NOMENCLATURE
- c
-
aerofoil chord length
- Cp
-
pressure coefficient
- Cp,i
-
instantaneous pressure coefficient
- C′p
-
root mean square of the unsteady pressure coefficient
- f
-
frequency
- k
-
protuberance height
- Lb
-
bubble length
- Lh
-
projected height (normal to freestream)
- N
-
number of samples
- Re
-
Reynolds number based on chord length
- RMS
-
root mean square
- s
-
model/aerofoil coordinate in surface length
- Stf
-
Strouhal number corresponding to shear-layer flapping
- Str
-
Strouhal number corresponding to regular mode
- V
-
freestream velocity
- x
-
coordinate in the aerofoil model chord-wise direction
- xMR
-
mean reattachment location
- w
-
protuberance base width
- α
-
aerofoil angle-of-attack
- θ
-
ice shape horn angle with respect to the chord line
1.0 INTRODUCTION
Determining the aerodynamic effects of ice accretion on aircraft surfaces is an important step in flight safety. Reductions in aerofoil maximum lift of over 50% and increases in minimum drag of more than 400% have been observed for some types of ice accretion(Reference Busch, Broeren and Bragg1,Reference Lynch and Khodadoust2) . It can also severely alter the stability and control characteristics of the aircraft. When an aircraft enters a region containing super-cooled water droplets, ice accretions of various shapes can form at different locations on its aerodynamic surfaces under different meteorological and flight conditions. The three primary ice shapes encountered are rime ice, glaze ice and ridge ice. Glaze ice (with a more irregular ice shape) forms at temperatures near freezing when some of the water droplets partly freeze on impact and the rest run back. This often results in the development of a horn-ice shape. Glaze ice accretions tend to be studied more than any other type of shape because of the large aerodynamic penalties. Glaze ice accretion dangerously affects and alters the shape of the original wing surface, producing aerodynamic penalties much more severe than ice roughness, rime ice and short ridge ice. For this reason, the present study has focused on glaze ice accretion.
As discussed by Bragg et al(Reference Bragg, Khodadoust and Spring3), the most dominant feature in the flowfield of an aerofoil with a horn-ice shape is the large separation bubble that forms due to the separation off the tip of the horn-ice shape. An instantaneous schematic of the horn-ice induced flowfield, including the ice-induced separation bubble and associated flowfield features, is shown in Fig. 1, after Gurbacki and Bragg(Reference Gurbaki and Bragg4). Air flows around the upper horn of the ice shape and separates due to a severe adverse pressure gradient. Shear-layer vortices enhance flow mixing, which leads to reattachment and the creation of a separation bubble(Reference Gurbaki and Bragg4). At higher angles of attack, the pressure recovery may not be achieved and stall may occur. Due to flow unsteadiness, the reattachment location on the aerofoil surface varies in time, forming a reattachment zone(Reference Gurbaki and Bragg4).
Figure 1. Instantaneous schematic of the flowfield downstream of a horn-ice shape, after Gurbacki and Bragg(Reference Gurbaki and Bragg4).
The behaviour of large-scale vortex shedding and the differences in the iced-aerofoil flowfields between a three-dimensional ice shape casting and a two-dimensional extrusion of the ice shape casting were identified by Jacobs and Bragg(Reference Jacobs and Bragg5,Reference Jacobs and Bragg6) . From this investigation, it was discovered that the three-dimensional horn-ice shape produced stream-wise vortex structures, which led to a faster pressure recovery of the separated boundary layer, and thus a shorter mean reattachment length than the two-dimensional extrusion of the ice shape.
Accurate prediction of aerofoil performance penalties rests partially on the ability to correctly predict the unsteady flowfield characteristics associated with the ice-induced separation bubble(Reference Gurbaki and Bragg4). Gurbacki and Bragg(Reference Gurbaki and Bragg4) identified two primary sources of ice-induced unsteadiness for an aerofoil with leading-edge horn-ice shapes.
The first source has been attributed to vortical motion, where large-scale vortices are regularly shed downstream of the separation bubble according to a bandwidth of frequencies. The source of the regular mode has almost unanimously been attributed to the Kelvin-Helmholtz instability, where the difference between the velocity within the recirculation region of the separation bubble and the external flow causes a roll-up and shedding of vortices in the shear layer(Reference Deck and Thorigny7–Reference Kiya, Shimizu and Mochizuki9).
