ACOUSTIC ANALOGY-BASED FORMULATIONS FOR AERO/HYDRO-ACOUSTIC ANALYSIS OF ROTARY WING DEVICES

Abstract

This thesis deals with the prediction of fluid dynamic generated noise from rotary-wing devices, operating both in air and water and characterized by significant vortical and turbulent flows. Nowadays, among the many theoretical approaches available for the aero/hydroacoustics predictions, the Acoustic Analogy-based methodologies seem to be the most effective way to deal with the sound induced by complex shaped bodies in relative motion with respect to the medium. As a matter of fact, among them, the Ffowcs Williams and Hawkings Equation (FWHE) represents a well known and widely used effective tool able to carry out reliable noise predictions due to fluid-fluid, fluid-body interactions. Since when the first integral solution was proposed by Farassat in 1975, it has been fruitfully used to investigate the noise of rotary-wing devices such helicopter rotors and propeller driven aircraft, yielding results in great accordancewith the experimental data. One of the strength of such model resides in the straightforward identification of the noise generation mechanisms, that, combined to the linearity of the acoustic problem, allows to split the acoustic effect of noise sources over the moving bodies from those associated with the flow field around it. The former are due to the shape, motion and pressure over the body, whereas the latter to the turbulence and vorticity flow field as well as cavitating phenomena (for underwater applications). Such capability undoubtedly represents a major advantage, in that, although the physics behind the sound generation of the rotary wing devices is the same (i.e. it does not matter what the field application is, marine or aeronautical) the relative weight among the volume and surface contributions differs. Evidence of this is represented by the huge know-how gained by the aeroacoustic community in the last thirty years; it indeed proves that, for applications involving thin bodies moving through air (such as helicopter rotors or aeronautical propellers) and in absence of shock waves (i.e. subsonic applications) the noise is dominated by the surface sources. In essence, when such technique is applied to the same configuration analyzed by the CFD solver, it yields the acoustic effects due to the rotor and the vortical flow downstream it without the contribution of turbulence phenomena. Hence, it is expected to be able to detect the same tonal noise sources identified by the CFD simulation. As a matter of fact it turn out to be true only in part, in that, noise sources arising from complex interactions between vortices (especially for underwater applications) are not well detected. Comparison between potential flows-based hydrodynamics against DES so lutions give, as well, the opportunity to understand the capability of the former approach to be able to provide a fruitful noise detection for the permeable ap proach at reasonable computational efforts. Interesting outcomes on this prove how it is true only if the goal is to achieve acoustic predictions ”near” the body where the noise detection is excellent. One of the more interesting part of the thesis concerns the identification and quantification of the role played by the boundary conditions of the CFD/DES solver in the noise detection process. Surprisingly, it is shown that their contribution is potentially harmful for the acoustic prediction if not well identified. The quantification of such phenomenon in terms of acoustic effects is made through an unusual application of the permeable FWHE technique which avoids the integration of the whole computational CFD domain, giving surprising and very interesting results. In general, however, the volume sources of noise may play a significant role; thus, limiting the radiation domain to the blade surfaces may leads to an inadequate prediction of the acoustic signature. This is the case of many applications of engineering interest involving rotary wings such as underwater propellers and wind turbines. The former, working underwater, have completely different geometrical features (compared to the analogues devices operating in air) which reflect in a different acoustic behavior. In addition, the operating condition behind the hull often involves the ingestion of a high turbulent inflow due to the separation phenomena in the boundary layer upon it. Besides, underwater applications are often characterized by an high vorticity and turbulent flow field generated by the propeller itself which persists both in space and time near the rotor. Such condition produces almost ever complex wake interactions and vortex coalescence that considerably affect the noise signature. Similarly, the acoustic behavior of wind turbines is often dominated by the volume noise sources induced essentially by the operating conditions. Indeed, large changes in the wind intensity and direction produce high angles of attack reflecting in wide zones of detached flow over the blade. Besides, turbulent inflow conditions due to the atmospheric boundary layer often interact with the blades causing flow field non linear noise contributions. Based on these findings, the inclusion of volume noise contributions became mandatory for a reliable acoustic predictions. To this aim, throughout the thesis the acoustic effects of field noise sources are accounted for by the use of the so called permeable approach. It represents a configuration of the FWHE in which the emitting body is replaced by an arbitrary shaped moving surface which embeds the body itself and all noise sources generated by its motion through the flow. It represents, de facto, a surface in the space radiating the sound induced by the sources embedded inside it. Besides, the same permeable approach is used to achieve noise predictions on the