The airfoil profile with a relative thickness of 20 % used for this study corresponds to the profile at a radius of 35 m on a wind turbine blade of the type LM45.3p as used on the 2 MW Senvion (formerly REpower) MM92 wind turbine. This corresponds to the test section of the experiment of interest. The study focuses on the flow past this airfoil at an angle of attack of α=4∘, which lies within the range measured during the experiment. A Reynolds number of Rec=105 based on the free-stream velocity u∞ and the chord length c was chosen for the current study. Note that all results presented below are non-dimensionalized by these two parameters. The current case is thought as a buildup to the higher Re numbers of the experiment, which lie on the order of a few million as described in Sect. . A parameter study with varying inflow turbulence intensities of TI =0, 1.4 %, 2.8 %, 5.6 % and 11.2 % was carried out.

Figure  depicts different characteristic properties of the airfoil, i.e., the pressure coefficient cp=(p-p∞)/(0.5ρu∞2), the friction coefficient cf=τw/(0.5ρu∞2), the shape factor H12 and the lift-to-drag ratio cL/cD, as a function of the inflow turbulence intensity. All these quantities are based on the averaged flow, i.e., averaging in time and in the spanwise direction. The separation and reattachment points in Table  are determined from the distribution of cf. The shape factor H12 is defined as the ratio between the displacement thickness δ1 and the momentum thickness δ2, both being integrated in the wall-normal direction from the surface of the airfoil to the location where the local dimensionless edge velocity Ue(x)/Umax(x)=0.99 is reached.

The distribution of the friction coefficient of the simulations at different turbulent inflow conditions shows an expected, albeit small, downstream shift of the separation point with increasing TI, up to a TI of 5.6 % as seen in Table . At TI = 11.2 % the separation bubble vanishes. have studied the influence of inflow turbulence with varying intensities and length scales on the NACA0018 airfoil, which has a similar thickness as the airfoil studied here. In their case the separation bubble already originates between 25 % and 35 % chord, which is further upstream than that seen in the current simulations. This can be attributed to the location of the maximum thickness of the airfoil since the adverse pressure gradient favors separation. In the case of the NACA0018, its maximum thickness is located at 30 % chord, while the airfoil studied here has its maximum thickness located at 36 % chord.

Downstream of the separation point, a nearly constant distribution of cf is found for approximately 10 % chord length beyond which the crucial transition onset is recognized through the development of a minimum of cf, which leads to a turbulent reattachment further downstream. For example, for the TI = 0 % case, the crucial transition onset lies somewhere in between the region where cf begins to drop (around 58 % chord length) and the point of minimum cf (around 64 % chord length). In the presence of a separation bubble, the transition process occurs within the bubble, i.e., between 50 % and 75 % chord. At a TI of 11.2 % the flow turns fully turbulent around 60 % to 70 % chord as indicated by the maximum slope of the friction coefficient.

The crucial transition onset can also be defined as the location where the maximum value of the shape factor is found on the suction side of the airfoil, similar to the investigations of . A good correlation with the previous definition that uses cf is seen. In the presence of added inflow turbulence, the maximum value of the shape factor is shifted upstream with increasing TI as a consequence of the earlier transition onset discussed below. In all cases, a shape factor of about 2.2 is found downstream of the turbulent reattachment. This is a typical value for the shape factor of turbulent flows near separation .

The area under the curve of the pressure coefficient decreases with rising TI, although the effect is marginal in some cases. On the other hand, with an increase in TI, a corresponding increase in the friction coefficient within the region upstream of transition is observed in Fig. b. The effect of these variations in cp and cf on the airfoil performance can be seen in the lift-to-drag ratio depicted in Fig. d. Thus, the performance of the airfoil characterized by its lift-to-drag ratio decreases with increasing TI, whereas the opposite trend is seen in the study by . A short discussion on the reason for this disparity follows.

