The influence of the flow separation bubble and transition location on the profile drag of three 4-digit NACA aerofoil profiles

Abstract

Modeling of the flow over aerofoil profiles at low Reynolds numbers is difficult due to the complex physics associated with the laminar flow separation mechanism. Two major problems arise in the estimation of profile drag: (1) the drag force at low Reynolds numbers is extremely small to be measured in a wind tunnel by force balance techniques, (2) the profile drag is usually calculated by pressure integration, hence the skin friction component of drag is excluded. In the present work, three different 4-digit NACA aerofoils are investigated. Measurements are conducted in an open-ended subsonic wind tunnel, while numerical work is performed by time Reynolds-averaged Navier Stokes (RANS) coupled with the laminar-kinetic-energy (K-kl-w) turbulence model. The influence of the flow separation bubbles and transition locations on the profile drag is discussed and addressed. This paper gives important insights into importance of measurements at low Reynolds numbers for better aerodynamic loads predictions.

Keywords

Profile drag low Reynolds number NACA aerofoil Reynolds-averaged Navier Stokes skin friction coefficient separation bubbles transition locations

Introduction

The laminar separation bubble (LSB) is formed in many practical flows as laminar boundary layer separation, transition to turbulence, and reattachment as shown in Figure 1(a). The length of the LSB depends on the transition process in the shear layer along with Reynolds numbers, angles of attack, and geometric shape of the aerofoil (Park et al., 2020). The appearance of the LSB can cause a significant influence on the aerodynamic characteristics of the aerofoil, such as aerodynamic noise, flow instability, decrease in lift and increase in pressure drag forces (Kojima et al., 2013; Winslow et al., 2018). The LSB can be characterized as a plateau in the pressure distribution through the laminar part of the separation bubble (where the flow velocity is circulated slowly leading to approximately zero pressure gradient), followed by a rapid pressure recovery through the turbulent part of the separation bubble (where the mixing and momentum transfer from the free-stream flow to the near-wall region is increased) (Jones et al., 2008; Marxen and Henningson, 2011; Ripley and Pauley, 1993; Spalart and Strelets, 2000; Watmuff, 1999). However, the trend of the pressure distribution under the inviscid flow conditions is different as illustrated in Figure 1(b).

Figure 1.

Schematic diagram of the LSB and its influence on the shape of pressure distribution: (a) laminar separation bubble and (b) pressure coefficient distribution.

The profile drag of the aerofoil usually increases with a rapid variation in the pressure, resulting in a LSB formation, which can be either short or long bubble. The short bubble is usually formed at low Reynolds numbers and its size decreases with any increase in the angle of attack until bursting occurs (Almutairi et al., 2010), forming either a long bubble or an unattached free shear layer. These cases are undesired since the bubble bursting leads to increasing the drag force, a reduction in lift, and an undesirable change in the pitching moment (Jahanmiri, 2011; Zhang et al., 2008). Indeed, the increase in the Reynolds number can also lead to the formation of a long bubble or an unattached free shear layer downstream (Lee et al., 2015).

Ohtake et al. (2007) investigated the characteristics of the NACA0012 aerofoil for angles of attack of 0°–14° at Reynolds number of 3 × 10³. It was observed that a separation bubble exists from the angle of attack of 0°–8°, which moves from the trailing edge to the leading edge of the upper surface of the aerofoil, influencing the transition point. On the other hand, at a Reynolds number of 1 × 10⁶, no separation bubble was observed.

Rinoie and Takemura (2004) performed measurements on a NACA 0012 aerofoil at a Reynolds number of 3 × 10³ to understand the flow behavior of the laminar separation bubble. It was shown that a long separation bubble is formed after the occurrence of a short bubble bursting at an angle of attack of 8°. This behavior is specifically followed by high oscillation of the flow between a short leading edge separation-reattachment bubble and a long separation bubble that is extended over most of the aerofoil upper surface. The same was also observed by Reda (1991) and Zaman et al. (1989).

Rinoie et al. (1990) used a laser doppler anemometry (LDA) to measure the mean velocity and turbulent stress distributions of short and long separation bubbles on NACA 63-009 at the Reynolds number of 8 × 10⁴ and angles of attack of 7° and 9°. At the angle of attack of 7°, a short separation bubble appears with a maximum shear stress upstream of the reattachment point, while at angle of attack of 9°, the maximum shear stress is found to be far from the reattachment point.

Park et al. (2020) conducted measurements on DAE51 aerofoil using particle image velocimetry (PIV) at five Reynolds numbers from 3.9 × 10⁴ to 1.18 × 10⁵ at angles of attack ranging from 0° to 10°. It was found that the formation of the separation bubble depends mainly on the Reynolds number and angle of attack. The separation and reattachment points are observed to move upstream with increasing angle of attack, but the separation bubble size decreases as the angle of attack is increased. Furthermore, the transition length tends to be shorter when Reynolds number is increased.

Lei et al. (2019) investigated the appearance of the LSB on the NACA2415 airfoil at a low Reynolds number of 2 × 10⁵, from 0° to 8° angles of attack. It was shown that the separation bubble appears at the middle chord of the aerofoil upper surface at 4°. Its length reduces in size and moves toward the airfoil leading edge when the angle of attack is increased to 8°. The same NACA2415 airfoil was experimentally investigated by Karasu et al. (2012) at Reynolds number of 5 × 10⁴ and angle of attack of 0°–15°, using hot-wire and flow visualization via smoke wire technique. For an angle of attack of 4°, Lei et al. (2019) reported that the length of the flow separation bubble is 23% chord, while Karasu et al. (2012) found that it is 40% chord. The difference in these results is primarily due to the influence of Reynolds number.