The unsteady content of the iced-aerofoil flowfield was analysed by Gurbacki and Bragg(Reference Gurbaki and Bragg4) for a NACA 0012 aerofoil with a leading-edge horn-ice shape. Power spectra of time-dependent surface pressure data near reattachment presented unsteadiness with non-dimensional frequency St = 0.53-0.73. These frequencies corresponded to shear-layer vortices and vortex shedding from the separation bubble. In a joint experimental wind-tunnel and Computational Fluid Dynamics (CFD) simulation, Mirzaei et al(Reference Mirzaeia, Ardekani and Doosttalab10) investigated the flowfield structure of the separation bubble formed on NLF-0414 aerofoil with glaze ice accretions. Measurements of the unsteadiness of the flowfield near reattachment location confirmed the existence of the vortices in the shear-layer with the non-dimensional frequency ranging from 0.44 to 0.78.
The flow structures downstream of horn-ice shapes have many similarities to the unsteady flowfield behaviour downstream of a backward-facing step or a blunt flat plate(Reference Gurbaki and Bragg4). Cherry et al(Reference Cherry, Hillier and Latour11) studied the unsteady structure of the 2D separation bubble present on a blunt flat plate using a combination of pressure and velocity measurements, along with flow visualisation. They observed vortex shedding at a Strouhal number of 0.7 from shear-layer velocity fluctuations. Driver et al(Reference Driver, Seegmiller and Marvin12) observed the maximum energy in the instantaneous pressure near reattachment of the backward-facing step's shear-layer at a Strouhal number of 0.6. For the same geometry, Eaton and Johnston(Reference Eaton and Johnston13) identified a value of 0.52 from the power spectrum of the stream-wise velocity fluctuations near reattachment. Kiya and Sasaki(Reference Kiya and Sasaki14) studied the large-scale vortex structure of the separation bubble across the surface of a blunt flat plate using unsteady velocity and surface pressure measurements. They observed a regular, periodic shedding of vortices with dimensionless frequency of 0.6.
The second source of unsteadiness is represented by a low-frequency ‘flapping’ of the shear layer, which causes large-scale unsteadiness in the separation bubble flowfield and a quasi-periodic enlargement and shrinking of the separation bubble. The source of this low-frequency flapping of the shear layer is not fully understood. Kiya et al(Reference Kiya, Shimizu and Mochizuki15) have theorised the existence of a feedback system that drives this low-frequency oscillation. This theory was later reinforced by the observations of Lee and Sung(Reference Lee and Sung16), who identified traits in the unsteady pressure that were characteristic of a standing wave at the shear-layer flapping frequency inside the separation bubble region. Sigurdson(Reference Sigurdson17) attributed this low-frequency flapping to a parallel version of a von Kármán vortex shedding process, where an instability is generated due to the interaction of the shear-layer vorticity with its image across a wall. Eaton and Johnston(Reference Eaton and Johnston13) believe that the low-frequency unsteadiness in the shear-layer reattachment is due to an instantaneous imbalance between shear layer entrainment from the re-circulating region on one hand and reinjection of fluid near the reattachment on the other hand.
The low-frequency oscillation on iced-aerofoils was first pursued in great detail by Zaman and Potapczuk(Reference Zaman and Potapczuk18), who characterised the low-frequency oscillations using computational methods and hot-wire data. These authors identified oscillations in the wake of a NACA 0012 aerofoil with a leading-edge ice accretion at Strouhal numbers (based on projected aerofoil height) near 0.02. Bragg et al(Reference Bragg, Khodadoust and Spring3) also identified a low-frequency oscillation in the split-film measurements acquired in the shear layer downstream of a horn-ice shape on a NACA 0012 aerofoil. A peak in the spectral content of the velocity in the shear layer at α = 4° revealed a low-frequency oscillation at 11.6 Hz. This frequency corresponded to a Strouhal number of 0.0185, which was similar to the Strouhal number reported in the experimental portion of Zaman and Potapczuk(Reference Zaman and Potapczuk18). In most simple-geometry flowfields, shear-layer flapping has been observed to be associated with Strouhal numbers on the order of 0.02 based on the height of the geometric feature and the freestream velocity, or on the order of 0.1 based on the mean length of the separation bubble and the freestream velocity(Reference Cherry, Hillier and Latour11,Reference Driver, Seegmiller and Marvin12) .
Almost all previous studies are focused on the effect of ice accretion with a fixed configuration on aerofoil aerodynamics(Reference Bragg, Khodadoust and Spring3–Reference Jacobs and Bragg6,Reference Mirzaeia, Ardekani and Doosttalab10) . Because the ice accretion process is dependent on both atmospheric and aerodynamic conditions, the ice shape with many different sizes, shapes, locations and textures is formed on unprotected aerodynamic surfaces. Therefore, more investigation with a wide range of varying ice shapes is required to acquire more insight into the flowfield characteristics of aerofoils under icing conditions. In the present work, for the first time the effect of height and location of ice accretion on the flowfield unsteadiness of the separation bubble formed on a NACA 0015 aerofoil has been investigated using time-dependent pressure measurements. Moreover, an attempt is made to characterise relevant modes of unsteadiness present in the iced-aerofoil flowfield by spectral analysis of stream-wise velocity fluctuations using a hot-wire anemometry.
