Lloyd E. Jones

Direct numerical simulations of forced and unforced separation bubbles on an airfoil at incidence

Direct numerical simulations (DNS) of laminar separation bubbles on a NACA-0012 airfoil at Re-c = 5 x 10(4) and incidence 5 degrees are presented. Initially volume forcing is introduced in order to promote transition to turbulence. After obtaining sufficient data from this forced case, the explicitly added disturbances are removed and the simulation run further. With no forcing the turbulence is observed to self-sustain, with increased turbulence intensity in the reattachment region. A comparison of the forced and unforced cases shows that the forcing improves the aerodynamic performance whilst requiring little energy input. Classical linear stability analysis is performed upon the time-averaged flow field; however no absolute instability is observed that could explain the presence of self-sustaining turbulence. Finally, a series of simplified DNS are presented that illustrate a three-dimensional absolute instability of the two-dimensional vortex shedding that occurs naturally. Three-dimensional perturbations are amplified in the braid region of developing vortices, and subsequently convected upstream by local regions of reverse flow, within which the upstream velocity magnitude greatly exceeds that of the time-average. The perturbations are convected into the braid region of the next developing vortex, where they are amplified further, hence the cycle repeats with increasing amplitude. The fact that this transition process is independent of upstream disturbances has implications for modelling separation bubbles.

Stability and receptivity characteristics of a laminar separation bubble on an aerofoil

Stability characteristics of aerofoil flows are investigated by linear stability analysis of time-averaged velocity profiles and by direct numerical simulations with time-dependent forcing terms. First the wake behind an aerofoil is investigated, illustrating the feasibility of detecting absolute instability using these methods. The time-averaged flow around an NACA-0012 aerofoil at incidence is then investigated in terms of its response to very low-amplitude hydrodynamic and acoustic perturbations. Flow fields obtained from both two- and three-dimensional simulations are investigated, for which the aerofoil flow exhibits a laminar separation bubble. Convective stability characteristics are documented, and the separation bubble is found to exhibit no absolute instability in the classical sense; i.e. no growing disturbances with zero group velocity are observed. The flow is however found to be globally unstable via an acoustic-feedback loop involving the aerofoil trailing edge as a source of acoustic excitation and the aerofoil leading-edge region as a site of receptivity. Evidence suggests that the feedback loop may play an important role in frequency selection of the vortex shedding that occurs in two dimensions. Further simulations are presented to investigate the receptivity process by which acoustic waves generate hydrodynamic instabilities within the aerofoil boundary layer. The dependency of the receptivity process to both frequency and source location is quantified. It is found that the amplitude of trailing-edge noise in the fully developed simulation is sufficient to promote transition via leading-edge receptivity.

Intermittent bursting of a laminar separation bubble on an airfoil

Large eddy simulation of flow around a NACA-0012 airfoil at a Reynolds number of 50,000 has been used to study the behavior of a laminar separation bubble near stall. The effects of the subgrid-scale model and explicit filtering were studied for a test case in which direct numerical simulation results were available. It was found that a method incorporating a mixed-time-scale model in addition to explicit filtering gave improved results compared with a method with filtering alone. Statistical results as well as snapshots of the flow below stall exhibit good agreement with the direct numerical simulations. For a configuration near still, the effect of the spanwise domain width was investigated by increasing the spanwise length from 20 to 50% chord. Two-point velocity correlations showed a significant improvement for the wider computational domain, in which the simulation was able to capture a low-frequency flow oscillation, in which intermittent bursting of the bubble was observed. The bubble bursting observed here is more irregular than in experiments at higher Reynolds number. The amplitude and frequency are compared with experimental results and with an unsteady viscous-inviscid interaction method which is shown to be capable of capturing unsteady behavior during stall.

Acoustic Source Identification for Transitional Airfoil Flows Using Cross Correlations

Direct numerical simulations have been conducted of the flow over NACA-0006 and NACA-0012 airfoils. For all cases multiple sources of noise have been observed. At low frequencies, the contribution of trailing-edge noise radiation is significant, while for the high frequencies, the radiated noise appears to be due only to flow events in the transition/reattachment region on the suction side. Cross correlations of acoustic and hydrodynamic quantities, combined with ray-acoustic theory, are used to identify the main source locations. While the physical origin of trailing-edge noise can be clearly identified using these methods, the situation is less clear for additional noise sources that radiate at high frequency. Evidence suggests that these additional noise sources are located downstream of transition on the suction side of the airfoil, in the region directly downstream of boundary-layer reattachment.

Direct numerical simulations of noise generated by turbulent flow over airfoils

A direct numerical simulation (DNS) is conducted of the turbulent ∞ow around a NACA0012 airfoil at incidence. The upper airfoil surface exhibits laminar separation, transition and reattachment as a turbulent boundary layer, whereas the lower surface remains laminar and attached for the entire airfoil chord. The aim of the study is to investigate the mechanisms of noise generation and to potentially identify sources of airfoil noise other than trailing edge noise. In particular we are interested in the conditions under which the airfoil self-noise can be predicted accurately using the classical trailing edge theory of Amiet, where the farfleld sound is evaluated from the convecting surface pressure spectrum upstream of the trailing edge. The DNS data are used to examine assumptions made in the theory. It is shown that for certain frequencies the sound radiation difiers signiflcantly from that expected from trailing edge theory, and that at least one additional noise source is present, distinct from the airfoil trailing edge.