On the relatively thinner airfoil (8.51 %) in the study by , separation takes place close to the leading edge at around 20 % chord length and moves downstream with increasing turbulence intensity. Furthermore, a corresponding reduction in the chordwise extension of the separation bubble is seen before it disappears at TI = 5.6 %. The time-averaged results showed a decrease in the drag coefficient with increasing TI. A more detailed analysis revealed that the contribution of the pressure component decreased due to the reduction in the length of the separation bubble, while that of the friction component increased with increasing inflow TI. In the current study on the flow around the thicker (20 % thickness) LM45 airfoil, the separation bubble moves slightly downstream with increasing TI before disappearing at TI = 11.2 %. However, here the length of the separation bubble does not decrease with increasing TI. The absence of a separation bubble at TI = 11.2 % is due to the increased momentum exchange within the boundary layer, with the flow being transitional and closer to the turbulent regime than the laminar regime (discussed in Sect. ) at the location, where it would have otherwise separated. Correspondingly, a resulting increase in the drag coefficient with increasing TI is seen.

In the study by a decrease in the lift coefficient is observed with an increase in TI up to 5.6 % before it stays constant. It is known that a separation bubble close to the leading edge could increase the lift coefficient due to the increase in the apparent camber caused by the presence of the separation bubble. With increasing TI and the downstream shift of the separation bubble, the lift coefficient then decreases. In the present study, the lift coefficient increases with increasing TI, however very slightly (a relative change of 3 %), and is likely caused by the slight downstream shift of the separation region, which increases the extent of the laminar flow along the chord.

A combination of these factors results in an increasing lift-to-drag ratio with increasing TI in , whereas the lift-to-drag ratio in the current study reduces.

To investigate the influence of the inflow turbulence intensity on the onset of transition xtr/c, several methods exist in the literature. In the case of attached flows, the transition from laminar to turbulent flow is easily distinguishable by a sudden and strong increase in the boundary-layer thickness or from the shear stress near the wall. The normalized Reynolds shear stress u′v′‾/u∞2 can be considered for the determination of the onset of transition as it is a quantity defining the exchange of momentum into the boundary layer. For flows with a laminar separation bubble, defined the onset of transition as the point where the normalized Reynolds shear stress -u′v′‾/u∞2 reaches a value of 0.001 and demonstrated a clearly visible rise. Figure a and b show contour plots of the Reynolds shear stress at an inflow TI of 0 % and 11.2 %, respectively. An obvious upstream shift in the onset of transition can be observed for rising TI. A plot showing the Reynolds shear stress at the height of the displacement thickness at different inflow TI is depicted in Fig. c and d. Obviously the transition onset moves upstream with rising TI. A brown dashed line marks the location where the threshold -u′v′‾/u∞2=0.001 is reached. Furthermore, Table  summarizes the location of the transition onset based on this criterion for the different cases simulated. However, the definition of a threshold is arbitrary, and this method yields the position of transition onset upstream of the separation point. Nonetheless, the results of the threshold method are qualitatively meaningful as it shows a clear upstream shift in the onset of transition even if the threshold value of -u′v′‾/u∞2 would be increased as seen in Fig. d.

Another method for the determination of transition onset is based on the investigation of the shape factor H12. The position of transition onset is defined as the location of the maximum value of H12 along the surface as already discussed in Sect. . The location of this transition onset is also included in Table . Using this method, the location of transition onset is within the separation bubble in the cases with laminar separation and is therefore a more reasonable approach for the current study.

For a better visualization of the transition process, Fig.  displays instantaneous snapshots of the dimensionless Q criterion normalized by u∞2/c2 and colored by the mean streamwise velocity averaged along the spanwise direction and in time. At an inflow turbulence intensity of 0 %, spanwise rolls which are characteristic for an inflectional instability with spanwise vortices are clearly visible. At their onset, they are more or less two-dimensional. As the flow progresses downstream, slightly three-dimensional effects are seen. This is in agreement with a study by where the inviscid instability interacts with viscous instabilities closer to the wall, leading to fully turbulent flow.