2.0 EXPERIMENTAL SET-UP
Flow measurements were carried out by using an open return wind tunnel with a test section height, width and length of 90, 90 and 2,000 cm, respectively. The maximum empty test section speed of this wind tunnel is approximately 70 m/s, resulting in a maximum Reynolds number of 1.5 × 106/m. The contraction ratio between the settling chamber and test section is 7.5:1 and a honeycomb and three turbulence reduction screens are located at the inlet settling chamber to reduce tunnel turbulence to less than 0.2% in the test section. The flowfield measurements require some equipment both inside and outside the test section. The wind-tunnel test section is equipped with a three-axis traverse system, which can be controlled by a LabVIEW computer program (Fig. 2(a)). This traverse system is mounted above the wind tunnel such that the hot-wire probe supporting structure enters the wind tunnel from the ceiling as shown in Fig. 2(b). Three step-motors are used in the traversing mechanism to control the vertical and horizontal position of the measurement probe of the hot-wire system with the accuracy of ±0.1 mm.
Figure 2. Wind-tunnel set-up: (a) traverse mechanism, (b) flowfield measurements apparatus installed in the test section.
The aerofoil model used for this investigation is aluminium NACA 0015 with a 38 cm chord and 90 cm span. The upper surface of aerofoil was instrumented with 27 surface pressure taps for acquiring pressure measurements (Fig. 3(a)). All pressure taps are connected to a pressure box. For this purpose, the PU plastic tubes with an inside diameter of 1.5 mm and length of 120 cm are employed. It should be pointed out that since the trailing edge is too thin, no pressure taps are installed for x/c > 0.90. In this investigation, all data are obtained at a chord-based Reynolds number of 1.0 × 106.
Figure 3. (a) Positions of the surface pressure taps, (b) geometry of a horn-ice shape, (c) glaze horn-ice simulations, (d) surface locations of simulated ice shape.
As discussed by Bragg et al(Reference Bragg, Broeren and Blumenthal19) the glaze ice shape can be characterised by its height, the angle it makes with respect to the chord line (θ) and its location indicated by s/c, the non-dimensional surface length (Fig. 3(b)). In this investigation, the simulated glaze horn-type ice accretions were determined from averaging geometry data from a set of actual ice accretions collected in a test at the NASA Glenn Icing Research tunnel(Reference Harold and Addy20). Leading-edge glaze ice accretions characteristically consist of an upper and lower surface horn. However, only single-horn simulations were used for this research. The simulated ice shapes were machined to the designed shape geometry from a solid aluminium bar to produce adequate shape accuracy. The simulated ice was tested in two heights: k = 7.6 (k/c = 0.02) and k = 16.45 (k/c = 0.0433) mm (Fig. 3(c)). Each of these shapes was positioned at four locations around the leading edge of aerofoil. Figure 3(d) shows the locations (s/c) of simulated ice shapes. Lee and Bragg(Reference Lee and Bragg21) showed that the horn radius had only a small effect on the aerofoil performance, so varying the glaze-ice horn leading-edge radius is ignored in the current study.
Surface pressure was sensed through ASDX series transducers, from Honeywell, with an accuracy of ±2% full-scale output and 1 kHz sample rate frequency. An estimate of the unsteady content present in the iced-aerofoil flowfield was determined by calculating the root mean square of the un-steady pressure coefficient, which was calculated by utilising the following relation:
$$\begin{equation}
{C'_p} = {\left( {\frac{1}{{N - 1}}\sum\limits_1^N {{{\left( {{C_{p,i}} - {C_p}} \right)}^2}} } \right)^{0.5}},
\end{equation}$$
where N represents the number of instantaneous pressure samples acquired. In this equation, Cp and Cp,i are the time-averaged pressure coefficient and the instantaneous pressure coefficient, respectively. Surface pressure coefficient fluctuations were acquired at 1,000 Hz for 10 sec. In unsteady measurements where the pressure changes with time continuously, it is important to determine the time lag of pressure-measuring system when the transducers are not installed inside the model. The time lag in the tubing is due to the viscosity, elasticity, mass of the air enclosed in the tube, inertia, material of which the tube is made and the condition of the inside surface of the tube. The lag due to the viscosity and elasticity of the air depends chiefly on the length and diameter of the tube and the time rate of change of the initial pressure(Reference Bynum, Ledford and Smotherman22,Reference Barlow, William and Pope23) . All of the tubes that were used in this investigation have the same length and diameter. Based on Soltani's(Reference Soltani, Rasi, Seddighi and Bakhshalipour24) results, the time lag of the tubes used in this study is about 0.005 sec. The uncertainties in relative time-average and time-dependent pressure measurements were obtained as 2.4% and 3.8%, respectively.
