Prediction of Airfoil Stall Based on a Modified k−v2¯−ω Turbulence Model

The accuracy of an airfoil stall prediction heavily depends on the computation of the separated shear layer. Capturing the strong non-equilibrium turbulence in the shear layer is crucial for the accuracy of a stall prediction. In this paper, different Reynolds-averaged Navier–Stokes turbulence models are adopted and compared for airfoil stall prediction. The results show that the separated shear layer fixed k−v2¯−ω (abbreviated as SPF k−v2¯−ω) turbulence model captures the non-equilibrium turbulence in the separated shear layer well and gives satisfactory predictions of both thin-airfoil stall and trailing-edge stall. At small Reynolds numbers (Re~105), the relative error between the predicted CL,max of NACA64A010 by the SPF k−v2¯−ω model and the experimental data is less than 3.5%. At high Reynolds numbers (Re~106), the CL,max of NACA64A010 and NACA64A006 predicted by the SPF k−v2¯−ω model also has an error of less than 5.5% relative to the experimental data. The stall of the NACA0012 airfoil, which features trailing-edge stall, is also computed by the SPF k−v2¯−ω model. The SPF k−v2¯−ω model is also applied to a NACA0012 airfoil, which features trailing-edge stall and an error of CL relative to the experiment at CL>1.0 is smaller than 3.5%. The SPF k−v2¯−ω model shows higher accuracy than other turbulence models.

The Impact of Steady Blowing from the Leading Edge of an Open Cavity Flow

Cavity flows occur in a wide range of low-speed applications (Mach number ≤0.3), such as aircraft wheel wells, ground transportation, and pipelines. In the current study, a steady jet is forced from a cavity leading edge at different momentum fluxes (0.11 kg/ms2, 0.44 kg/m·s2, and 0.96 kg/m·s2). The investigation was performed for an open cavity with length to depth ratio of 4 at the Reynolds number based on a cavity depth of approximately 50,000. Particle image velocimetry, surface oil flow visualisation, constant temperature anemometry, and pressure measurements were performed in this investigation. The aim of the jet blowing is to separate the cavity separated shear layer from the recirculation zone to reduce the cavity return flow, and hence stabilise the cavity separated shear layer. It was found that increasing the jet momentum flux causes an increase in the cavity return flow due to the increase in the thickness of the cavity separated shear layer. The study also found that the jet populates the separated shear layer with a large number of small-scale disturbances. These disturbances increase the broad band level of the pressure power spectra and Reynolds shear stress in the cavity separated shear layer. On the other hand, the jet disturbances make the shedding of the large vortical structures more intermittent.

Surface Roughness Impact on Boundary Layer Transition and Loss Mechanisms over a Flat-Plate under a Low-Pressure Turbine Pressure Gradient

An experimental study has been conducted to investigate the effects of surface roughness on the profile loss of a flat-plate with a contoured wall. All of the measurements have been conducted for the suction side pressure gradient of a high-lift low pressure turbine airfoil at the fixed Reynolds number (Rec) and freestream turbulence intensity (Tu) of 1.2 · 105 and 3.2%, respectively, representing a cruise condition. The time-resolved streamwise and wall-normal velocity fields for three different surface roughness values of Ra/C · 105 = 0.065, 4.417 and 7.428 have been measured with a 2D hot-wire probe. For the smooth surface, a laminar separation bubble forms from about 60% of the chord; and laminar-to-turbulent transition occurs during reattachment. Since the portion of turbulent flow over the flat-plate is relatively small, the overall profile loss is mainly determined by the momentum deficit generated during transition. Increased roughness decreases the maximum height and length of the separation bubble but does not affect the separation bubble onset location. The beneficial effects of increased surface roughness on the profile loss appear in the separated shear layer and reattachment. Increased surface roughness increases turbulent mixing in the separated shear layer. Thus, the shear layer thickness and momentum deficit are reduced. In addition, increased surface roughness reduces the length scale and turbulence intensity of the shed vortices. Consequently, turbulent mixing and momentum deficit during reattachment of boundary layers are decreased, resulting in a lower profile loss.