Similar spanwise rolls are also visible at an inflow turbulence intensity of 1.4 %, albeit occurring with relatively more three-dimensional effects. One reason for the increased three-dimensional effects is the presence of Klebanoff streaks within the boundary layer. These streaks are further discussed and illustrated in Sect. . With an increase in the turbulence intensity to 2.8 % and 5.6 %, the influence of boundary layer streaks becomes even more pronounced as will be discussed in Sect. . However, the presence of spanwise rolls is still apparent.

For the case with a very high turbulence intensity of 11.2 %, the flow does not separate, and spanwise rolls are no longer present while the streaks take over the transition process.

Similar observations with a three dimensionality of the separated flow and spanwise waviness of the separated shear layer with increasing inflow turbulence have been made in studies by , , and . showed that at relatively high inflow turbulence intensity (>6.5 % for their studied case) bypass transition precedes separation and maintains an attached turbulent flow, which is similar to the case with an inflow TI of 11.2 % presented here where the transitional region prevents flow separation.

Figure  shows the development of the rms values of the streamwise velocity fluctuations u′=(u(x,y,z,t)-u‾(x,y))/u∞, i.e., averaged along the spanwise direction and in time at a location corresponding to the boundary layer displacement thickness. In the case without inflow turbulence the growth of the fluctuations follows a somewhat exponential trajectory (linear on the log-scale) beginning at about 30 % chord. This corresponds to the location that marks the beginning of an adverse pressure gradient (APG) as seen in Fig. a. An APG could promote the amplification of inflectional instabilities, resulting in large growth rates of the u′ disturbance as seen in Fig. a. The presence of an inflectional instability within the boundary layer will be shortly discussed below. The linear growth seen in Fig. a continues until the flow turns fully turbulent as will be shown in Sect. .

At inflow turbulence intensities of 1.4 % to 5.6 % the rms values of u′ are obviously elevated in comparison with the case without inflow turbulence on account of the receptivity of the boundary layer to external disturbances. The influence of the APG on the growth of inflectional instabilities is observed, similar to the case without inflow turbulence. The APG in addition to the growth of inflectional instabilities also allows for the growth of Klebanoff modes , which, if present, could lead to turbulent bursts as seen in Sect. . With a rise in inflow turbulence intensity to 11.2 % the growth in u′ is no longer associated with an inflectional instability, but is attributed to the growth of Klebanoff modes.

Figure b depicts the relative growth or amplification of u′ normalized by u′ at the location x/c=0.1 for each case. The data are extracted at the height of the displacement thickness. It must be noted that an obvious decrease in the relative amplification factor with increasing TI is seen with a clear differentiation between the cases with added inflow turbulence (TI = 1.4 % and higher) compared to the case without inflow turbulence. The reduced relative increase in the amplification factor in cases with added inflow turbulence is due to the receptivity of the boundary layer to disturbances and the presence of Klebanoff streaks that have developed within the boundary layer which are already present at 10 % chord, i.e., the point used for the normalization. It is interesting to note that there is a drop in the amplitude of u′ from 60 % to 70 % chord in the case of an inflow turbulence intensity of 5.6 % and 11.2 %, while the drop is seen between 70 % and 80 % chord in the other cases. If this is used as an indication for transition to turbulent flow, it is once more clear that transition does move upstream with increasing turbulence intensity.

In the absence of added inflow turbulence, an inflectional profile of the averaged streamwise velocity is observed from approximately 38 % up to 66 % chord followed by the reattachment of the fully turbulent flow at 73.8 % chord. It is interesting to note that an inflectional instability is seen upstream of the separation point (50.06 % chord) and is convected downstream into the separation region, where a K–H type of instability develops near the maximum separation bubble height (59.73 % chord) and finally breaks down to turbulent flow. This observation is in good agreement with the experimental and theoretical study by , where an exponential growth rate of disturbances according to an inflectional instability upstream of the separation region is followed by a K–H type of instability in the separation bubble. Using a method similar to that used by to determine the importance of the contribution of the inflectional mode to the disturbance dynamics, a ratio of yin to ymax is plotted in Fig. , where yin is the wall-normal distance at which the inflectional point of the mean streamwise velocity is located and ymax=max⁡(u′v′‾∂U∂y) is the location of the peak production of the turbulent kinetic energy of the disturbance. As discussed in , if the ratio tends towards zero, the wall mode is stronger, and as the ratio approaches unity the inflectional mode is dominant. For a separated profile this value is expected to be unity while it is expected to be zero for a Blasius profile since yin=0. This behavior is visible in Fig.  with the ratio approaching unity just prior to the maximum height of the separation bubble. This is again similar to the experimental data of , where the ratio approached unity after separation. Furthermore, the onset of the inflectional instability at 38 % chord is in good agreement with the observations of spanwise rolls as seen in Fig. a, indicating that these rolls are inflectional in nature even though they are presently upstream of the separation.