The turbulence intensity and spectral analysis data were measured using a single hot-wire probe. The probe was calibrated both statically and dynamically and all data were low-pass filtered. Data were recorded via a 12-bit A/D. In order to quantify the uncertainty of the hot-wire anemometer, the methodology provided in Reference JorgensonRefs 25 and Reference Yavuzkurt26 were followed. The uncertainty of the results obtained with the CTA anemometer is a combination of the uncertainties of the individually acquired voltages converted into velocity. The uncertainty of each individual velocity sample was determined by non-statistical means based on detailed knowledge about the instrumentation, calibration equipment and experimental conditions. The hot-wire anemometer has low drift, low noise and good repeatability, so that these factors do not add significantly to the uncertainty in comparison with other error sources(Reference Jorgenson25). Temperature variations from calibration to experiment or during an experiment introduce systematic errors. Because of this, every CTA is equipped with a temperature corrective probe that is placed in the flow and applies the effect of temperature variation during airflow measurement. The independent parameters such as curve-fitting error in the calibration, A/D resolution uncertainty and probe positioning are also considered in the uncertainty analysis. The uncertainty of the Turbulence Intensity (TI) was found to be around 6%.
3.0 RESULTS
Both time-averaged and time-dependent measurements were acquired in order to determine the steady and unsteady features in the flowfield of an aerofoil with a horn ice shape.
3.1 Time-averaged measurements
The effect of the simulated ice accretion on the aerofoil flowfield will be discussed first by fluorescent oil flow visualisation technique and time-average pressure measurements to provide a better understanding of the integrated results that will be shown later. Figure 4 shows the result of the fluorescent oil flow visualisation at α = 0° and Re = 1.0 × 106. The k/c = 0.0433 simulated ice shape is located at s/c = 0.034. Use of fluorescent oil flow visualisation technique allows for the identification of key features in the time-averaged flowfield, including regions of separated flow and mean shear-layer reattachment location. The time-averaged reattachment location was estimated using the flow bifurcation that occurs at shear-layer reattachment (Fig. 4(a)). As a result of the flow bifurcation, the oil streaks upstream of the reattachment location are scrubbed upstream and the oil streaks downstream of the reattachment location are scrubbed downstream. The speckled region in Fig. 4(b) indicates the mean reattachment zone of the separation bubble, which ranges from x/c = 0.2 to x/c = 0.3. Upstream of this location inside the separation bubble is a region of reverse flow, indicated by the oil streaks flowing from right to left and downstream, where the flow has reattached as a turbulent boundary layer and moves toward the trailing-edge.
Figure 4. (a) Schematic of shear-layer reattachment on aerofoil surface, after Ansell and Bragg(Reference Ansell and Bragg27), (b) fluorescent oil flow visualisation (α = 0° and Re = 1.0 × 106).
Figure 5 shows the surface pressure distribution on the upper surface of aerofoil with k/c = 0.0433 ice shape simulation that is placed at various chord-wise locations (between s/c = 0 and 0.034) at α = 0° and is compared with the clean aerofoil. The surface pressure was not measured over the simulated ice shape. Thus the Cp from the last pressure tap upstream of the simulated ice shape is connected to the first pressure tap downstream of the simulated ice shape by a straight line. It is important to note that the shear-layer reattachment location can be approximated by the location where the iced-aerofoil pressure distribution intersects the clean aerofoil one(Reference Bragg, Khodadoust and Spring3,Reference Broeren and Bragg28) .
Figure 5. Effect of k/c = 0.0433 simulated ice shape location on a NACA 0015 aerofoil pressure distribution (α = 0° and Re = 1.0 × 106).
