1. Introduction
Atmospheric icing occurs when supercooled liquid droplets collide with a structure—for example, an aircraft or a wind turbine—and freeze. Such meteorological conditions can be found in clouds or during freezing precipitation events. The resulting ice accretions are responsible for significant aerodynamic performance penalties [
1].
The topic of atmospheric in-flight icing has been primarily studied on manned aircraft since the 1940s and 1950s [
2]. Since then, studies have been conducted to understand the physics of icing, to develop computational tools to simulate icing, and to generate experimental datasets for Validation [
3]. Most of this research has been performed at high Reynolds numbers, which in aviation are typically the order of
Re = 10
7–10
8 (e.g., [
1,
4,
5]).
More recently, applications have emerged wherein in-flight icing occurs at significantly lower Reynolds numbers compared to manned aircraft; for example, in wind energy and unmanned aerial vehicles (UAVs). This creates a need for more detailed information on low Reynolds icing flows, or at a minimum, a demonstration that the tools used for high Reynolds number flows are adequate.
Icing became an issue for wind turbines around the 1990s, driven by increased demand for renewable energy, especially in the cold climate areas of Northern America and Northern Europe [
6]. Icing on wind turbines is a source for many problems, such as reduced power generation, risk of ice throw, increased fatigue, and increased noise [
7]. Wind turbine blades experience a wide range of Reynolds numbers, with low values near the hub, that increase towards the tip. Commercial large wind turbines typically operate in the Reynolds number regime of
Re = 10
6–10
7 [
8].
Small wind turbines (SWTs) with power ratings typically below 50 kW are a renewable energy source that can be used in locations where conventional large wind turbines are not feasible [
9]. Typical applications of SWTs are in the electrification of rural or remote areas [
10], as hybrid systems in combination with other energy sources, such as solar radiation or hydrogen [
11], or in microgeneration to reduce carbon emissions [
12]. Icing on SWTs has similar effects to icing on larger wind turbines, although due to their smaller size and different designs, the sensitivity to icing can be increased [
13,
14]. Typically, SWTs operate at comparatively low Reynolds numbers in the order of
Re = 10
4–10
5 [
9].
UAVs are an emerging technology which are also affected by icing. Icing was identified in the 1990s as a major hazard to UAVs and as a severe limitation to their operational envelope [
15]. Since then, icing has shifted into the focus of research. This development is related to the increasing availability of the technology and proposals for wide-spread use of UAVs (e.g., for package deliveries, urban air mobility).
Studies on UAVs have shown that the Reynolds number has a significant influence on the physics of ice accretion and also on the subsequent aerodynamic performance penalties [
16,
17,
18]. Icing on UAVs is similar to icing on manned aircraft with some key differences related to airframe size, mission profiles, and icing sensitivity [
19]. Most UAVs (except for the largest) operate at Reynolds numbers in between large and small wind turbines, typically in the order of
Re = 10
5–10
6.
The difference in the Reynolds number regime between the majority of the existing research data and the low-Reynolds applications of wind turbines, SWT, and UAVs is important because the flow physics are closely linked to the Reynolds number. At low Reynolds numbers (here defined as
Re < 10
6), laminar flow characteristics and laminar separation bubbles become more dominant [
20]. The boundary layer thickness is also larger. This may have an effect on both the ice accretion and the consequent aerodynamic performance degradation. A numerical study by Szilder and McIlwan [
21] on the influence of the Reynolds number on UAV ice accretion suggests that there are significant Reynolds number influences on ice mass, area, and location between
Re = 5 × 10
4 – 5 × 10
6. These parameters govern the geometry of the ice accretions, which in turn are strongly linked to performance penalties [
1].
One aspect of this question is that there is a lack of data that can be used to validate numerical simulation tools for icing at low Reynolds numbers. This includes typical validation data, such as ice shapes from experimental icing wind tunnel (IWT) tests and aerodynamic performance experiments of iced airfoils. In the open literature, few experimental studies exist that are suitable for the validation of numerical tools.
Table 1 gives an overview of available data in the fields of wind energy and UAVs. The table reveals that there is a gap when it comes to datasets that can be used for the validation of predicting aerodynamic icing penalties at low Reynolds numbers. The existing datasets in the literature lack well-defined experimental ice geometries [
22,
23,
24], have no or limited performance data [
25,
26], offer only one data point for lift and drag for each icing case [
27,
28], or are performed at low or high Reynolds numbers [
16,
29]. Additionally, none of these datasets share the coordinates of the ice geometries or the tabularized data of lift and drag.