Development of the boundary layer on the aerofoil surfaces is due to the influence of air viscosity, in which the resulting skin friction, depending on the flow conditions, can significantly contribute to the total drag or profile drag, which is the sum of skin friction and pressure drag contributions (Eppler, 2003; Phillips, 1988). The drag force is created due to the reduction in streamwise momentum presented in the boundary layer. The wake formed downstream of the aerofoil profile has a momentum deficit that results from the developed boundary layer on the upper and lower surfaces of the aerofoil (Eppler, 2003; Phillips, 1988). Since there is a direct relationship between the profile drag and the existing momentum deficit downstream of the aerofoil, an integration scheme is commonly applied to estimate the drag force from the wake pressure/velocity distributions (Barlow et al., 1999; Ellen and Goetz, 2013).

There are three main wake survey types used to collect pressure data behind an aerofoil section. These are the (1) conventional wake rake, (2) traversing probe, and (3) integrating wake rake (Barlow et al., 1999; Popelka et al., 2011). The conventional wake consists of a series of pitot probes to cover the entire range of the wake, in which the pressure data are collected by the use of a manometer, individual pressure transducers or a scanivalve (Arunvinthan and Nadaraja Pillai, 2019). The advantage of this method is the ability to accurately determine the height and shape of the wake, and subsequently the drag force. The traversing wake probe contains a mechanical actuator that moves the wake-survey probe along with one transducer to capture the width of the wake. However, surveying the wake by the probe is a challenge since stable flow conditions are necessary. The integrating wake rake is a simpler method that is reasonable to the conventional wake survey, but its individual tubes are connected to a single manifold in order to collect and average the pressure data under equilibrium conditions (Barlow et al., 1999; Popelka et al., 2011).

Modeling the flow over aerofoils at low Reynolds numbers is still challenging, especially in the presence of laminar separation and transition to turbulent flow. This is particularly attributed to the complex physical behavior of laminar separation bubbles. Furthermore, there are large discrepancies in the aerodynamic loads determined from different wind-tunnel facilities (Abdallah et al., 2015; Bottasso et al., 2014; Robert, 2016). The reasons behind this disparity of the results are mainly related to the differences in free-stream turbulence characteristics, wind tunnel corrections, and measurement techniques. For instance, Guglielmo and Selig (1996) and Selig et al. (1995) suggested that measurement of the extremely small drag force on aerofoils at low Reynolds number should be conducted by the momentum method rather than a force balance for better accuracy, while the lift force can be obtained with acceptable accuracy by a force balance. To the authors’ knowledge, there is a lack of analysis for the relation between friction drag and pressure drag along with the influence of laminar separation bubbles on the profile drag components at low Reynolds numbers. Thus, accurate profile drag measurements in wind-tunnel are still required.

This paper is intended to provide important insights for performing measurements or computational fluid dynamics (CFD) simulations on aerofoil profiles at low Reynolds numbers, for better predictions of the profile drag. The paper first presents an overview of the wind tunnel facilities and the used correction method along with the tested aerofoil models. The theory of the wake survey and measurements of the wake pressure profiles are then described, followed by an overview on the time Reynolds-averaged Navier Stokes (RANS) and the selected laminar-kinetic-energy (K-kl-w) turbulence model. Validations and discussions are finally given to reveal the influence of various parameters such as the laminar separation bubble, transition and turbulent reattachment on the profile drag at Reynolds number of 3 × 10⁵.

Wind tunnel facilities and corrections

In the present paper, the measurements are conducted in an open-ended subsonic wind tunnel located at the laboratory of the Omar Al-Mukhtar University, Derna, Libya. The subsonic wind tunnel, being shown in Figure 2, has a five-bladed fan driven by a DC variable speed motor unit located downstream of the working section in order to create airspeed in the test section up to 26 m/s, whereas the inlet of the tunnel has an aluminum honeycomb flow straightener to provide a uniform flow and also to break the large vortexes to small vortexes within the working test section. The wind tunnel turbulence intensity at the maximum airspeed is 0.5% and the mean velocity variation is ±0.2 m/s. The dimensions of the wind tunnel are shown in Table 1. The airspeed and static pressure in the wind tunnel can be read directly by calibrated inclined and multi-tube manometers. The first is connected to a manifold surrounding the upstream end of the working test section, while the latter is connected with four equally spaced static orifices to minimize the interference effects which may occur from the tested model in the working test section.

Figure 2.

Open-ended subsonic wind tunnel.

Table 1.

Dimensions of the subsonic wind tunnel.

Total length (m)	Total height (m)	Total width (m)	Test section (cm)
2.98	1.83	0.80	30 × 30 × 45

The title angle of the multi-tube manometer can be adjusted to three different angles of 30°, 40.8°, and 90°. The subsonic wind tunnel also has a wake rake and pitot static tube (see Figure 3(a) and (b)) connected to the multi-tube manometer by tappings in order to measure the difference in pressure between the total and static tappings using equation (1), and subsequently to determine the air speed in the working test section with the use of equation (2).

Δ P = ρ_{w} g Δ h

(1)

U_{\infty} = \sqrt{\frac{2 Δ P}{ρ_{air}}}

(2)

Figure 3.

(a)Pitot tube and (b) wake rake used with the subsonic wind tunnel measurements.

where r_air is the air density (kg/m³), DP is the difference in pressure between the total and static tappings (N/m²), g is the acceleration due to gravity (m/s²), U_∞ is the free stream velocity, and Dh is the difference in the multi-tube water height (m).