When the simulated ice shape is located at the leading-edge of aerofoil (s/c = 0) the pressure distribution appears approximately identical to that of the clean case. In fact, the separation bubble is so small that it is nearly undetectable through pressure distribution comparisons. In Fig. 5 the pressure distribution significantly changes when the simulated ice shape is located at s/c = 0.0085. The pressure distribution shows a suction peak (Cp = −0.91) immediately downstream of simulated ice shape as the flow accelerates over it and separates. The pressure coefficients then increases as the reattachment process begins and the shear-layer reattachment location occurs where the iced-aerofoil pressure coefficients approach the clean value at x/c = 0.036. The extremely small bubble is due to the very favourable pressure gradient in which the simulated ice shape is located and the bubble is quickly able to reattach. As the simulated ice shape is moved downstream from the leading edge to s/c = 0.0174, initially the pressure coefficients decreases sharply, indicating the acceleration of flow due to the separation of shear layer from the tip of the ice shape. Pressure recovery is delayed from x/c = 0.04 to x/c = 0.12, resulting in a constant pressure plateau until the shear-layer transitions to turbulent flow(Reference Jacobs and Bragg5,Reference Jacobs and Bragg6) . Entrainment of high-energy external flow by the turbulent shear layer allows for adequate pressure recovery and results in flow reattachment. After transition, pressure recovery in the separation bubble begins and the reattachment occurs at x/c = 0.18.
Based on Fig. 6, similar trends in the pressure distribution are observed at α = 4°, although estimates of shear-layer reattachment location from surface pressures indicate that as the angle-of-attack increases, the bubble length increases as well.
Figure 6. Effect of k/c = 0.0433 simulated ice shape location on a NACA0015 aerofoil pressure distribution (α = 4° and Re = 1.0 × 106).
At α = 4°, the pressure distribution for the upper surface of clean aerofoil shows a suction peak (with C p,min = −1.52) near x/c = 0.03, followed by a severe pressure recovery region (with an adverse pressure gradient). When the simulated ice shape is placed at s/c = 0.0174, the resulting separation bubble would be located in a very adverse pressure gradient where it cannot easily reattach. Thus, the separation bubble for this simulated ice shape location is much larger than when the simulated ice shape is located at s/c = 0.0085. It is interesting to note that when the simulated ice shape is located in the critical location of s/c = 0.0174, the separation bubble eliminates the large leading-edge suction peak of the clean aerofoil. By locating the ice shape at s/c = 0.034, a very long separation bubble will be formed downstream of the ice shape. In this case, both the simulated ice shape and the separation bubble are located in the clean aerofoil adverse pressure gradient region. The effect of a growth in the separation bubble size is associated with a further decrease in the magnitude of the clean aerofoil leading-edge suction peak and a longer length of constant pressure across the aerofoil upper surface. In this situation, determining the reattachment location from the surface pressure distribution is difficult and it is unclear whether or not the separation bubble has reattached.
Figure 7 indicates the effect of height and location of ice shape on the bubble reattachment location at Re = 1.0 × 106, based on the surface pressure distribution. The uncertainty of the time-averaged shear-layer reattachment location was determined from the distance between the pressure taps. The maximum uncertainty in the value of reattachment location was 5%. It can be seen that the bubble length is a function of aerofoil angle-of-attack, the height and the location of ice shape. When the k/c = 0.042 ice shape is located near the leading edge (s/c = 0.0085), the separation bubble remains very small and does not grow significantly with angle-of-attack (Fig. 7(a)). As the k/c = 0.02 ice shape is moved downstream from s/c = 0.0085 to 0.0174, the growth rate of bubble length increases, although it is not considerable until α = 4o. By increasing the angle-of-attack to α = 5° a dramatic growth in bubble length is observed and the bubble approximately doubles in size from α = 5° to 7°. Figure 7(a) shows a considerable increase in bubble length by moving the k/c = 0.02 ice shape to s/c = 0.034. The bubble formed at α=0° is eight times longer than the one formed downstream of simulated ice shape located at s/c = 0.0085. With an increasing angle-of-attack, the bubble length grows sharply from x/c = 0.16 at α = 0° to x/c = 0.40 at α = 4°.
Figure 7. Time-averaged shear-layer reattachment location with (a) k/c = 0.02 simulated ice shape and (b) k/c = 0.0433 simulated ice shape (Re = 1.0 × 106).
When k/c = 0.0433 simulated ice shape is placed at s/c = 0.0085 (Fig. 7(b)), the variations of ice height don't cause any appreciable change in reattachment location because the bubble is able to attach quickly in the very favourable pressure gradient. Figure 7 reveals that as the simulated-ice shape is moved downstream from the leading edge to s/c = 0.0174 and s/c = 0.034, the differences in the ice shape height have a progressively larger effect on the reattachment location. For example, when the simulated ice shape is located at s/c = 0.0174 (α = 0), increasing the ice shape height from k/c = 0.02 to k/c = 0.0433 approximately quadruples the bubble length.
