Lift and the leading-edge vortex

Flapping wings often feature a leading-edge vortex (LEV) that is thought to enhance the lift generated by the wing. Here the lift on a wing featuring a leading-edge vortex is considered by performing experiments on a translating flat-plate aerofoil that is accelerated from rest in a water towing tank at a fixed angle of attack of 15°. The unsteady flow is investigated with dye flow visualization, particle image velocimetry (PIV) and force measurements. Leading-and trailing-edge vortex circulation and position are calculated directly from the velocity vectors obtained using PIV. In order to determine the most appropriate value of bound circulation, a two-dimensional potential flow model is employed and flow fields are calculated for a range of values of bound circulation. In this way, the value of bound circulation is selected to give the best fit between the experimental velocity field and the potential flow field. Early in the trajectory, the value of bound circulation calculated using this potential flow method is in accordance with Kelvin's circulation theorem, but differs from the values predicted by Wagner's growth of bound circulation and the Kutta condition. Later the Kutta condition is established but the bound circulation remains small; most of the circulation is contained instead in the LEVs. The growth of wake circulation can be approximated by Wagner's circulation curve. Superimposing the non-circulatory lift, approximated from the potential flow model, and Wagner's lift curve gives a first-order approximation of the measured lift. Lift is generated by inertial effects and the slow buildup of circulation, which is contained in shed vortices rather than bound circulation. © 2013 Cambridge University Press.

Structural sensitivity of spiral vortex breakdown

Previous numerical simulations have shown that vortex breakdown starts with the formation of a steady axisymmetric bubble and that an unsteady spiralling mode then develops on top of this. We investigate this spiral mode with a linear global stability analysis around the steady bubble and its wake. We obtain the linear direct and adjoint global modes of the linearized Navier-Stokes equations and overlap these to obtain the structural sensitivity of the spiral mode, which identifies the wavemaker region. We also identify regions of absolute instability with a local stability analysis. At moderate swirls, we find that the m=-1 azimuthal mode is the most unstable and that the wavemaker regions of the m=-1 mode lie around the bubble, which is absolutely unstable. The mode is most sensitive to feedback involving the radial and azimuthal components of momentum in the region just upstream of the bubble. To a lesser extent, the mode is also sensitive to feedback involving the axial component of momentum in regions of high shear around the bubble. At an intermediate swirl, in which the bubble and wake have similar absolute growth rates, other researchers have found that the wavemaker of the nonlinear global mode lies in the wake. We agree with their analysis but find that the regions around the bubble are more influential than the wake in determining the growth rate and frequency of the linear global mode. The results from this paper provide the first steps towards passive control strategies for spiral vortex breakdown. © 2013 Cambridge University Press.

Large eddy simulation of turbine internal cooling ducts

Abstract Large-Eddy Simulation (LES) and hybrid Reynolds-averaged Navier–Stokes–LES (RANS–LES) methods are applied to a turbine blade ribbed internal duct with a 180° bend containing 24 pairs of ribs. Flow and heat transfer predictions are compared with experimental data and found to be in agreement. The choice of LES model is found to be of minor importance as the flow is dominated by large geometric scale structures. This is in contrast to several linear and nonlinear RANS models, which display turbulence model sensitivity. For LES, the influence of inlet turbulence is also tested and has a minor impact due to the strong turbulence generated by the ribs. Large scale turbulent motions destroy any classical boundary layer reducing near wall grid requirements. The wake-type flow structure makes this and similar flows nearly Reynolds number independent, allowing a range of flows to be studied at similar cost. Hence LES is a relatively cheap method for obtaining accurate heat transfer predictions in these types of flows.