Although wind tunnels are powerful tools to perform measurements under an unbounded air stream, inaccurate measurements can exist due to the solid tunnel boundaries which lead to variations in the flow field from the real free-air flow. This, in turn, can cause differences in the aerodynamic forces acting on the aerofoil body. More specifically, four different phenomena are created by the wind tunnel walls: (1) horizontal buoyancy, (2) solid blockage, (3) wake blockage, and (4) streamline curvature. These corrections are all considered in the current measurements based on the work of Barlow et al. (1999) and Allen and Vincenti (1944).

Descriptions of the wind tunnel aerofoil models

Three different aerofoil profiles, namely: NACA0015, NACA6415, and NACA6421, developed by the National Advisory Committee for Aeronautics (NACA) (Anderson and Anderson, 2002) were fabricated, each with a chord of 10 cm. The models were investigated experimentally in the subsonic wind tunnel (see Section 2) to reveal the influence of wake on the profile drag (due to contribution of pressure drag and skin friction). As seen from Figure 4, the NACA0015 aerofoil has no camber, with a maximum thickness of 12% of the chord. On the other hand, the NACA6415 has a maximum camber of 6%, located 40% (0.4 chords) from the leading edge with a maximum thickness of 15% of the chord, whereas the NACA6421 aerofoil has a maximum camber of 6% located 40% (0.4 chords) from the leading edge with a maximum thickness of 21% of the chord. These aerofoil profiles have been selected in this study in order to investigate the influence of the flow separation bubbles and transition considering different aerofoil geometries (i.e. symmetry, thickness, and camber).

Figure 4.

The geometry of the NACA0015, NACA 6415, and NACA6421 aerofoil profiles.

Wake survey theory and profile drag measurements

The basic idea of the wake survey methods is to compare the measured static pressure and the decrease in the total pressure of the downstream wake with the free-stream total pressure. The loss of momentum (pressure deficit) of the flow is in a direct relationship with the profile drag. In this work, the profile drag is determined based on the method of Schlichting (1960).

Figure 5 illustrates the velocity distributions upstream and downstream of an aerofoil, where the momentum loss of the flow is clearly seen. The total pressure deficit is a maximum at the center of the wake and recovers to the free-stream total pressure at the wake edge. The profile drag is determined by integrating the difference in the pressure readings upstream and downstream of the aerofoil, representing the total momentum loss. Using Bernoulli’s equation, the profile drag coefficient can be determined as a function of the total pressure deficit as

C_{D} = \frac{1}{c q_{\infty}} \int_{wake} (p_{t \infty} - p_{t}) dy

(3)

q_{\infty} = 0.5 ρ_{air} U_{\infty}^{2}

(4)

Figure 5.

Schematic of the velocity/pressure deficit in the wake.

where c is the aerofoil chord, q_∞ is the dynamic pressure, and p_t is the total pressure.

It is vital to ensure that the wake pressure deficit is measured at a sufficient location downstream from the trailing edge to ensure that the static pressure is recovered to free-stream conditions.

Figure 6 shows the experimental setup for the location of the wake rake survey (horizontal wake traverse consists of 18 total-head pressure measurements spaced 4 mm) downstream of the aerofoil in the subsonic wind tunnel. The wake measurements were conducted 10 cm (1 c) downstream of the aerofoil trailing edge to make sure that the wake is recovered to the wind tunnel static pressure. In this work, it should be noticed that the measured pressure distributions downstream of the aerofoil profiles were limited to the angles of attack ranging from 0° to 6°. This is due to the fact that the wake deflections from the upper and lower surfaces increase with increasing the angle of attack and Reynolds number. Therefore, the wake was merely captured only up to an angle of attack of 6°. Outside of that range, the wake rake could not be moved to handle the associated wake deflections. However, it is still reasonable to analyze the profile drag for the angles of attack between 0° and 6°, given that there is no stall (causing large wake size and wake unsteadiness) and the flow separation bubble is often present within that range.

Figure 6.

Measurements of the pressure distribution in the downstream wake of the aerofoil in the subsonic wind tunnel.

Governing equations, turbulence model, computational grid, boundary conditions, and sensitivity analysis

The time Reynolds-averaged Navier Stokes (RANS) along with the laminar-kinetic-energy (K-kl-w) turbulence model (Walters and Cokljat, 2008) are used in this work to analyze the flow around and downstream of the aerofoil profiles (see Section 3). The RANS equations are: the continuity equation, representing the conservation of mass, and the momentum equation, representing the conservation of momentum. The basic forms of these equations are:

\frac{\partial ρ}{\partial t} + \frac{\partial}{\partial x_{i}} (ρ u_{i}) = 0

(5)

\frac{\partial}{\partial t} (ρ u_{i}) + \frac{\partial}{\partial x_{j}} (ρ u_{i} u_{j}) = - \frac{\partial p}{\partial x_{i}} + \frac{\partial}{\partial x_{j}} [μ (\frac{\partial u_{i}}{\partial x_{j}} + \frac{\partial u_{j}}{\partial x_{i}} - \frac{2}{3} δ_{ij} \frac{\partial u_{i}}{\partial x_{j}})] + \frac{\partial}{\partial x_{j}} (ρ \bar{u_{i}^{'} u_{j}^{'}})

(6)

where t is the time, r is the fluid density, m is the molecular viscosity, p is the ensemble averaged pressures, u_i and u_j are the ensemble averaged velocity vectors in the i-and j-directions, x_i and x_j are position vectors, u_i′ and u_j′ are the turbulent fluctuating velocities in the i-and j-directions respectively, (r $\bar{u}'_{i}$ ^¯ $\bar{u}'^{\bar{}}$ ) is the Reynolds stress term, and d_ij is the Kronecker delta.

