Richard D. Sandberg

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.

Direct numerical simulation of turbulent flow past a trailing edge and the associated noise generation

Direct numerical simulations (DNS) are conducted of turbulent flow passing an infinitely thin trailing edge. The objective is to investigate the turbulent flow field in the vicinity of the trailing edge and the associated broadband noise generation. To generate a turbulent boundary layer a short distance from the inflow boundary, highamplitude lifted streaks and disturbances that can be associated with coherent outerlayer vortices are introduced at the inflow boundary. A rapid increase in skin friction and a decrease in boundary layer thickness and pressure fluctuations is observed at the trailing edge. It is demonstrated that the behaviour of the hydrodynamic field in the vicinity of the trailing edge can be predicted with reasonable accuracy using triple-deck theory if the eddy viscosity is accounted for. Point spectra of surface pressure difference are shown to vary considerably towards the trailing edge, with a significant reduction of amplitude occurring in the low-frequency range. The acoustic pressure obtained from the DNS is compared with predictions from two- and three-dimensional acoustic analogies and the classical trailing-edge theory of Amiet. For low frequencies, two-dimensional theory succeeds in predicting the acoustic pressure in the far field with reasonable accuracy due to a significant spanwise coherence of the surface pressure difference and predominantly two-dimensional sound radiation. For higher frequencies, however, the full three-dimensional theory is required for an accurate prediction of the acoustic far field. DNS data are used to test some of the key assumptions invoked by Amiet for the derivation of the classical trailing-edge theory. Even though most of the approximations are shown to be reasonable, they collectively lead to a deviation from the DNS results, in particular for higher frequencies. Moreover, because the three-dimensional acoustic analogy does not provide significantly improved results, it is suggested that some of the discrepancies can be attributed to the approach of evaluating the far-field sound using a Kirchhoff-type integration of the surface pressure difference.

Numerical investigation of transitional supersonic axisymmetric wakes

Transitional supersonic axisymmetric wakes are investigated by conducting various numerical experiments. The main objective is to identify hydrodynamic instability mechanisms in the flow at M =2 .46 for several Reynolds numbers, and to relate these to coherent structures that are found from various visualization techniques. The premise for this approach is the assumption that flow instabilities lead to the formation of coherent structures. Three high-order accurate compressible codes were developed in cylindrical coordinates for this work: a spatial Navier–Stokes (N-S) code to conduct direct numerical simulations (DNS), a linearized N-S code for linear stability investigations using axisymmetric basic states, and a temporal N-S code for performing local stability analyses. The ability of numerical simulations to exclude physical effects deliberately is exploited. This includes intentionally eliminating certain azimuthal/helical modes by employing DNS for various circumferential domain sizes. With this approach, the impact of structures associated with certain modes on the global wake-behaviour can be scrutinized. Complementary spatial and temporal calculations are carried out to investigate whether instabilities are of local or global nature. Circumstantial evidence is presented that absolutely unstable global modes within the recirculation region co-exist with convectively unstable shear-layer modes. The flow is found to be absolutely unstable with respect to modes k> 0f orReD > 5000 and with respect to the axisymmetric mode k =0 forReD > 100 000. It is concluded that azimuthal modes k =2 andk = 4 are the dominant modes in the trailing wake, producing a ‘four-lobe’ wake pattern. Two possible mechanisms responsible for the generation of longitudinal structures within the recirculation region are suggested.

Direct numerical simulation of the early development of a turbulent mixing layer downstream of a splitter plate

A direct numerical simulation is carried out of the initial stages of development of a mixing layer with a velocity ratio of ten, a fast stream Mach number of 0.6 and equal free-stream temperatures. The fast stream is a fully developed turbulent boundary layer with a trailing-edge displacement thickness Reynolds number of 2300, while the slow stream is laminar. The computations include a splitter plate with zero thickness. The initial flow development is dominated by the rapid spreading of an internal shear layer formed as the viscous sublayer of the upstream turbulent boundary layer crosses the trailing edge. A tendency towards spanwise-coherent structures is observed very early in the shear layer development, within five displacement thicknesses of the trailing edge, despite such structures not being present in the upstream boundary layer. A numerical search for a global mode in the vicinity of the splitter plate trailing edge found only convective growth of disturbances. Instead, a convective mechanism is examined and found to be a plausible explanation for the rapid change of observed flow structure near the trailing edge. The same mechanism indicates a trend towards more two-dimensional structures in the fully developed mixing layer.

Direct Numerical Simulations of Transitional Supersonic Base Flows

Transitional supersonic base flows at M=2.46 are investigated using Direct Numerical Simulations. Results are presented for Reynolds numbers based on the cylinder diameter ReD=30,000-100,000. As a consequence of flow instabilities, coherent structures develop that have a profound impact on the global flow behavior. Simulations with various circumferential domain sizes are conducted to investigate the effect of coherent structures associated with different azimuthal modes on the mean flow, in particular on the base pressure which determines the base drag. Temporal spectra reveal that frequencies found in the axisymmetric mode can be related to dominant higher modes present in the flow. It is shown that azimuthal modes with low wavenumbers cause a flat base pressure distribution and that the mean base pressure value increases when the most dominant modes are deliberately eliminated. Visualizations of instantaneous flow quantities and turbulence statistics at ReD=100,000 show good agreement with experiments at a significantly higher Reynolds number. For these investigations, a high-order accurate compressible Navier-Stokes solver in cylindrical coordinates developed specifically for this research was used.

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.

Compressible Direct Numerical Simulation of Low-Pressure Turbines—Part I: Methodology

Modern low pressure turbines (LPT) feature high pressure ratios and moderate Mach and Reynolds numbers, increasing the possibility of laminar boundary-layer separation on the blades. Upstream disturbances including background turbulence and incoming wakes have a profound effect on the behavior of separation bubbles and the type/location of laminar-turbulent transition and therefore need to be considered in LPT design. Unsteady Reynolds-averaged Navier–Stokes (URANS) are often found inadequate to resolve the complex wake dynamics and impact of these environmental parameters on the boundary layers and may not drive the design to the best aerodynamic efficiency. LES can partly improve the accuracy, but has difficulties in predicting boundary layer transition and capturing the delay of laminar separation with varying inlet turbulence levels. Direct numerical simulation (DNS) is able to overcome these limitations but has to date been considered too computationally expensive. Here, a novel compressible DNS code is presented and validated, promising to make DNS practical for LPT studies. Also, the sensitivity of wake loss coefficient with respect to freestream turbulence levels below 1% is discussed.

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.