This study served three objectives. The first objective was to investigate the aerodynamic performance of an iced airfoil at low Reynolds numbers. The second objective was to make the experimental data available to be used for the validation of other numerical methods in the future. The last objective was to exemplify the use of the validation dataset by comparing it to FENSAP, a computational fluid dynamics (CFD) tool commonly used for icing simulations.
3. Experimental Setup
The experimental part of this work was performed in the closed-loop, low-speed wind tunnel at the Norwegian University of Science and Technology (NTNU). An NREL S826 airfoil with a chord of
c = 0.45 m was used in this study. This work follows the experimental methods described by Bartl et al. and their extensive study on the clean S826 airfoil, previously at NTNU [
32].
The dimensions of the wind tunnel test section are 1.8 m × 2.7 m × 12 m (height × width × length), with the height increasing to 1.85 m at the end of the test section to compensate for the boundary-layer growth of the wind tunnel walls. Measurements were conducted for angle of attacks (AOAs) ranging from α = −7.5–17.5° at three Reynolds numbers:
Re = 2 × 10
5, 4 × 10
5, and 6 × 10
5. The corresponding inflow turbulence intensities for each Reynolds number are
I = 0.44%, 0.30%, and 0.26% [
32].
Figure 2a shows the experimental setup, watching at the leading edge of the wing, which spans the whole wind tunnel height. The wing consists of two “dummy” parts near the tunnel walls and the main section. The total height is
h = 1.78 m. Only the middle section was connected to a force balance. All wing elements were computer numerical control milled from Ebazell foam and coated with black paint. Surface roughness measurements confirmed that the surface was hydraulically smooth. The trailing edge thickness was 2 mm.
A six-axis force balance recorded the aerodynamic forces acting on the main wing section during a period of 30 s with a sampling rate of 2000 Hz. Two load cells were aligned with the flow direction of the wind tunnel and one was perpendicular to it. The results from Bartl et al. [
32] showed that lift measurements could be accurately obtained with the force balance, but the accuracy was insufficient for drag estimations due to excessive signal-to-noise ratios. Instead, drag was measured with a wake rake using an integrated momentum deficit method. The rake is constructed with 21 uniformly distributed tubes of 1mm diameter, with 10mm spacing between the centerline of each tube. It was located at a distance of 0.7
c downstream of the trailing edge, mounted on a traverse. All pressure ports were connected to a pressure scanner and were sampled for a duration of 20 s with a sampling rate of 200 Hz.
In addition, 32 pressure taps are located in the middle of the main section and connected to a piezoresistive pressure scanner inside the wing. The reference pressure is taken from the static pitot tube upstream of the wing. Surface pressure data were collected at a sampling rate of 800 Hz for 30 s. The artificial ice shapes covered the pressure taps near the leading edge up to x/c = 0.09–0.15 (depending on the coverage by the different ice shapes). Therefore, the pressure readings were not used for any force calculation, but only to calculate the local pressure coefficients. The flow velocity and the reference pressures for the wake rake and surface pressures were measured with a pitot-static tube at a distance of 5c upstream of the wing.
In order to change the angle of attack, the entire set-up, including the force balance, was mounted on a turntable with a rotational accuracy of ±0.25°. The largest blockage ratio occurring between the model and the flow cross-section was σ
max = 5.1% at the highest angle of attack α = 18°. This was below the limit of σ = 10%, above which blockage correction needs to be considered [
41]. Earlier investigations showed that small losses in static pressure between the upstream pitot probe and the downstream rake occurred. Measurements also showed that the static pressure at the location of the rake is not fully stabilized. Both these effects contribute to a reduction of the drag coefficients, which has been approximated to be in the order of up to 20% [
32]. In addition, the wake rake measurements were only reliable as long as no strong separation effects occurred. This is because the rake cannot capture the resulting 3D velocity field. This means that for high angles of attack α > 12° for clean and α > 6–12° (depending on the ice shape) drag measurements from the wake rake were increasingly erroneous. More details on the general wind tunnel configuration and measurement method can be found with Bartl et al. [
32].
Artificial ice shapes were 3D-printed via fused deposition modeling at NTNU in polylactide plastic, on an Ultimaker S5 and S2+ printer with a layer height of 100 μm, see
Figure 2b. The artificial ice shapes cover the entire height of the wing, including the dummy sections, and were attached with tape.