To further investigate the mode and process of transition as well as the influence of the turbulence energy spectra on the boundary layer receptivity in the case of bypass transition through the formation of boundary layer streaks, it was necessary to analyze the power spectral densities along the chord for the different inflow turbulence intensities under consideration. Figure  shows the turbulent kinetic energy PSD plots computed using a Hann windowing function on the data which were collected at every 10 % of the chord. A total of 216 data points covering 3.28 dimensionless time units were used. In order to follow the transition process even in the laminar separation region, data evaluations were carried out at the height of the boundary layer displacement thickness and at the mid-span. Figure f indicates the locations where these data are evaluated.

At an inflow turbulence intensity of 0 % the growth of inflectional instabilities (see disturbance velocity in Fig. ) is apparent at about 30 % chord as discussed in Sect. . It must be noted that spanwise rolls were already seen at 30 % chord at some instances in time, thus making their presence visible in the PSD plot. This corresponds to the green solid line in Fig. a. A clear increase in energy up to 1000 dimensionless units is recognized. The inflectional instability continues to grow in the downstream direction. This growth is seen at 40 % chord without any noticeable irregularity in the PSD plot compared to the upstream location. However, at 50 % chord, a further increase in energy between approximately 70 and 150 dimensionless units is found, indicated by the purple solid line. This increase in energy corresponds to the location (at some instants in time) of breakdown of the roll-up, through the Kelvin–Helmholtz mechanism. This is in a similar dimensionless frequency range seen in the experiment by for the separated shear layer on the NACA 0018 profile at Re=100k and a similar angle of attack.

At an inflow turbulence intensity of 1.4 %, the growth of inflectional instabilities beginning at about 30 % chord is visible in Fig. b. Here, again, the disturbances continue to grow in the downstream direction at 40 % and 50 % chord recognized by the increase in energy up to 1000 dimensionless units. At 70 % chord the flow is fully turbulent, indicated by the rise in energy in the PSD plot, similar to that at the downstream locations. It is obvious that transition to turbulence takes place further downstream than in the case with TI = 0 % where the flow is turbulent close to 60 % chord, as seen in the PSD plot. This unexpected downstream shift of the transition onset with an increase in TI from 0 to 1.4 % is caused by the presence of a high-speed boundary layer streak which delays separation (see discussion in Sect. ) near the mid-span for considerably large parts of the time period during which the data were collected.

At an increased inflow turbulence intensity of 2.8 %, a rise in energy up to 1000 dimensionless units is already visible at 20 % chord in the PSD plot in Fig. c, which is similar to that observed at lower TI in the presence of inflectional instabilities, indicating an earlier growth of these instabilities beginning within the region of the FPG. In this case, spanwise rolls were not visible by a Q-criterion analysis, but waves which eventually lead to the formation of spanwise rolls were noticed at some instances. Similar waves are seen at 30 % chord in the case without inflow turbulence. At 40 % chord a further increase in energy, is observed, similar to that seen at 50 % chord in Fig. a. This corresponds to the breakdown of the K–H rolls.