Absolute and convective instability in gas turbine fuel injectors

Hydrodynamic instabilities in gas turbine fuel injectors help to mix the fuel and air but can sometimes lock into acoustic oscillations and contribute to thermoacoustic instability. This paper describes a linear stability analysis that predicts the frequencies and strengths of hydrodynamic instabilities and identifies the regions of the flow that cause them. It distinguishes between convective instabilities, which grow in time but are convected away by the flow, and absolute instabilities, which grow in time without being convected away. Convectively unstable flows amplify external perturbations, while absolutely unstable flows also oscillate at intrinsic frequencies. As an input, this analysis requires velocity and density fields, either from a steady but unstable solution to the Navier-Stokes equations, or from time-averaged numerical simulations. In the former case, the analysis is a predictive tool. In the latter case, it is a diagnostic tool. This technique is applied to three flows: a swirling wake at Re = 400, a single stream swirling fuel injector at Re - 106, and a lean premixed gas turbine injector with five swirling streams at Re - 106. Its application to the swirling wake demonstrates that this technique can correctly predict the frequency, growth rate and dominant wavemaker region of the flow. It also shows that the zone of absolute instability found from the spatio-temporal analysis is a good approximation to the wavemaker region, which is found by overlapping the direct and adjoint global modes. This approximation is used in the other two flows because it is difficult to calculate their adjoint global modes. Its application to the single stream fuel injector demonstrates that it can identify the regions of the flow that are responsible for generating the hydrodynamic oscillations seen in LES and experimental data. The frequencies predicted by this technique are within a few percent of the measured frequencies. The technique also explains why these oscillations become weaker when a central jet is injected along the centreline. This is because the absolutely unstable region that causes the oscillations becomes convectively unstable. Its application to the lean premixed gas turbine injector reveals that several regions of the flow are hydrodynamically unstable, each with a different frequency and a different strength. For example, it reveals that the central region of confined swirling flow is strongly absolutely unstable and sets up a precessing vortex core, which is likely to aid mixing throughout the injector. It also reveals that the region between the second and third streams is slightly absolutely unstable at a frequency that is likely to coincide with acoustic modes within the combustion chamber. This technique, coupled with knowledge of the acoustic modes in a combustion chamber, is likely to be a useful design tool for the passive control of mixing and combustion instability. Copyright © 2012 by ASME.

Angle-of-attack effects on counter-rotating propellers at take-off

Due to their potential for significant fuel consumption savings, Counter-Rotating Open Rotors (CRORs) are currently being considered as an alternative to high-bypass turbofans. When CRORs are mounted on an aircraft, several 'installation effects' arise which are not present when the engine is operated in isolation. This paper investigates how flow features arising from one such effect - The angle-of-attack of the engine centre-line relative to the oncoming flow - can influence the design of CROR engines. Three-dimensional full-annulus unsteady CFD simulations are used to predict the time-varying flow field experienced by each rotor and emphasis is put on the interaction of the frontrotor wake and tip vortex with the rear-rotor. A parametric study is presented that quantifies the rotorrotor interaction as a function of the angle-of-attack. It is shown that angle-of-attack operation significantly changes the flow field and the unsteady lift on both rotors. In particular, a frequency analysis shows that the unsteady lift exhibits sidebands around the rotor-rotor interaction frequencies. Further, a non-linear increase in the total rear-rotor tip unsteadiness is observed for moderate and high angles-of-attack. The results presented in this paper demonstrate that common techniques used to mitigate CROR noise, such as modifying the rotor-rotor axial spacing and rear-rotor crop, can not be applied correctly unless angle-of-attack effects are taken into account. Copyright © 2012 by ASME.

Vortical structures on three-dimensional shock control bumps

The vortical wake structure produced by a three-dimensional shock control bump (SCB) is thought to be useful for controlling transonic buffet on airfoils. However, at present the vorticity produced is relatively weak and the production mechanism is not well understood. Using a combined experimental and computational approach, a preliminary investigation on the wake vorticity for different bump geometries has been carried out. The structure of the wake for on and off-design conditions are considered, and the effects on the downstream boundary layer demonstrated. Three main vortical structures are observed: a primary vortex pair, weak inter-bump vortices and shear flow in the lambda-shock region. The effect of pressure gradients on vortex strength is examined and it is found that spanwise pressure gradients on the front section of the bump are the most significant parameter influencing vortex strength. © 2013 by S.P. Colliss et al.

On high-frequency noise scattering by aerofoils in flow

Abstract A theoretical model is developed for the sound scattered when a sound wave is incident on a cambered aerofoil at non-zero angle of attack. The model is based on the linearization of the Euler equations about a steady subsonic flow, and is an adaptation of previous work which considered incident vortical disturbances. Only high-frequency sound waves are considered. The aerofoil thickness, camber and angle of attack are restricted such that the steady flow past the aerofoil is a small perturbation to a uniform flow. The singular perturbation analysis identifies asymptotic regions around the aerofoil; local 'inner' regions, which scale on the incident wavelength, at the leading and trailing edges of the aerofoil; Fresnel regions emanating from the leading and trailing edges of the aerofoil due to the coalescence of singularities and points of stationary phase; a wake transition region downstream of the aerofoil leading and trailing edge; and an outer region far from the aerofoil and wake. An acoustic boundary layer on the aerofoil surface and within the transition region accounts for the effects of curvature. The final result is a uniformly-valid solution for the far-field sound; the effects of angle of attack, camber and thickness are investigated. © 2013 Cambridge University Press.