The laminar-kinetic-energy (K-kl-w) turbulence model (Walters and Cokljat, 2008) is developed for transition flows. This model was found to be very reliable by Choudary et al. (2015) for estimation of the flow separation bubble formation, growth, transition, and reattachment, and hence it was selected in this work. The model solves three transport equations for laminar and turbulent kinetic energy and the specific dissipation rate as follows:

\frac{D k_{T}}{Dt} = P_{k_{T}} + R_{BP} + R_{NAT} - ω k_{T} - D_{T} + \frac{\partial}{\partial x_{j}} [(υ + \frac{α_{T}}{σ_{k}}) \frac{\partial k_{T}}{\partial x_{j}}]

(7)

\frac{D k_{L}}{Dt} = P_{k_{L}} - R_{BP} - R_{NAT} - D_{T} + \frac{\partial}{\partial x_{j}} [υ \frac{\partial k_{L}}{\partial x_{j}}]

(8)

\frac{D ω}{Dt} = C_{ω 1} \frac{ω}{k_{T}} P_{kT} + (\frac{C_{ω R}}{f_{W}} - 1) \frac{ω}{k_{T}} (R_{BP} + R_{NAT}) - C_{ω 2} ω^{2} + C_{ω 3} f_{ω} α_{T} f_{W}^{2} \frac{k_{T}^{1 / 2}}{d^{3}} + \frac{\partial}{\partial x_{j}} [(υ + \frac{α_{T}}{σ_{ω}}) \frac{\partial ω}{\partial x_{j}}]

(9)

In these equations, k_T and k_L are utilized to model the turbulent kinetic energy and the laminar kinetic energy respectively and w is the scale-determining variable which is modeled as w = e/kT, where e is the isotropic dissipation, P_kT and P_kL are the production of turbulent and laminar kinetic energy by mean strain respectively, f_W is the inviscid near-wall damping function, aT is the effective diffusivity for turbulence dependent variables, C_wR, C_w1, C_w2, C_w3, sk, sw are constants, d is the wall distance, R_BP is the bypass transition production term, R_NAT is the natural transition production term, u is the kinematic viscosity, D_T is the anisotropic near-wall dissipation term for k_T, and f_w is the boundary layer wake term damping function in w equation. More details can be found in the work of Walters and Cokljat (2008).

The CFD simulations were performed by the free open source code, OpenFoam, with structured grids for modeling the flow around the aerofoil profiles. The length of the computational domain was 32.5 times of the chord length and the width was 25 times of the chord length. These are reasonable to ensure that the air flow is fully expanded as depicted in Figure 7. In all the CFD simulation results, turbulence intensity of 0.05% and characteristic turbulence intensity of 0.05% were also considered.

Figure 7.

The geometry and boundary conditions of the flow computational domain.

For the computational domain presented in Figure 7, various grids/meshes were utilized using quadrilateral cells as shown in Table 2. Each grid was made very dense (with a starting cell height of 1e⁻⁴) close to the aerofoil surface to predict the pressure gradient at the boundary layer with sufficient accuracy. This is vital since the adverse pressure gradient causes the flow separation. On the other hand, the far-field computational domain was made with a standard grid because the flow gradients approach zero away from the aerofoil.

Table 2.

Comparisons of the lift force coefficients of NACA0015 aerofoil between experiment (Rethmel, 2011) and CFD results for different grids at α = 12° at Re = 1 × 10⁵ and 1 × 10⁶.

Grids	Number of cells	Average y⁺	Re = 1 × 10⁵		Re = 1 × 10⁶
			C_L (Exp.)	C_L (CFD)	C_L (Exp.)	C_L (CFD)
Grid 1	6200	49.5	0.90 ± 0.05	0.730	1.12 ± 0.05	1.326
Grid 2	10,080	34.8	0.90 ± 0.05	0.810	1.12 ± 0.05	1.315
Grid 3	219,600	2.06	0.90 ± 0.05	0.906	1.12 ± 0.05	1.212
Grid 4	379,160	0.45	0.90 ± 0.05	0.901	1.12 ± 0.05	1.118

From Table 2, it is obvious that the results of grids 1 and 2 are still far compared to measurements (Rethmel, 2011), while the grids 3 and 4 give satisfactory results. The average wall y⁺ distributions over the NACA0015 aerofoil at α = 12° at Re = 1 × 10⁵ and 1 × 10⁶ are presented in Table 2. Figure 8 shows the wall y⁺ distributions over NACA0015 aerofoil at α = 12° for Grids 3 and 4. In this study, the wall y⁺ was selected to be <1 for best accuracy (Versteeg and Malalasekera, 2007). Therefore, the Grid 4 has been selected for simulating the flow around and downstream of the aerofoil in this work as depicted in Figure 9. This analysis also shows a clear evidence for validation of the obtained results from the CFD OpenFoam code with the K-kl-w turbulence model for the determined lift force coefficients, given that the agreement with the experimental results (Rethmel, 2011) is good for low and high Reynolds numbers.

Figure 8.

y ⁺ distribution over the NACA 0015 aerofoil at α = 12°.

Figure 9.

Mesh of the computational domain and around the aerofoil using the structured grid: (a) mesh of the computational domain and (b) mesh around the aerofoil surfaces.

