal dissipation ratio in the near-wall region, which represents a major deviation from high-Mach-number perfect gas boundary layers. Other significant deviations are represented by the more symmetric probability distributions of fluctuating quantities such as the density and velocity divergence, due to the more balanced occurrence of strong expansion and compression events.
Sun, 01 Mar 2020 00:00:00 GMThttp://hdl.handle.net/10985/218962020-03-01T00:00:00ZPASSIATORE, DonatellaCINNELLA, PaolaGRASSO, FrancescoSCIACOVELLI, LucaGLOERFELT, XavierHigh-speed turbulent boundary layers of a dense gas (PP11) and a perfect gas (air) over flat plates are investigated by means of direct numerical simulations and large eddy simulations. The thermodynamic conditions of the incoming flow are chosen to highlight dense gas effects, and laminar-to-turbulent transition is triggered by suction and blowing. In the paper, the behavior of the fully developed turbulent flow region is investigated. Due to the low characteristic Eckert number of dense gas flows ( Ec = U2
∞∕cp,∞T∞ ), the mean velocity profiles are largely insensitive to the Mach number and very close to the incompressible
case even at high speeds. Second-order velocity statistics are also weakly affected by the flow Mach number and the velocity spectra are characterized by a secondary peak in the outer region of the boundary layer because of the higher local friction Reynolds number. Despite the incompressible-like velocity and Reynolds-stress profiles, the strongly nonideal
thermodynamic and transport-property behavior of the dense gas results in unconventional distributions of the fluctuating thermo-physical quantities. Specifically, density and viscosity fluctuations reach a peak close to the wall, instead of vanishing as in perfect
gas flows. Additionally, dense gas boundary layers exhibit higher values of the fluctuating Mach number and velocity divergence and a larger dilatational-to-solenoidal dissipation ratio in the near-wall region, which represents a major deviation from high-Mach-number perfect gas boundary layers. Other significant deviations are represented by the more symmetric probability distributions of fluctuating quantities such as the density and velocity divergence, due to the more balanced occurrence of strong expansion and compression events.Aeroacoustic Study of the Interaction of a Rotating Blade with a Batchelor Vortex
http://hdl.handle.net/10985/17799
Aeroacoustic Study of the Interaction of a Rotating Blade with a Batchelor Vortex
ZEHNER, Paul; FALISSARD, Fabrice; GLOERFELT, Xavier
The aeroacoustic response of the orthogonal interaction of a rotating blade with an isolated Batchelor vortex is studied by means of numerical simulation. The relative influence of the vortex tangential and axial velocity on the blade aerodynamics and on the acoustics radiated in the far field is analyzed by comparing the interaction with a Batchelor vortex to the interactions considering the vortex tangential or axial velocity components. Analyses show that the vortex tangential velocity contributes mostly to the noise level at low frequencies, whereas the vortex axial velocity is responsible for the contribution at high frequencies. For the range of frequencies in between, the interaction noise results from constructive interferences of the noise radiated separately by each velocity component of the vortex.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/177992018-01-01T00:00:00ZZEHNER, PaulFALISSARD, FabriceGLOERFELT, XavierThe aeroacoustic response of the orthogonal interaction of a rotating blade with an isolated Batchelor vortex is studied by means of numerical simulation. The relative influence of the vortex tangential and axial velocity on the blade aerodynamics and on the acoustics radiated in the far field is analyzed by comparing the interaction with a Batchelor vortex to the interactions considering the vortex tangential or axial velocity components. Analyses show that the vortex tangential velocity contributes mostly to the noise level at low frequencies, whereas the vortex axial velocity is responsible for the contribution at high frequencies. For the range of frequencies in between, the interaction noise results from constructive interferences of the noise radiated separately by each velocity component of the vortex.