In order to assess the influence of the laminar-turbulent transition, a series of runs were performed with a tripped boundary-layer. For this purpose, self-adhesive zig-zag tape, acting as a turbulator was applied to the upper and lower side of the leading edge at the location x/c = 0.05. The tape thickness was 0.4 mm with a width of 8 mm and a pattern angle of 60°.
4. Numerical Methods
The aerodynamic performance degradation due to icing was simulated with FENSAP, a state-of-the-art Navier–Stokes CFD solver [
42]. The solver is part of the software package ANSYS FENSAP-ICE (version 19.2) [
43], which is a second generation icing simulation tool suitable for a wide range of applications but with limited published validation data—in particular, for low Reynolds numbers. One objective of this study was to use FENSAP as an example to compare it to the experimental dataset and assess its capability to capture icing performance penalties at low Reynolds numbers. All FENSAP calculations were run as steady-state 2D simulations with a streamline upwind artificial viscosity model. The airfoil geometries were discretized in Pointwise (version 18.2R2) as a hybrid O-grid with a far-field diameter of 60
c. The boundary-layer was resolved with a structured 3D anisotropic tetrahedral extrusion (T-Rex) with a growth factor of 1.1 [
44]; see
Figure 3.
The comparison consisted of three steps. First, the clean airfoil aerodynamics were simulated and compared to the experiments. One of the main challenges for the clean airfoil simulation is the laminar-turbulent transition. Two turbulence models were implemented in FENSAP [
45]. The Spalart-Allmaras (SA) turbulence model is a classical one-equation model (eddy-viscosity), whereas the Menter’s k-ω SST model is a two-equation model (turbulence kinetic energy and eddy dissipation rate) [
46]. For both these turbulence formulations, a transition model is available. For the SA model, free transition is captured based on adverse pressure gradients, whereas the Menter’s k-ω SST model uses a one-equation local correlation-based intermittency transition mode [
45].
The second comparison step was to ensure that the chosen numerical discretization (grid) of the iced airfoils did not significantly affect the results. For this, a 2D grid convergence study was performed in order to find a grid resolution that was sufficiently accurate while optimizing computational power and time. The grid dependency study was performed on four grid resolutions, at three different angles of attack α = [0°, 5°, 10°] on one of the ice shapes (glaze ice, see
Section 5.2). The results are shown in
Figure 4a with the drag and lift coefficients normalized by a Richardson extrapolation ∆c
lift = c
lift/c
lift,Richardson and c
drag = c
drag/c
drag,Richardson [
47]. The results showed good convergence for lift and drag for all angles of attack. In order to limit the computational requirements for this study, the second-coarsest grid (ca. 170,000 points) was used for all subsequent simulations.
The third comparison step consisted of a study to compare the differences between the 3D constrained flow in the wind tunnel to the 2D simulations. For this purpose, the entire wind tunnel and test section was modelled in 3D. Lift and drag forces were calculated on the main wing section, excluding the dummy parts.
Figure 4b compares the simulated 3D results to the 2D solution with ∆c
3D/2D = [c
3D/c
2D − 1] for five angles of attack. The results show that for angles of attack up till α = 10° the difference between the 2D and the 3D solution is about 3% and increases to about 7% for the highest angle of attack. These deviations are assumed to be comparatively minor and justify the use of 2D simulations (e.g., [
48]).
5. Experimental Results
This section presents the experimental measurements of lift and drag from the NTNU wind tunnel for the two types of ice shapes. In addition, the influence of the small-scale surface roughness was investigated by comparing the (rough) IWT ice shapes to smooth ice shapes.
5.1. Comparison to Existing Data
Figure 5 compares the experimental lift and drag results for the clean airfoil from this study to the results from Bartl et al. [
32]. In general, the datasets are in good agreement, which is not surprising because identical facilities and methods were used. The largest deviations occurred in the stall area, particularly for drag, which is most likely related to the high measurement uncertainty of the wake rake in that area. The small level of Reynolds-dependency for
Re = 2–6 × 10
5 that was observed by Bartl et al., was also reproduced in this work. The decision to investigate three Reynolds numbers in this work was based on the possibility that iced airfoils may show a higher degree of Reynolds dependency. In conclusion, the good match between the clean curves gives us confidence that the experimental setup was accurate, and that data are repeatable.