The pressure distributions on the upper and lower surfaces of the NACA0015 aerofoil were also measured in the subsonic wind tunnel (Figure 2) at angles of attack of 10° and 15° at Re = 3 × 10⁵. The pressure coefficient distributions were then determined using the equation below:

C_{p} = \frac{P_{i} - P_{\infty}}{\frac{1}{2} ρ U_{\infty}^{2}}

(10)

where P_i is the surface pressure measured at location i on the surface. The results are presented in Figure 10. Very good agreement was obtained between measurements and the CFD results.

Figure 10.

Comparisons of the pressure coefficients of NACA0015 aerofoil between measurements and CFD results at α = 10° and 15° at Re = 3 × 10⁵: (a) α = 10° and (b) α = 15°.

Results and discussion

To determine the profile drag under the effect of the aerofoil wake, measurements were performed 10 cm downstream of the trailing edges of the NACA0015, NACA6415, and NACA6421 aerofoils at a Reynolds number of 3 × 10⁵ and angles of attack of 4° and 6°. The measured wake pressure profiles are illustrated in Figure 11. The measured downstream velocity deficits along with the CFD results are shown in Figures 12 to 14. The error bars corresponding to these measurements represent the standard deviation determined at each wake rake position downstream of the aerofoil. For each measured data set, a total of 30 data points were recorded at each downstream wake rake position, making 540 data points for the whole data set. The measured data throughout the tests were binned and the standard deviations were calculated at each bin accordingly as presented in Figures 11 to 14. The minimum and maximum standard deviations in the pressure loss, normalized by the mean values, were found to be 0.02 and 0.12. The corresponding values for the velocity distributions were found to be 0.01 and 0.05, respectively.

Figure 11.

Measurements of the downstream wake pressure profiles at Re = 3 × 10⁵: (a) NACA0015, (b) NACA6415, and (c) NACA6421

Figure 12.

Wake velocity profiles of NACA0015 aerofoil at Re = 3 × 10⁵. The wake rake is located 10 cm (1 chord) downstream, where velocity profiles are measured: (a) CFD velocity distributions at α = 4°, (b) wake velocity deficit at α = 4°, (c) CFD velocity distributions at α = 6°, and (d) wake velocity deficit α = 6

Figure 13.

Wake velocity profiles of NACA6415 aerofoil at Re = 3 × 10⁵. The wake rake is located 10 cm (1 chord) downstream, where velocity profiles are measured: (a) CFD velocity distributions at α = 4°, (b) wake velocity deficit at α = 4°, (c) CFD velocity distributions at α = 6°, and (d) wake velocity deficit α = 6.

Figure 14.

Wake velocity profiles of NACA6421 aerofoil at Re = 3 × 10⁵. The wake rake is located 10 cm (1 chord) downstream, where velocity profiles are measured: (a) CFD velocity distributions at α = 4°, (b) wake velocity deficit at α = 4°, (c) CFD velocity distributions at α = 6°, and (d) wake velocity deficit α = 6°.

The white dashed lines in Figures 12 to 14 represent the wake centerline. It is obvious from these results that the wake thickness increases monotonically as the angle of attack increases and the velocity outside of the wake zone recovers to the free stream velocity at a distance of 10 cm from the trailing edge. The normalized total pressure loss (DP_total/q_∞) outside of the wake zone indicates almost zero values, which mean that the wake is recovered to the free-stream conditions. Indeed, the shifts occurred in the wake centerline match those observed on the wake pressure profiles for all test cases. This ensures the accuracy of the measurements and the determined profile drag with the use of the wake survey method presented in Section 4.

Table 3 shows the measured profile drag in comparison to the CFD OpenFoam code with the K-kl-w turbulence model (see Section 5) along with the absolute true relative errors. From these results, beside the influences of the aerofoil thickness and curvature, it seems that the angle of attack, Reynolds number, and the formation of the wake downstream of the aerofoil play an important role on the magnitudes of the profile drag. From Figures 11 to 14 and Table 3, it can be observed that the momentum loss increases with increasing angle of attack since the wake size becomes larger and the turbulent stress is higher in the flow separation zone (Rinoie et al., 1990). This influence indicates that the transition location from laminar to turbulent flow, the laminar separation bubble, and the developed wake are significant. The aerofoil thickness has also a significant effect on the profile drag. As the aerofoil thickness increases, the drag force coefficient also increases as illustrated in Table 3 for the thicker NACA6421 aerofoil profile compared to the others. It is also clear that both measurements and CFD results are, to some extent, in a good agreement.

Table 3.

Comparison between measurements and CFD results of the profile drag at Re = 3 × 10⁵.

α	NACA0015			NACA6415			NACA6421
α	CFD	Exp.	Error (%)	CFD	Exp.	Error (%)	CFD	Exp.	Error (%)
4°	0.009	0.009	0	0.015	0.016	6.2	0.015	0.017	11.7
6°	0.012	0.013	7.6	0.025	0.025	0	0.019	0.019	0

In Figure 12, it can be seen that when the angle of attack is increased from 4° to 6°, the wake of the NACA0015 aerofoil is deflected to the pressure side of the aerofoil. Indeed, the wake velocity deficit is significantly increased which indicates a higher profile drag as seen from Table 3. From Figures 13 and 14, it could be observed that the wake flows of the NACA6415 and NACA6421 aerofoils are also shifted toward the pressure side with higher wake velocity deficits (higher profile drags) than those observed on the NACA0015 aerofoil with increasing the angle of attack. The highest profile drag observed on the NACA6415 aerofoil (see Table 3) can be explained after careful examination for Figure 13. In this figure, when the boundary layer separates, its displacement thickness is increased, and subsequently the wake flow becomes wider resulting in an increase in total drag.