3.2 Ice-induced flowfield unsteadiness
Figure 8 presents a comparison between the time-average surface pressure distribution and the variation of root-mean-square pressure fluctuations (C′ p ) for the upper surface of iced-aerofoil at α = 0° (k/c = 0.0433 and s/c = 0.034). In Fig. 8 the reattachment region is marked with purple and yellow colours, and the location where the maximum C′ p occurs is marked with blue and yellow colours. The yellow colour has been used to mark the area where an overlap of maximum C′ p and reattachment position is seen. This minor overlap between the location of maximum C′ p and reattachment region only occurs at low angles of attack. It's shown that as the flow approaches the simulated ice shape and the separation region, the RMS pressure fluctuations begins to increase. The highest value of RMS pressure fluctuations is observed upstream of reattachment location. This phenomenon is due to roll-up of vortices immediately originated from the separation edge and shedding of the large-scale vortex structures. Vortex shedding causes high velocity fluctuations, and in turn, high pressure fluctuations in the reattachment region. Downstream of the reattachment, the RM values of pressure fluctuations begin to decay due to the boundary layer relaxation process following reattachment region and settle down to the smooth surface values.
Figure 8. Distribution of Cp and C′ p for a NACA 0015 aerofoil with simulated horn-ice shape (α = 0°, Re = 1.0 × 106, k/c = 0.0433 and s/c = 0.034).
Similar observations were reported by Gurbacki(Reference Gurbaki29), who stated that immediately downstream of the ice horn, the RMS fluctuations in Cp are small—only slightly above those measured for the clean aerofoil at the same chord-wise position. However, C′ p increased rapidly with increasing chord-wise position, reaching a maximum value of 0.10 just upstream of the reattachment zone. Moreover, in an attempt to measure the wall pressure fluctuations for a backward-facing step by Feng et al(Reference Feng, Ying Zheng and Han-Ping30), a maximum of RMS surface pressure was detected near the reattachment point, which confirms the above mentioned distribution of C′ p . A comparison of the locations of maximum C′ p and time-averaged reattachment location are shown in Fig. 9 (k/c = 0.0433 and s/c = 0.0174). It can be seen that the location of maximum unsteadiness in the flowfield corresponding to the location of maximum C′ p does not exactly correspond to the location of mean shear-layer reattachment. Furthermore with increasing angle-of-attack, the location of maximum C′ p tends to reside farther upstream of the reattachment location. For the angle-of-attack range included in Fig. 9, the location of maximum C′ p occurs between x/xMR = 0.67 and x/xMR = 0.9.
Figure 9. Comparison of chord-wise location of mean reattachment and maximum C′ p (Re = 1.0 × 106).
At an angle-of-attack range from α = 0° to 5°, Gurbacki(Reference Gurbaki29) identified the maximum unsteadiness in surface pressure occurring between x/xMR = 0.60 and x/xMR = 0.75. As discussed by Mabey(Reference Mabey31), the location of maximum fluctuation in pressure on a surface with reattaching flows typically resides between x/xMR = 0.75 and x/xMR = 0.90, which confirms the results of the current study. Moreover, Heenan and Morrison(Reference Heenan and Morrison32) observed that the location of maximum unsteadiness in the surface pressure downstream of a backward-facing step resided between x/ xMR = 0.8 and x/xMR = 0.90.
Figure 10 shows the effect of height and location of ice shape on distribution of C′ p . The simulated ice shape is located at s/c = 0.0085, 0.00174 and 0.034. It can be seen that the maximum value of C′ p increases when the simulated ice shape is moved from s/c = 0.0085 to s/c = 0.034. It can be also observed that with increasing the height of the ice shape (for a fixed angle-of-attack), the value of maximum C′ p generally increases and the corresponding location of this maximum value moves downstream.
Figure 10. Effect of simulated ice shape location on C′ p : (a) k/c = 0.02, (b) k/c = 0.0433 (α = 2° and Re = 1.0 × 106).
The upper surface distribution of C′ p at various angles of attack for the NACA 0015 aerofoil with simulated ice shape is shown in Fig. 11 (k/c = 0.0433 and s/c = 0.034). At low angles of attack (α = 0° and 1°), the elevated levels of unsteadiness are primarily constrained to the leading-edge section of the aerofoil from approximately x/c = 0.1 to x/c = 0.3. With increasing the angles of attack to α = 2° and 3°, the maximum value of C′ p reached across the upper surface increases and moves further downstream. As seen in Fig. 11(b) for α = 4° and 5°, the unsteadiness in the leading-edge region from x/c = 0.0 to x/c = 0.3 begins to increase. An increase in angle-of-attack to 6° and 7° reveals that the value of maximum C′ p begins to decrease and the distribution of unsteadiness across the aerofoil flowfield moves closer to being uniform. The trends in the flowfield unsteadiness are qualitatively consistent with the observations of Ansell(Reference Ansell33), who reported increasing in the flowfield unsteadiness with angle-of-attack until stall. This author also stated that flowfield unsteadiness decreased when the angle-of-attack was increased past stall.