5.2. IWT Ice Shapes
The lift and drag results for the three experimental IWT ice shapes are shown in
Figure 6a–c in comparison to the clean airfoil. The first observation was that all ice shapes introduced significant penalties on lift and drag. Lift decreased and drag increased over the entire range of angles of attack values. The degree of degradation depended on the ice shape type. The low Reynolds number results generally showed higher drag levels and lower lift for both clean and iced airfoils.
The glaze ice shapes gave the largest penalties. For zero angle of attack, the lift was decreased between ∆cl = −26–31% and drag was increased by ∆cd = +220–290%, as a function of the Reynolds number. The stall angle seemed unaffected, but the maximum achievable lift and the drag were both substantially reduced. Furthermore, the stall behavior was more aggressive, with a rapid loss of lift, especially for the higher Reynolds numbers.
For rime ice the degree of degradation was smaller with ∆cl = −17–19% and ∆cd = +100–190% at zero angle of attack. The drag curve at the lowest Reynolds number showed a significant increase compared to the other drag curves. In addition, the stall region showed an irregular behavior. The linear lift region ends at around α ≈ 7° with an apparent onset of stall. However, at about α ≈ 11° lift was suddenly increased, reaching a maximum at α ≈ 13–14° before showing a docile lift decrease. This uncharacteristic behavior occurred at all Reynolds numbers but was most distinct at the lowest Reynolds number. Potential explanations for this will be addressed in the discussion section.
Last, mixed ice exhibited the lowest performance penalties with ∆cl = −15–18% and ∆cd = +80–130% at a zero angle of attack. In the stall region, the same unexpected behavior with a sudden lift increase was observed, similarly to the rime case. This lift behavior showed a dependency on the Reynold number and decreased in distinction at higher Reynolds numbers.
5.3. LEWICE Ice Shapes
The experimental results for the ice shapes obtained from LEWICE simulations are shown in
Figure 7. Due to time limitations and because the IWT ice shapes did not show a major Reynolds number dependency, the LEWICE ice shapes were conducted only at
Re = 4 × 10
5. The largest penalties occurred for the horn* ice shape. At zero angle of attack, lift was decreased by ∆c
l = −26% and drag more than quadrupled with an increase of ∆c
d = +330%. The maximum lift angle occurred significantly earlier compared to the clean airfoil, at α ≈ 7°.
The rime* and glaze* ice shapes showed similar degrees of degradation in both lift and drag with ∆cl = −16–17% and ∆cd = +40–60% at zero angle of attack. Differences showed up in the stall region, where the glaze ice shape displayed a similar lift behavior as the IWT rime and mixed ice shapes. However, in this case, the lift increase arose significantly later, at α ≈ 14° and the maximum lift was reached at α ≈ 15°. The rime ice shape exhibited a normal stall behavior
5.4. Influence of Roughness
Figure 8 shows the comparison of smooth and rough IWT ice shapes to highlight the influence of the small-scale roughness. The general trend that was observed for all lines is that the additional surface roughness led to a decrease in lift and an increase in drag.
For the glaze ice shapes, the smooth surfaces seemed to delay the maximum stall angles by ∆α ≈ 1° while increasing the maximum lift slightly. The sudden lift increase in the stall region of the rime and mixed ice shapes prevailed in the absence of the surface roughness. The results indicated that the effect may be slightly more pronounced for the rough airfoils, especially for rime ice.
7. Discussion
7.1. Experiments
In general, the experiments showed that the performance degradation is linked to the geometry of the ice shape. The largest differences between the results can be observed for the drag curves. The most streamlined ice shapes (glaze* and rime*) resulted in the smallest increases in drag, compared to the more complex IWT ice shapes. The largest drag penalties occurred for the glaze and horn* ice shapes, which can be explained by the large horn geometry that resulted in large separation bubbles. The correlation between performance degradation and ice shape geometry can also be detected for lift. In the linear lift region, this effect is less obvious, but it can be observed for the stall behavior—especially for glaze and horn*, which exhibited earlier stall, lower maximum lift, and rapid lift decrease.
The variation of the Reynolds numbers seemed to have a lesser effect on the results. The general trends were that higher Reynolds numbers led to increased lift and a decrease in drag levels. One notable occurrence was found for the rime ice shape at Re = 2 × 105, where the drag was increased substantially compared to the higher Reynolds numbers. This can most likely be linked to the relatively high measurement uncertainties related to the small forces acting on the measurement balance.