Numerical investigation of airfoil self-noise reduction by addition of trailing-edge serrations

DNS of the flow around a NACA-0012 airfoil are conducted, employing an immersed boundary method to represent flat-plate trailing-edge extensions both with and without serrations. Properties of the turbulent boundary layer convecting over the trailing-edge are similar for all cases. For cases with serrations, the trailing-edge noise produced by the flow over the airfoil is observed to decrease in amplitude, and the frequency interval over which the noise reduction occurs differs depending on the serration length. The trailingedge noise appears otherwise largely unaffected by the serrations in terms of its directivity and spanwise coherence. The hydrodynamic behaviour in the vicinity of the trailing-edge extensions is investigated. The streamwise discontinuity imparted upon the turbulent flow by the straight trailing-edge can clearly be observed in statistical quantities, whereas for the serrated case no spanwise-homogeneous discontinuities are observed. The turbulent flow through the serrations promotes the development of horshoe vortices originating at the serrations themselves, which appear to promote a more rapid mixing within the airfoil wake.

Direct numerical simulations of noise generated by the flow over an airfoil with trailing edge serrations

An immersed boundary method is developed for use with direct numerical simulations (DNS) employing high-order accuracy spatial schemes. Two DNS of the ∞ow around a NACA-0012 airfoil are conducted, employing the immersed boundary method to represent a ∞at-plate trailing-edge extension both with and without serrations. The aim is to investigate the efiect of the trailing-edge serrations upon airfoil trailing-edge noise. The trailing edge serrations are observed to reduce the spanwise correlation of low-frequency vortical events that lead to tonal behaviour, as well as to reduce the amplitude of trailing-edge noise over a flnite frequency band. Pressure spectra within the turbulent boundary layers convecting over the trailing-edge appear similar, hence the trailing-edge noise reduction appears to be caused by the efiect of the serrations upon the difiraction process as opposed to any modiflcation of the hydrodynamic behaviour.

Investigation and prediction of transitional airfoil self-noise

Direct numerical simulations (DNS) have been conducted of the flow over NACA-0006 and NACA-0012 airfoils. The airfoil flows have been found to exhibit pronounced transitional phenomena and multiple sources of noise have been observed. Data transformed to the frequency domain, and third-octave averaged, reveal that for low frequencies, the contribution of trailing edge noise radiation is significant while for the high frequencies the radiated noise appears to be due only to the flow events in the transition/reattachment region on the suction side. Cross-correlations of acoustic and hydrodynamic quantities, combined with ray-acoustic theory, are shown to identify the main source locations. Even though the cross-correlation maps capture the trailing edge contribution, the highest correlation with the farfield observer locations is found in the transition/reattachment region, implying that this is the main source region for the transitional cases investigated here. Surface pressure peaks associated with the transitional behavior lead to decreased accuracy when predicting self-noise using classical trailing edge theory based on surface pressure difference. Using data from the DNS the application of ramping functions to Amiets surface pressure jump function are evaluated. It is shown that the right choice of ramping function can considerably improve predictions of the scattered pressure field and the total surface pressure difference.

Numerical investigation of tonal airfoil self-noise generated by an acoustic feedback loop

In this study the role of acoustic feedback instabilities in the tonal airfoil self-noise phenomenon is investigated. First, direct numerical simulations are conducted of the flow around a NACA-0012 airfoil at Re =1 × 10 5 and four angles of attack. At the two lowest angles of attack considered the airfoil self-noise exhibits a clear tonal contribution, whereas at the two higher angles of attack the tonal contribution becomes less significant in comparison to the broadband noise. Classical linear stability analysis of time-averaged boundary layer profiles shows that the tonal noise occurs at a frequency significantly lower than that of the most convectively amplified instability wave. Two-dimensional linear stability analysis of the time-averaged flowfield is then performed, illustrating the presence of an acoustic feedback loop involving the airfoil trailing-edge. The feedback loop is found to be unstable only for the cases where tonal self-noise is prominent, and is found to self-select a frequency almost identical to that of the tonal self-noise. The constituent mechanisms of the acoustic feedback loop are considered, which appear to explain why the preferred frequency is lower than that of the most convectively amplified instability wave.

Re-engineering a DNS code for high-performance computation of turbulent flows

Software re-engineering of a direct numerical simul ation (DNS) code for highperformance computation of turbulent flows has been carried out. The SBLI parallel highorder finite-difference code was primarily develope d for simulation of a shock wave interacting with a turbulent boundary layer developing over a bump geometry. The code has proved to be very adaptable with its variants being used for a wide range of turbulent flows, including transonic cavity flows, turbulent spot in teractions and separation bubbles on an airfoil at incidence. To bring these recent develop ments back to a unique version, the code has been re-engineered, applying modern software engineering concepts and techniques, including modular design and concurrent version control, as well as a comprehensive approach to verification and validation for both fu nctional tests and benchmark cases that were designed to exercise key elements of the code. Furthermore, the code has been upgraded from a quasi-3D curvilinear to a fully-3D curvilinear grid treatment. A new version has shown good agreements with theoretical and experimental data, and other published results. To improve the efficiency when t he code is applied to simpler geometries, a pre-compiler is developed and used. Finally, this re-engineered SBLI code has demonstrated very good parallel scalability.