At an inflow turbulence intensity of 5.6 %, a noticeable increase in energy up to around 100 dimensionless units is seen in Fig. d when compared to the cases with lower inflow turbulence intensities. This is attributed to the presence of streaks within the boundary layer which will be discussed in Sect. . At an inflow TI of 2.8 % a similar effect, albeit with somewhat reduced energy is seen at 10 % chord. The increased energy at TI = 5.6 % is due to the increased frequency of streak formation within the boundary layer observed for increasing inflow turbulence, thus making their presence more prominent with increasing TI. It must be noted that the data for the generation of the PSD were collected over a period of 3.28 dimensionless units; therefore, it is not unexpected to see both the influence of streaks and inflectional instabilities simultaneously in the PSD plots. For instance, at a TI of 2.8 %, inflectional instabilities dominate while at TI = 5.6 % an increase in energy at 20 % chord up to 1000 dimensionless units indicates the presence of an inflectional type of instability. Note that this increase in energy is not present downstream of this chord position due to the increased contribution of streaks to the transition process. An increase in energy up to approximately 100 dimensionless units up to 50 % chord is seen before the flow turns fully turbulent between 60 % and 70 % chord, indicating the dominance of boundary layer streaks.

At an inflow TI of 11.2 % the energy content in the vicinity of the leading edge, i.e., as seen at 10 % chord and further downstream in Fig. e, is similar to the energy level in the transition region at TI = 0 %. At this highest TI level of 11.2 % no clear laminar region can be distinguished in the PSD plot. The energy levels are comparable to those of the transitional region of lower TI inflow cases. The increase in energy from transition to turbulence, however, is clearly visible at 60 % chord and further downstream.

One of the key objectives of running a PSD analysis was to study the receptivity of the boundary layer in response to increasing TI. An experiment by showed that the initial energy in the boundary layer is proportional to the square of the turbulence intensity. Their study included FST between 1.4 % and 6.7 % over a flat plate. A similar analysis was carried out here, with the total energy plotted against the square of TI as seen in Fig. . Since the boundary layer is receptive to low frequencies, especially near the leading edge, it was decided to plot the total energy including the frequency content up to 10 dimensionless frequency units and at 10 % chord. Since the influence of streaks was observed up to 100 dimensionless frequency units (see Sect. ), a second line with the energy including the content up to 100 dimensionless units is plotted. In both cases, ignoring the anomaly at an inflow TI of 2.8 % (the dashed lines ignore this data point), a proportionality via a nearly linear relationship between the energy content and the square of TI is seen. This is in good agreement with the study by .

As discussed in Sect.  a noticeable increase in energy up to around 100 dimensionless units is seen at an inflow TI of 5.6 % compared to the cases with lower inflow TI. It is assumed that this is due to the relative increase in the formation of streaks within the boundary layer such that they can be detected in the PSD plot. This is now investigated based on the case of TI = 5.6 %.

Due to the formation of multiple streaks within the boundary layer during the simulation, it was found necessary to isolate, extract and analyze data prior to the entry of a selected streak and compare the generated PSD plot to a PSD plot generated during the passing of the streak through the region of interest. This is done in order to study the frequency characteristics of the streaks. For this purpose, data were extracted over 300 000 time steps covering an interval of 1.5 dimensionless time units. The data are sampled at every 10th time step, resulting in 30 000 data points. This is a sufficiently large number of data points allowing for the resolution of low frequencies. According to these data, the streak as seen in Fig. a passes through 10 % chord at around the 12 000th data point. A comparison between the PSD plots at this chord location before and after the passing of the streak is depicted in Fig. b. An increase in energy up to 100 dimensionless units is seen. Similar increases in energy up to 100 dimensionless units are also detected when the streak passed through downstream chord positions.

Thus, the increase in energy up to 100 dimensionless units in the PSD plots of Sect.  is indeed an indication for the presence of streaks. It must be noted that streaks are clearly visible within the boundary layer also at lower inflow TI and near the leading edge as seen in Fig. , which shows boundary layer streaks at inflow turbulence intensities of 1.4 and 11.2 % at a wall-normal location corresponding to the displacement thickness at 20 % chord.

As stated earlier and to clarify this issue, the rate of formation of streaks is much lower at low TI, which is obvious by comparison of Fig. a with b. Therefore, an obvious indication of their presence is not seen in the PSD plots at lower TI.