Table 4 presents the CFD results of the profile drag along with its pressure and skin friction components at Re = 3 × 10⁵. In these results, the skin friction accounts for 46.6% and 40.8% of the total drag at α = 4° and 6° respectively for the NACA0015 aerofoil, while for the NACA6415 aerofoil, these are 32% and 30% of the total drag. These percentage values are reduced further for the NACA6421 aerofoil to be 26% and 23% respectively.

Table 4.

CFD result of profile drag, pressure drag (C_Dp) and skin friction drag (C_Df) at Re = 3 × 10⁵.

α	NACA0015			NACA6415			NACA6421
	C_D	C_Dp	C_Df	C_D	C_Dp	C_Df	C_D	C_Dp	C_Df
4°	0.009	0.0048	0.0042	0.015	0.0102	0.0048	0.015	0.0111	0.0039
6°	0.012	0.0071	0.0049	0.025	0.0175	0.0075	0.019	0.0146	0.0044

Currently, it is obvious that the skin friction components for the symmetrical NACA0015 aerofoil make higher percentage values of the total drag compared to the others. Indeed, these are reduced with increasing angle of attack, camber, and thickness. In the following discussion, the relation between the flow separation bubble and the profile drag components will be further revealed.

The locations of the laminar separation (x_s/c), transition (x_t/c), and reattachment (x_r/c) on the upper surfaces of the NACA0015, NACA6415, and NACA6421 aerofoils at angles of attack of 4° and 6° at Re = 3 × 10⁵ are presented in Table 5. These results are determined based on the skin friction coefficient depicted in Figures 15(a) to 17(a). It should be noted here that the exact location of the transition point is hard to predict because it depends on various parameters such as roughness, Reynolds number, pressure gradient, level of flow turbulence, and surface heat flow. Therefore, its location is roughly approximated from the skin friction coefficient distributions. More specifically, the methodology utilized to identify the location of the laminar separation (x_s/c) and reattachment (x_r/c) points is by observing a reduction in the skin frictions to nearly zero/negative values for the laminar separation points and changing sign from negative to positive for the reattachment points, whereas the transition points are identified by a sudden raise in the skin friction coefficients. The LSB is also evident from the jump in the pressure coefficient C_p distributions illustrated in Figures 15(b) to 17(b), which is consistent with a strong adverse pressure gradient, leading transition to turbulent flow. The skin friction coefficients for the laminar boundary layer are lower than those for the turbulent boundary layer. In Table 5, it is obvious that the location of the transition moves toward the leading edge with increasing angle of attack. This behavior is due to the increase in the pressure gradients close to the leading edge that lead to earlier separation and the increase in the disturbance levels that yield to earlier reattachment. Interestingly, the NACA0015 aerofoil has closer laminar separation and transition points to the leading edge than those on the NACA6415 and NACA6421 aerofoil profiles. The lengths of the flow separation bubbles observed on the NACA0015 aerofoil are also longer than the others as given in Table 5. The lengths of the flow separation bubbles on the NACA6415 and NACA6421 aerofoils are on average 11% of the chord. The locations of their transition points are also nearly the same.

Table 5.

Locations of the separation (x_s/c), transition (x_t/c), reattachment (x_r/c) points, and separation bubble length (L) on the upper surfaces of the NACA0015, NACA6415, and NACA6421 aerofoils at Re = 3 × 10⁵.

α	NACA0015				NACA6415				NACA6421
α	xs/c	xt/c	xr/c	L (%c)	xs/c	xt/c	xr/c	L (%c)	xs/c	xt/c	xr/c	L (%c)
4°	0.30	0.43	0.46	16	0.40	0.46	0.52	12	0.38	0.45	0.48	10
6°	0.17	0.26	0.30	13	0.37	0.40	0.49	12	0.36	0.45	0.48	12

Figure 15.

Distributions of the skin friction and pressure coefficients on the upper surface of the NACA0015 aerofoil at Re = 3 × 10⁵: (a) skin friction coefficient and (b) pressure coefficient.

Figure 16.

Distributions of the skin friction and pressure coefficients on the upper surface of the NACA6415 aerofoil at Re = 3 × 10⁵: (a) skin friction coefficient and (b) pressure coefficient.

Figure 17.

Distributions of the skin friction and pressure coefficients on the upper surface of the NACA6421 aerofoil at Re = 3 × 10⁵: (a) skin friction coefficient and (b) pressure coefficient.

The relation between the flow separation bubble lengths (Table 5) and the profile drag components (Table 4) depends mainly on the aerofoil geometry. Comparing the NACA0015 and NACA6415 aerofoils, which have the same thickness and different cambers, it could be seen that the symmetrical NACA0015 aerofoil has longer LSB and higher skin friction drag, whereas the NACA6415 aerofoil has shorter LSB, but higher pressure drag. On other hand, comparing the NACA6415 and NACA6421 aerofoils, which have the same camber and different thicknesses, it could be observed that the thickness leads to increasing the pressure drag although both aerofoils have almost the same flow separation bubble lengths. Overall, it is clear that the pressure drag is very important component of the profile drag as it accounts for around 60%–80% of the profile drag.