Figure 11. Distribution of C′ p for a NACA 0015 aerofoil with k/c = 0.0433 simulated horn-ice shape (s/c = 0.034): (a) angle-of-attack range from 0° to 3°, (b) angle-of-attack range from 4° to 7°.
3.3 Regular mode of vortical motion
In addition to estimating the distribution of unsteadiness across the aerofoil surface using the calculated C′ p values, it is also helpful to identify frequency scales associated with the unsteadiness. As mentioned before one of the sources of unsteadiness present in most separated flows is due to vortices that form in the shear-layer and vortex shedding downstream of the reattachment location in regular frequencies. According to the general trends of the upper surface velocity spectra, the iced aerofoil flowfield unsteadiness associated with the vortices frequency was examined in the velocity spectra at the nearest point to the reattachment location(Reference Mirzaeia, Ardekani and Doosttalab10). Near the reattachment region, the vortex structures are well defined and close to the aerofoil surface, and therefore are easily sensed by the hot-wire probe.
Figure 12 shows the regular frequency of the vortices motion in the shear-layer of the iced-aerofoil (k/c = 0.0433 and s/c = 0.034) at Reynolds number of 1.0 × 106 and angles of attack of α = 0°, 1°, 2° and 3°. The central frequency of the local maximum spectrum amplitude corresponds to the regular frequency of the vortices.
Figure 12. Regular vortex frequency: power spectral density function of the time-dependent velocity fluctuation near reattachment location (Re = 1.0 × 106, k/c = 0.0433, s/c = 0.034). (a) α = 0°, (b) α = 1°, (c) α = 2°, (d) α = 3°.
It is seen that the bandwidth and central frequency of the regular mode spectral peaks decrease with increasing the angle-of-attack. At α = 0°, energy in the low frequency range decreases somewhat near 50 Hz, after which the amplitudes increase slightly to a local maximum that is centred near the frequency of 220 Hz. An increase in angle-of-attack to 1° and 2° reveals a local maximum amplitude at 175 Hz and 135 Hz, respectively. Finally, at a = 3°, the regular frequency occurs at 125 Hz. It can also be observed from Fig. 12 that the amplitude of the regular mode spectral peak increases with increasing the angle-of-attack. This phenomenon indicates that as the adverse pressure gradient imposed across the separation region increases and as the separation bubble elongates, the oscillations imposed by vortical motion become more energetic.
A comparison of the Strouhal number values for the regular mode from the current study were made with values reported in the literature. This comparison is presented in Table 1. The Strouhal number Str = fLR/V is calculated for each case based on the length of the separation bubble (LR) and the freestream velocity (V). These values range from 0.5 to 0.63 and are in good agreement with those of other separated flow fields reported in Refs Reference Mirzaeia, Ardekani and Doosttalab10-Reference Driver, Seegmiller and Marvin12 and Reference Kiya and Sasaki14.
Table 1 Comparison of Str for regular mode determined in the current study with those reported in the literature
Figure 13 shows the regular frequency of the vortices downstream of the reattachment location at α = 3° and Re = 1.0×106 (k/c = 0.0433, s/c = 0.034). These frequencies were captured with hot-wire anemometry normal to the chord-wise direction where the turbulence intensity is maximum. Figure 13 reveals a decrease in the regular mode frequency, with increasing distance downstream of the reattachment location. It can also be seen in Fig. 13 that the frequency of the regular mode remains unchanged from x/xMR = 1.7 to x/xMR = 1.9. Similar trends were observed at other angles of attacks. These data are in good agreement with the results of Cherry et al(Reference Cherry, Hillier and Latour11) who reported decreasing in the regular mode frequency of the pressure spectrum downstream of a backward facing step. They attributed the decrease in frequency to changes in the shear-layer structure that occur upstream of the reattachment zone, until a constant shedding frequency is reached.
Figure 13. Vortex frequency distribution downstream of the reattachment location (α = 3° and Re = 1.0 × 106, k/c = 0.0433, s/c = 0.034).