Just as in the study by streaks of different sizes, amplitudes and orientations were found in the collected data and at different inflow TI. Additionally, the maximum spanwise dimension of the streaks decreased with increasing TI. This is in line with the findings of .

At low inflow turbulence intensities, for example at 1.4 % and 2.8 %, the time-averaged results summarized in Table  indicate that the free-stream turbulence has negligible effects on the onset of separation. However, the instantaneous perturbation fields shown in Fig.  show that boundary layer streaks affect the instantaneous separation point. The black rectangular box marks the location of the mean separation region. Instantaneous separation as indicated by the slightly translucent orange iso-surface is shifted upstream in the presence of negative perturbation velocity (dark streaks) and downstream in the presence of positive perturbation velocity (light streaks). These results are in line with earlier studies . also observed the influence of inflow turbulence on the separation bubble. The separation region was found to be delayed in some spanwise regions compared to the case without added turbulence.

On account of an APG, the inner mode of instability was observed at all inflow turbulence intensities. A common scenario attributed to this mode is a local overlap of the trailing edge of a low-speed streak and the leading edge of a high-speed streak, which results in the wall-normal velocity profile to become inflectional. This leads to the development of a predominantly varicose instability near the wall. This scenario is the one observed in the present simulations. That is illustrated in Fig.  for the case with an inflow TI of 2.8 %. Each image is taken at a dimensionless time period of 0.1 units apart and at a wall-normal distance corresponding to the displacement thickness at 20 % chord. Figure a marks the early stages of the overlap between the light high-speed streak and the dark low-speed streak. The overlap takes place with the lower of the two marked streaks. The two streaks have been marked to distinguish them as two separate streaks, a fact that was confirmed by going back in time to the formation of the individual streaks. In Fig. b the varicose inner instability is seen. At the onset of its formation, the instability has the same spanwise dimension as the parent streak. A similar observation was made in . As the instability develops, the varicose formation becomes clearer and is highlighted in Fig. c. After further 0.1 dimensionless time units, the instability breaks down to form a turbulent spot as seen in Fig. b. This turbulent spot grows and progresses downstream to finally join the fully turbulent flow.

As mentioned above, the origin of the inner instability mode is an overlap of the leading edge of a high-speed streak with the trailing edge of a low-speed streak. An investigation into the formation of the instability must therefore take both streaks into account. Figure  shows the corresponding u′ perturbations of the low-speed streak (Fig. a), which is in time overlapped by the high-speed streak (Fig. b). For this purpose, consider a slowly moving low-speed streak upstream of which a high-speed streak has formed. The high-speed streak catches up and overlaps the trailing edge of the low-speed streak. This phenomenon causes an inflectional instability. The profiles were generated over a sequence of time steps. The perturbation profile chosen to be plotted is that which possesses the maximum perturbation velocity on the passing of the two relevant streaks.

As seen in Fig. a, the negative perturbation velocity increases as the streak progresses downstream and the streak rises within the boundary layer from 20 % to 30 % chord, which is to be expected for a low-speed streak. Even though a slight increase in the negative perturbation velocity is seen at 40 % chord, the streak oddly drops within the boundary layer while it is expected to rise. The time instant of this perturbation velocity plot corresponds to an instant where the varicose instability has already begun to develop upstream of the streak due to shear from the overlap of the high-speed streak. This effectively alters the streak and is a possible cause for this behavior. Figure b shows the perturbation velocity due to the high-speed streak. In this case, the streak has a typical form of a high-speed streak at 20 % chord but begins to overlap with the low-speed streak at about 30 % chord, which is evident from the points of inflection. The streak amplitude increases up to 20 % chord, reaching a value of 32 % of the free-stream velocity prior to the development of the instability. Similar values leading to the development of the inner instability are found at other locations and other TI values. This is in agreement with the work by , who observed the critical streak amplitude to be 37 % of the free-stream velocity for the varicose mode.

It must be noted that no evidence was found for an outer type of instability mode. This is attributed to the relatively strong APG on the suction side , while it is known that a zero-pressure or favorable pressure gradient is decisive for such a mode .