Since the NACA0015 aerofoil has different LSB length, while the NACA6415 and NACA6421 aerofoils have the same LSB lengths, it is interesting to investigate the influence of the LSB length on the total drag components with respect to the aerofoil camber and thickness. Therefore, the absolute differences between the pressure and skin friction drag components of these aerofoils (see Table 4) are calculated and presented in Table 6. In these results, it is obvious that the absolute differences in the pressure and skin friction drag components between the NACA0015 and NACA6415 aerofoils are totally different, whereas, the differences between NACA6415 and NACA6421 aerofoils are almost the same as shown from Table 6 at different angles of attack. This indicates that the LSB has the same influence on the total drag components of the NACA6415 and NACA6421 aerofoils at different angles of attack as long as the lengths are equal, while the effect on the total drag is different at various angles of attack if the LSB has different lengths.

Table 6.

The absolute differences between the pressure and skin friction drag components of NACA0015 and NACA6415 aerofoils, and NACA6415 and NACA6421 aerofoils.

α	NACA0015 and NACA6415		NACA6415 and NACA6421
α	\|DC_Dp\|	\|DC_Df\|	\|DCDp\|	\|DC_Df\|
4°	0.0054	0.0006	0.0009	0.0009
6°	0.0104	0.0026	0.0029	0.0031

Figures 18 to 23 show the velocity profiles and Reynolds stress distributions near the detected flow separation bubbles at the angles of attack of 4° and 6° at Re = 3 × 10⁵. From these results, the LSB reduces in size and moves toward the leading edge of the aerofoil as the angle of attack increases. Due to the adverse pressure gradient, the reversed flow inside the turbulent part of the flow separation bubbles are higher than those occurring in the laminar separation parts of the flow separation bubbles and also in the flow separation zone downstream of the flow separation bubbles. As already illustrated from Figures 15(a) to 17(a), it is noticed that the shear boundary layer separates without turbulent separation for the NACA0015 aerofoil, while turbulent separations at the trailing edges of the NACA6415 and NACA6421 aerofoils are clearly seen. This is followed by higher Reynolds stress distributions at the vicinity of the laminar separation bubbles of the NACA6415 and NACA6421 aerofoils (see Figures 20 –23). This behavior could explain the reasons behind the increase in the drag force coefficients for the NACA6415 and NACA6421 aerofoils, given that the components of the pressure and skin friction drags encountered by these aerofoils get increased compared with the NACA0015 aerofoil. On the other hand, the high growth rates of turbulent fluctuations on the NACA6415 and NACA6421 aerofoils yield to delay in separation and reattachment and a thinner turbulent boundary layer compared to the NACA0015 aerofoil. These benefit the lift force coefficient as they lead to a greater increase in lift force coefficients, and subsequently in the lift-to-drag ratios as depicted in Table 7. Indeed, it is should be noted that although the lift force coefficient increases as long as the LSB is long, the associated drag also increases, leading to degrade in the overall lift-to-drag ratio as occurred on the NACA0015 aerofoil (see Table 7).

Figure 18.

Velocity profile and Reynolds stress distributions with stream lines of the laminar separation on NACA0015 aerofoil at α = 4° at Re = 3 × 10⁵.

Figure 19.

Velocity profile and Reynolds stress distributions with stream lines of the laminar separation bubble on NACA0015 at α = 6° at Re = 3 × 10⁵.

Figure 20.

Velocity profile and Reynolds stress distributions with stream lines of the laminar separation bubble on NACA6415 at α = 4° at Re = 3 × 10⁵.

Figure 21.

Velocity profile and Reynolds stress distributions with stream lines of the laminar separation bubble on NACA6415 at α = 6° at Re = 3 × 10⁵.

Figure 22.

Velocity profile and Reynolds stress distributions with stream lines of the laminar separation bubble on NACA6421 at α = 4° at Re = 3 × 10⁵.

Figure 23.

Velocity profile and Reynolds stress distributions with stream lines of the laminar separation bubble on NACA6421 at α = 6° at Re = 3 × 10⁵.

Table 7.

Lift-to-drag ratios at Re = 3 × 10⁵.

α	NACA0015	NACA6415	NACA6421
4°	36.661	75.672	60.499
6°	50.332	77.793	61.599

The relationship between the flow field, the airfoil geometry and the angle of attack is a function of the wake thickness (see Figures 11 –14). The formation of thinner laminar separation bubbles (see Figures 18 –23) are suppressed due to the interaction with the wake, which has a momentum deficit created by the developed boundary layer on the upper and lower surfaces of the aerofoil. Therefore, the level of reduction/increase in streamwise momentum of the developed boundary layer is mainly responsible for creating low/high drag forces on the aerofoil.

Conclusion

The current paper presented an experimental approach to determine the profile drag of three different aerofoil profiles at relatively low Reynolds number of 3 × 10⁵. The measurements were conducted in an open-ended subsonic wind tunnel. The collected wake pressure data were achieved by a wake survey method. Further important information regarding the laminar separation bubbles and transition locations were obtained by the time Reynolds-averaged Navier Stokes (RANS) integrated with the laminar-kinetic-energy (K-kl-w) turbulence model. The following summarizes the main conclusions from this study:

Comparisons of the CFD results (RANS equations coupled with K-kl-w turbulence model) with measurements of the profile drag showed that the former is reasonably accurate numerical tool for modeling the flow physics around the aerofoil and in the downstream wake.

Comparisons of the profile drag of the NACA0015, NACA6415, and NACA6421 aerofoils at angles of attack of 4° and 6° at Re = 3 × 10⁵ have shown that:

The NACA6415 and NACA6421 aerofoils have almost the same laminar separation length of 11% chord and transition locations of 0.45 and 0.43 c, respectively. It was found that the influence of the laminar separation bubble on the profile drag components of these aerofoils is the same at various angles of attack. The effect of the LSB on the profile drag components is different as long as the LSB has different lengths.