3.4 Shear-layer flapping
As discussed before, the shear-layer flapping phenomenon is a low frequency source of unsteadiness associated with separation bubbles that is characterised by a vertical ‘flapping’ motion of the shear layer and a stream-wise oscillation of the shear-layer reattachment location. The effects of the shear-layer flapping phenomenon on the iced-aerofoil wake velocities of the aerofoil could be observed downstream of the aerofoil upper surface. As the separation bubble underwent a quasi-periodic surface-normal flapping, the streamlines just above the separation bubble were forced to oscillate with the flapping motion. This motion then cause the streamlines to sweep across the hot-wire probe in the wake downstream of the separation bubble according to the flapping frequency. An example of the shear-layer flapping mode in wake velocity spectra is shown in Fig. 14 for the iced aerofoil (k/c = 0.02 and s/c = 0.0174) at Reynolds number of 1.0 × 106 and angles of attack of α = 6° and 7°. Since the shear-layer flapping phenomenon has been observed to affect the entire separation bubble, its effects in the wake could be seen across the entire upper-surface wake region. Anyway, the shear-layer flapping mode were measured at x/c = 1.45 and y/c = 0.16. It should be stressed that these low-frequency oscillations are not attributed to any instabilities induced by the wind-tunnel fan. The frequencies of fan blade passing were identified as occurring at frequencies much higher than those observed for the shear-layer flapping mode.
Figure 14. Frequency of shear-layer flapping mode (Re = 1.0 × 106, k/c = 0.02, s/c = 0.0174), (a) α = 6°, (b) α = 7°.
Strouhal numbers based on the aerofoil projected height and the freestream velocity are calculated for the peak frequencies identified in wake velocity spectra (Stf). The Strouhal numbers associated with this shear-layer flapping mode correspond to Stf = 0.0210 and 0.0186. The values of Strouhal numbers of the shear-layer flapping mode are compared with those reported in the literature. A summary of this comparison is presented in Table 2.
Table 2 Comparison of Stf for shear-layer flapping determined in the current study with those reported in the literature
From Table 2, the values of Stf for shear-layer flapping obtained in the current study are consistent with the range of values reported in the literature. This suggests that the low-frequency peak that is identified in the current study with central frequency between 11 Hz and 13 Hz can be attributed to the same shear-layer flapping mechanism observed in separation bubble flowfields about iced aerofoils and simple geometries.
3.5 Turbulence intensity
The turbulence intensity contours for the separated shear-layer regions were found to be in agreement with results from other separated flows. In this case, the turbulence intensity was calculated as the root mean square of the fluctuating stream-wise velocity and normalised by the freestream velocity. An example of these data is shown in Fig. 15 for the iced aerofoil at α = 3° and 6° (k/c = 0.0433 and s/c = 0.034). The separated shear-layer is visible in RMS stream-wise velocity as the region where large fluctuations are observed(Reference Broeren and Bragg28). As shown in Fig. 15(a), a region with high velocity fluctuation in the range of 23%-28% in the middle of the separated shear layer in the vicinity of reattachment location is evident (the reattachment location is marked with a dashed line). This region of peak turbulence intensity begins downstream of x/c = 0.3, which has been identified as the location of maximum unsteadiness from the pressure data (Fig. 11(a)).
Figure 15. Contour of turbulence intensity, (a) α = 3°, (b) α = 6° (Re = 1.0 × 106, k/c = 0.0433, s/c = 0.034).
With increasing the angle-of-attack to 6° (Fig. 15(b)), the separation bubble fails to reattach; consequently, the flowfield separates completely. It is interesting to note that at α = 3° downstream of the reattachment location, the turbulence intensity levels decrease gradually, but at α = 6°, this high turbulence intensity region extends to downstream of trailing edge and the decay of maximum turbulent intensity cannot be seen until x/c = 1.2.
4.0 CONCLUSION
The main purpose of this investigation was to identify the dominant sources of unsteadiness in the flowfield of the separation bubble formed on a NACA 0015 aerofoil with glaze ice accretion. The unsteady flow features were determined using measurements of the time-dependent aerofoil surface pressure distribution and spectral analysis of stream-wise velocity fluctuations at a Reynolds number of 1.0 × 106. The maximum amount of unsteadiness (C′ p ) in the iced-aerofoil flowfield consistently resided upstream of the mean shear-layer reattachment location. In this study, the average location of maximum flowfield unsteadiness was determined at x/xMR = 0.8. Furthermore, spectral analysis of the stream-wise velocity fluctuations confirmed the existence of the two distinct sources of unsteadiness in the iced-aerofoil flowfield including the regular mode of vortical motion and the shear-layer flapping mode. The regular mode was attributed to flowfield unsteadiness due to vortical motion in the separated shear-layer and vortex pairing and shedding from the separation bubble. The centre frequency of the regular mode typically occurred between 220 Hz and 125 Hz. The effects of shear-layer flapping were observed across a narrow-band, low-frequency range. The centre frequency of the shear-layer flapping mode typically occurred between 11 Hz and 13 Hz.