Large eddy simulations in low-pressure turbines: Effect of wakes at elevated free-stream turbulence

The transition of a separated shear layer over a flat plate, in the presence of periodic wakes and elevated free-stream turbulence (FST), is numerically investigated using Large Eddy Simulation (LES). The upper wall of the test section is inviscid and specifically contoured to impose a streamwise pressure distribution over the flat plate to simulate the suction surface of a low-pressure turbine (LPT) blade. Two different distributions representative of a 'high-lift' and an 'ultra high-lift' turbine blade are examined. Results obtained from the current LES compare favourably with the extensive experimental data previously obtained for these configurations. The LES results are then used to further investigate the flow physics involved in the transition process.In line with experimental experience, the benefit of wakes and FST obtained by suppressing the separation bubble, is more pronounced in 'ultra high-lift' design when compared to the 'high-lift' design. Stronger 'Klebanoff streaks' are formed in the presence of wakes when compared to the streaks due to FST alone. These streaks promoted much early transition. The weak Klebanoff streaks due to FST continued to trigger transition in between the wake passing cycles.The experimental inference regarding the origin of Klebanoff streaks at the leading edge has been confirmed by the current simulations. While the wake convects at local free-stream velocity, its impression in the boundary layer in the form of streaks convects much slowly. The 'part-span' Kelvin-Helmholtz structures, which were observed in the experiments when the wake passes over the separation bubble, are also captured. The non-phase averaged space-time plots manifest that reattachment is a localized process across the span unlike the impression of global reattachment portrayed by phase averaging. © 2013 Elsevier Inc.

CFD investigation of turbulent premixed flame response to transverse forcing

Screech is a high frequency oscillation that is usually characterized by instabilities caused by large-scale coherent flow structures in the wake of bluff-body flameholders and shear layers. Such oscillations can lead to changes in flame surface area which can cause the flame to burn unsteadily, but also couple with the acoustic modes and inherent fluid-mechanical instabilities that are present in the system. In this study, the flame response to hydrodynamic oscillations is analyzed in a controlled manner using high-fidelity Computational Fluid Dynamics (CFD) with an unsteady Reynolds-averaged Navier-Stokes approach. The response of a premixed flame with and without transverse velocity forcing is analyzed. When unforced, the flame is shown to exhibit a self-excitation that is attributed to the anti-symmetric shedding of vortices in the wake of the flameholder. The flame is also forced using two different kinds of low-amplitude out-of-phase inlet velocity forcing signals. The first forcing method is harmonic forcing with a single characteristic frequency, while the second forcing method involves a broadband forcing signal with frequencies in the range of 500 - 1000 Hz. For the harmonic forcing method, the flame is perturbed only lightly about its mean position and exhibits a limit cycle oscillation that is characteristic of the forcing frequency. For the broadband forcing method, larger changes in the flame surface area and detachment of the flame sheet can be seen. Transition to a complicated trajectory in the phase space is observed. When analyzed systematically with system identification methods, the CFD results, expressed in the form of the Flame Transfer Function (FTF) are capable of elucidating the flame response to the imposed perturbation. The FTF also serves to identify, both spatially and temporally, regions where the flame responds linearly and nonlinearly. Locking-in between the flame's natural self-excited frequency and the subharmonic frequencies of the broadband forcing signal is found to alter the dynamical behaviour of the flame. Copyright © 2013 by ASME.

Modelling and validation of wet steam flow in a low pressure steam turbine

Results of numerical investigations of the wet steam flow in a three stage low pressure steam turbine test rig are presented. The test rig is a scale model of a modern steam turbine design and provides flow measurements over a range of operating conditions which are used for detailed comparisons with the numerical results. For the numerical analysis a modern CFD code with user defined models for specific wet steam modelling is used. The effect of different theoretical models for nucleation and droplet growth are examined. It is shown that heterogeneous condensation is highly dependent on steam quality and, in this model turbine with high quality steam, a homogeneous theory appears to be the best choice. The homogeneous theory gives good agreement between the test rig traverse measurements and the numerical results. The differences in the droplet size distribution of the three stage turbine are shown for different loads and modelling assumptions. The different droplet growth models can influence the droplet size by a factor of two. An estimate of the influence of unsteady effects is made by means of an unsteady two-dimensional simulation. The unsteady modelling leads to a shift of nucleation into the next blade row. For the investigated three stage turbine the influence due to wake chopping on the condensation process is weak but to confirm this conclusion further investigations are needed in complete three dimensions and on turbines with more stages. Copyright © 2011 by ASME.