base of a new Acoustic Analogy-based formulation. It is derived starting from the conservation laws (continuity and momentum equations) by applying the same special mathematical tools used to achieve the FWHE, namely Hybrid Lighthill-Ffowcs Williams and Hawkings Equation (H-FWHE). Along the thesis it is shown how the permeable approach of this formulation recasts into the well known K-Equation. Comparisons between them confirm, once more and in agreement with the literature outcomes, how the FWHE is nowadays the best Acoustic Analogy based approach to carry out reliable aero/hydro-acoustic analysis. Theoretical and numerical findings (available by the literature works) high light how the surface location does not influence the acoustic predictions, provided that it contains all noise sources. In view of this, a wide part of the thesis concern with the assessment of the influence of shape and position of the porous surface through comparisons against analytic solutions of the wave equation. Such process allows to confirm the reliability in the noise prediction and get a deep awareness of its features. Particularly, a first methodological approach based on the velocity potential flows theory along with the Bernoulli Equation allows to provide the fluid dynamic data over the permeable surface as well as the reference pressure signals for the acoustic observers. The case studies concern with moving monopoles and rototranslating vortex ring; the last, especially, allows to get a better insight into the principles behind the porous approach particularly with respect to the End Cap issue (i.e. the effect of eddies convected through the permeable surface). The first application of the acoustic models to rotating wing devices is done by the means of a potential flows based aerodynamics for a slender lifting blade. Issues concerning with the potential wake convected through the porous surface soon highlight the generation of spurious noise contributions as the most important limitation to the applicability of such technique, confirming the outcomes of the vortex ring case study. Thus, such unwanted effect is at first deeply investigated from a theoretical point of view, then, some possible solutions are given in view of the application to configurations of engineering interest. Pushing through such aspect, the extension of the classic FWHE porous approach to account with the acoustic effects of thin vorticity layers (as potential wakes) crossing and going outside the permeable surface is proposed. It turn out in a novel formulation obtained by combining the H-FWHE (over the wake) and the FWHE (over a surface, either permeable or the rotor itself), namely Combined FWHE/H-FWHE which seems to provide good findings. A significant part of the thesis is devoted to the assessment of noise sources detection capabilities for different types of fluid dynamic solutions (a suitability analysis). Such process is of crucial importance, in that, from it depend the features of the predicted acoustic signatures. Particularly, the fluid dynamic solution are carried out by the means of a 3D full unsteady potential flows-based panel method along with the Bernoulli Equation and a in house fully validated CFD solver. Both solvers, with different strength points and weakness, are able to give an accurate prediction of the hydro/aero-dynamic loads and a consistent description of flow field velocity and pressure around and past the blades. In view of this, the capability of the CFD solver to account with the viscous effects in the resolution of the flow field give the possibility to assess the effects of both, turbulence and vorticity field, on the noise generation mechanisms. However, it is worth to note that the currently available computational resources do not allow to carry out Direct Numerical Simulation (DNS) (able to numerically resolve the lowest time space scale of turbulence phenomena) at least for Reynolds numbers greater than 4000, that is, orders of magnitude lower than those inhere faced. Hence, models based on the functional (eddy–viscosity) such as Reynolds Averaged Navier Stokes Equation (RANSE), Large Eddy Simulation (LES) and Detached Eddy Simulation (DES) are used to model the fluid dynamic effects of turbulence yielding an insight of its role in the noise generation mechanism with respect to the other noise sources. As a matter of fact, it turns out how the detection of fluctuating velocity and pressure flow field induced by the turbulence phenomena is one of the key point for an accurate prediction of the rotary-wing noise signature. Such condition appears to be especially true for underwater propeller applications, where the effects of nonlinearities (i.e. zones of the flow field where the behaviour of the fluid is non linear) dominate the noise generation phenomena. From this standpoint the RANSE simulations, which inherently dissipates the fluctuation component of the flow field just outside the boundary layer, turn out to be not suited for acoustic purposes. Differently, the use of a DES turbulence model proves to be an effective detector of noise sources due to both vorticity and turbulence phenomena. A statistical based approach allows to separate, for the noise sources de tected by the DES model, those related with the vortical flow field from those induced by fluctuating phenomena due to the turbulence; thus giving their mutual contribution to the acoustic signature. The thesis shows how, for the kinds of rotating blade devices analyzed, the vorticity induced noise plays a secondary role with respect to the turbulence one. The effectiveness of this decoupling procedure is also assessed through the comparisons with acoustic predictions arising by aero/hydro-dynamic data provided by a 3D panel method for lifting bodies, based on the hypothesis of po tential flows and the Bernoulli Equation.