Some Observations of the Behaviour of an Adverse Pressure Gradient Laminar Boundary Layer under Wake Impingement

The problem of laminar to turbulent transition in a boundary layer flow subjected to an adverse pressure gradient is relevant to many engineering applications. Under such conditions, the initially laminar flow within the boundary layer can undergo separation and then become turbulent upon reattachment, as transition is triggered by instabilities within the separated shear layer. In turbomachinery blades with high loading, the transition mechanism is further complicated by the presence of periodic wake disturbances shed by blades that move relatively in the upstream flow. The paper reports an experimental study of the effect of wake disturbances generated upstream on the development of a laminar boundary layer over a flat plate imposed with an adverse pressure gradient that is typical of a highly loaded front-stage compressor blade. Detailed velocity measurements using a hotwire are performed along the plate and the results are analysed both in the time domain and the frequency domain. Description of the major features identified is provided and the leading mechanisms that trigger the transition process are identified to be a possible combination of amplified Tollmien–Schlichting waves and the roll-up of vortices due to the Kelvin–Helmholtz instability of the separated shear layer.

Suction effects on transitional bubbles

The effects of suction on the structure of a transitional bubble forming on a low-Reynolds-number airfoil are examined using the Reynolds-averaged Navier–Stokes and k–kL–ω transition model. The suction effects on the laminar and turbulent portions of the separation bubble and the locations of the main points in the separation bubble are discussed in relation to the transition process of the bubble. A single suction distribution located in the region of the baseline transitional bubble is used with two suction rates. One suction rate is sufficiently strong to eliminate the bubble from its original location and a lower suction rate that is only sufficient to create shallower bubbles. Eliminating the bubble from its original location maintains a laminar boundary layer downstream of the baseline transition location until a shallower separation bubble forms near the trailing edge. The lower suction rate shortens the separation bubble and reduces its height while approximately maintaining its original location. Analyzing the lengths of different portions of the bubble suggests that suction affects the instability growth rate and the nonlinear interactions in the separated shear layer. The lower suction rate shortens the distance between the separation and transition onset suggesting a higher growth rate of the inviscid instability. The higher suction rate, on the other hand, increases the distance between the separation and transition onset indicating a stabilizing effect by slowing down the growth rate of the inviscid instability. However, the percentage of distance between transition and separation to the total length is only slightly affected by the suction and the angle of attack.

Dynamic Mode Decomposition Analysis of Separated Boundary Layers Under Variable Reynolds Number and Free-Stream Turbulence

A flat plate boundary layer has been surveyed by means of time-resolved particle image velocimetry (PIV) under variable Reynolds number (70000 < Re < 150000) and turbulence intensity level (1.5% < Tu < 2.5%). The PIV visualizations were completed in two measuring planes, that are oriented both normal and parallel to the wall. For the wall-parallel configuration, the measuring plane is located inside the boundary layer. The PIV data were post-processed by applying Dynamic Mode Decomposition (DMD), which provides frequency based modes and their corresponding growth rate. The effects of Re and Tu variation on the amplification of the dominant wavelength within the separated shear layer, which is responsible for transition, is the main subject of the present work. The DMD modes and related eigenvalues were computed with reference to the main streamwise coordinate. This allowed discussing the effects due to the main flow parameters on the amplification of the dominant streamwise wavelengths within the separated shear layer (Kelvin-Helmholtz modes). The growth of such streamwise modes ends with the formation of large scale vortices, whose breakup forces transition. In order to obtain the effective distribution of the maximum growth rate of fluctuations at different locations and times, the DMD domain was continuously extended in the streamwise direction, accounting for a specified number of periods characterizing the large scale K-H vortices. In order to reduce the time-space dependent results obtained by the DMD procedure, a probability density function of the most unstable wavelength and the corresponding growth rate has been computed. For the present data set, the spatial growth rate of fluctuations is found to increase at the higher Reynolds number, while it slightly reduces with increasing the Tu level. The procedure and findings discussed in this work shall be suitable for designing active control systems, such as harmonic blowing for separation control.