A surprise from the experimental data was the stall behavior occurring for the IWT mixed, IWT rime, and the LEWICE glaze* ice shapes. In all these cases, a sudden lift increase occurred in the stall region. A measurement error was very unlikely, as this effect was reliably reproduced for the ice shapes in question. No unsteady behavior was found, either in the force balance measurements or the pressure tap data. The effect showed a slight tendency to decrease for higher Reynolds numbers; see
Figure 8b–c.
To investigate the stall behavior, the pressure distributions over the clean and an iced airfoil were examined.
Figure 12a displays the distribution of the pressure coefficient c
p over the clean airfoil and shows how the stall was starting from the trailing-edge. For the iced airfoil, the LEWICE glaze* case was investigated, since it showed the clearest lift increase behavior; see
Figure 7. The glaze* pressure distribution in
Figure 12b showed that the additional lift seemed to originate from the leading-edge, where increased suction pressure occurred at
x/c < 0.3 for α = 13.5–15.5°.
One hypothesis for the origin of this increase in leading-edge suction is an increase of the airfoil camber. According to this idea, the initial break in the lift curve (α ≈ 9°) occurs due to the onset of trailing-edge separation. The lift increase (α ≈ 14°) would originate either from the ice shape acting as a nose droop [
49], or possibly, from a localized separation bubble [
50]. This effect would decrease at higher Reynolds numbers because the onset of the trailing-edge separation moves to higher angles of attack due to the higher boundary-layer inertia. This would explain why this effect has not been observed on a wider scale for high-Reynolds applications. Comparable effects have indeed been documented before at low Reynolds numbers by Jasinski et al., who suggested a “leading-edge flap”-like behavior as an explanation, ([
23], pp. 61–62). Additionally, a lesser degree lift increase occurs in Seifert and Richert’s experiments, without them addressing it explicitly ([
22], pp. 459–460).
The exact mechanism of the unexpected stall behavior could not be fully proven within the scope of this work. To test the hypothesis, flow visualization techniques, wider Reynolds number range, moment measurements, and pressure measurements on the ice shapes should be conducted in follow-up studies.
7.2. Simulations
The experimental results were qualitatively compared to FENSAP, using the SA and k-ω SST turbulence models. For the clean airfoil with free transition and tripped boundary-layer, both turbulence models showed a good match in lift and drag with the experiments and were able to reproduce the linear drag behavior of the airfoil. Larger differences occur in the stall regions, where both models did not capture the experimental stall behavior. The SA model tended to predict higher lift values, whereas the k-ω SST tended to predict lower maximum lift angles and earlier stall.
The quality of the lift and drag prediction of iced airfoils appeared to depend on the ice shape. For the most streamlined cases (LEWICE rime* and glaze*) both turbulence models captured the drag well. In the linear lift region, the k-ω SST model seemed to match the experiments better, whereas the SA model tended to overpredict the lift. The stall behavior was not captured well by either of the turbulence models, resulting in an earlier stall and lower maximum lift values. This was likely to be related to the shortcomings of the turbulence models in the presence of large separation zones [
46]. For the more rugged shapes of the IWT rime and mixed ice shapes, the codes behaved similarly, with exception to the drag results, which were significantly lower compared to the experiments. This was likely to be related to the ruggedness of the surface and the inability of the turbulence models to capture the associated drag increase. This trend amplifies for the more complex ice shapes of glaze and horn*, where the large separation areas also occurred in the linear lift region; see
Figure 13a–d.
The unexpected stall behavior of some of the ice shapes was not captured by the simulation with any of the turbulence models. This was not entirely surprising and was most likely related to the limitations of the SA and k-ω SST turbulence models. Further work should investigate the possibility of 3D flow effects, transient flow behavior, and the use of higher-order models.
In summary, the comparison between FENSAP and the experimental data showed that even CFD-RANS can be used to get reasonable lift and drag predictions at low Reynolds numbers. Limitations seem to exist in the stall area and for complex ice shapes with large leading-edge separation zones. Consequently, FENAP may be suited, for example, to predict intercycle ice penalties for the design of de-icing systems at low Reynolds numbers [
51]. Similarly, effects on wind turbine power production or UAV flight behavior may be simulated with sufficient accuracy with FENSAP.