Investigation of the base flow of a generic space launcher with dual-bell nozzle

The typical afterbody flow of a space launcher is characterized by a strong interaction of the engine’s exhaust jet and the separated shear layer emerging from the main body. This interaction is further complicated by strong changes in the spatial and temporal behavior of the afterbody flow during the atmospheric ascent of a launcher. Theoretically, a dual-bell nozzle not only allows for a gain in payload compared to standard single-bell nozzles, but also it alters the wake flow topology due to the two nozzle modes. To predict the benefits as well as the additional risks, the afterbody flow of a generic space launcher model equipped with a cold-flow dual-bell nozzle is investigated in detail. The flow was analyzed for sub-, trans- and supersonic Mach numbers ranging from 0.3 to 2.9 for a variety of nozzle pressure ratios. Particle image velocimetry measurements and schlieren measurements with high repetition rate were performed to determine the dynamics of the separated shear layer, the nozzle jet and their interaction. It is shown that the reattachment length of the base flow decreases with increasing nozzle pressure ratio. Furthermore, the nozzle pressure ratio at which the dual-bell nozzle switches from sea-level mode to altitude mode is reduced by $$15\%$$ 15 % with high subsonic outer flow and by as much as $$65\%$$ 65 % for an outer flow at a Mach number of 1.6. Even for a constant nozzle pressure ratio, the nozzle flow topology depends on the Mach number of the outer flow.

Energetic scales in a bluff body shear layer

A detailed experimental campaign into separated shear layers stemming from rectangular sections (having aspect ratios of 5 : 1, 3 : 1 and 1 : 1) was carried out at Reynolds numbers range between $1.34\times 10^{4}$ and $1.18\times 10^{5}$ based on the body thickness. Particle image velocimetry was used to locate the highest concentration of fluctuations in the velocity field and subsequent hot-wire measurements at those locations provided adequate spectral resolution to follow the evolution of various instabilities that are active within the separated shear layer. Similar to recent findings by this same group, the shear layer behaviour is observed to contain a combination of Reynolds invariant characteristics, including its time-averaged position, while other properties demonstrate clear Reynolds number dependency, including the spatial amplification of turbulent kinetic energy. Additional results here show that the ratio of side lengths of the body is a key parameter in revealing these effects. One reason for this is the level of coupling between modes of instability, which is evaluated using two-point correlation methods. These findings indicate that the separated shear layer on a bluff body is highly nonlinear. A specific set of scales responsible for these unique behaviours is identified and discussed, along with their relationship to other scales in the flow.

Numerical investigation of laminar–turbulent transition in laminar separation bubbles: the effect of free-stream turbulence

The role of free-stream turbulence (FST) in the hydrodynamic instability mechanisms and transition to turbulence in laminar separation bubbles (LSBs) was investigated using direct numerical simulations (DNS). Towards this end, a set of highly resolved DNS have been carried out, where isotropic FST fluctuations with intensities from 0.1 % to 3 % are introduced to investigate the relevant physical mechanisms governing the interaction of separation and transition in LSBs. For disturbance-free simulations, i.e. without FST, laminar–turbulent transition involves a Kelvin–Helmholtz (KH) instability of the separated shear layer. For LSBs subjected to FST, vortical FST fluctuations penetrate the approaching attached laminar boundary layer upstream of the separation location and induce slowly growing low-frequency disturbances, so-called Klebanoff (K) modes, which cause a spanwise modulation with a distinct spanwise wavelength. Simultaneously, the FST enhances the initial levels of instability waves with frequencies in the frequency range of the KH instability, but at much smaller amplitude levels compared to the K-modes. Results from the calculations based on the linearized Navier–Stokes equations and comparison with DNS results reveal that the K-mode exhibits exponential growth in the separated shear layer until it reaches a peak amplitude. At the same time, two-dimensional (2D) disturbance waves are also exponentially amplified, in fact at larger growth rate compared to the K-mode, due to the primary (convective) shear-layer instability mechanism until they saturate downstream of the peak amplitude associated with the K-mode. Therefore, based on detailed spectral analysis and modal decompositions for the separation bubbles investigated, the transition process is the result of two different mechanisms: (i) strong amplification of high-frequency (order of the shedding frequency), essentially 2D or weakly oblique fluctuating disturbances and (ii) low-frequency, three-dimensional K-modes caused by FST. Depending on the intensity of the FST, one of these mechanisms would dominate the transition process, or both mechanisms act together and contribute simultaneously. The net effect of these two events is an acceleration of transition for an increased level of FST intensity, which in turn leads to a reduction of the extent of the separation bubble in streamwise and wall-normal directions. The ‘roll-up’ into spanwise large-scale vortical structures resulting from the shear-layer instability, and the eventual breakdown of these structures, strongly contribute to the reattachment process. The spanwise coherence of these ‘rollers’ deteriorates due to the presence of large-amplitude K-modes, thus effectively weakening their strength for high levels of FST intensities ($Tu>1\,\%$).