It was found that the symmetrical aerofoil encounters a high skin friction drag (around 40% of the total drag) and a low lift-to-drag ratio compared to the cambered aerofoils in which the skin friction drag accounts for approximately 20%–30% of the total drag, but with a high lift-to-drag ratio.

The NACA6421 aerofoil experiences a higher drag profile than the NACA6415 aerofoil owing to the thickness of the aerofoil. It also exhibits higher turbulent stresses in the vicinity of the laminar separation bubble, turbulent reattachment and separation, and higher velocity fluctuations in the downstream wake. These yield high momentum of the flow around the aerofoil, but less pressure difference (preserves lower surface pressure) compared to the NACA6415 aerofoil.

The lengths of the laminar separation bubbles at angles of attack of 4° and 6° for the NACA0015 aerofoil were found to be 20% and 15% chord, respectively. Although a long separation bubble benefits the lift coefficient, the drag is increased and the lift-to-drag ratio is subsequently degraded. More specifically, long separation bubbles result in an increase in lift but greater increase in drag, particularly if the laminar separation bubble is close to the leading edge of the aerofoil.

It was observed that the shear boundary layer separates without turbulent separation for the NACA0015 aerofoil, whereas turbulent separations at the trailing edges of the NACA6415 and NACA6421 aerofoils were found with higher Reynolds stress distributions at the vicinity of the laminar separation bubbles. On the other hand, the high growth rates of turbulent fluctuations on the NACA6415 and NACA6421 aerofoils was found to cause delay in separation and reattachment and a thinner turbulent boundary layer compared to the NACA0015 aerofoil. This behavior mainly benefits the lift force coefficient.

The current study was conducted at low angles of attack because no flow separation bubbles were detected at high angles of attack, particularly at stall. Therefore, it is being recommended that further work investigates the influence of the flow LSBs on the profile drag components of aerofoils having LSBs near/at stall.

The current study emphasizes on the necessity of conducting tests in wind tunnels at low Reynolds numbers using momentum methods, given that it is not reliable to measure the profile drag by force balance techniques since the drag forces on aerofoils at low Reynolds numbers are very small. This is of significance for analysts and designers to improve aerofoil profiles with better design.

Footnotes

Appendix

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Moutaz Elgammi

References

Abdallah

Natarajan

Sørensen

(2015) Impact of uncertainty in airfoil characteristics on wind turbine extreme loads. Renewable Energy 75: 283–300.

Allen

Vincenti

(1944) Wall interference in a two-dimensional-flow wind tunnel, with consideration of the effect of compressibility. NACA-TR-782.

Almutairi

Jones

Sandham

(2010) Intermittent bursting of a laminar separation bubble on an airfoil. AIAA Journal 48: 414–426.

Anderson

Jr (2002) The Airplane, a History of Its Technology. Reston: AIAA.

Arunvinthan

Nadaraja Pillai

SNS

(2019) Aerodynamic characteristics of unsymmetrical aerofoil at various turbulence intensities. Chinese Journal of Aeronautics 32(11): 2395–2407.

Barlow

Rae

Alan

(1999) Low-Speed Wind Tunnel Testing, 3rd edn. New York, NY: John Wiley & Sons.

Bottasso

Cacciola

Iriarte

(2014) Calibration of wind turbine lifting line models from rotor loads. Journal of Wind Engineering and Industrial Aerodynamics 124: 29–45.

Choudhry

Arjomandi

Kelso

(2015) A study of long separation bubble on thick airfoils and its consequent effects. International Journal of Heat and Fluid Flow 52: 84–96.

Ellen

Goetz

(2013) Measuring wing profile drag using an integrating wake rake. Technical Soaring 36(3): 74–82.

10.

Eppler

(2003) About classical problems of airfoil drag. Aerospace Science and Technology 7: 289–297.

11.

Guglielmo

Selig

(1996) Spanwise variations in profile drag for airfoils at low Reynolds numbers. Journal of Aircraft 33(4): 699–707.

12.

Jahanmiri

(2011) Laminar separation bubble: Its structure, dynamics and control. Research report. Chalmers University of Technology, Gothenburg, Sweden.

13.

Jones

Sandberg

Sandham

(2008) Direct numerical simulations of forced and unforced separation bubbles on an airfoil at incidence. Journal of Fluid Mechanics 602: 175–207.

14.

Karasu

Genc

Acikel

, et al. (2012) An experimental study on laminar separation bubble and transition over an aerofoil at low Reynolds number. In: 30th AIAA applied aerodynamics conference, New Orleans, Louisiana, 25–28 June 2012.

15.

Kojima

Nonomura

Oyama

, et al. (2013) Large-eddy simulation of low-Reynolds-number flow over thick and thin NACA airfoils. Journal of Aircraft 50(1): 187–196.

16.

Lee

Kawai

Nonomura

, et al. (2015) Mechanisms of surface pressure distribution within a laminar separation bubble at different Reynolds numbers. Physics of Fluids 27: 023602.

17.

Lei

Liu

(2019) Suction control of laminar separation bubble over an airfoil at low Reynolds number. Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering 233(1): 81–90.

18.

Marxen

Henningson

(2011) The effect of small-amplitude convective disturbances on the size and bursting of a laminar separation bubble. Journal of Fluid Mechanics 671: 1–33.

19.

Ohtake

Nakae

Motohashi

(2007) Nonlinearity of the aerodynamic characteristics of NACA0012 aerofoil at low Reynolds numbers. Journal of the Japan Society for Aeronautical and Space Sciences 55(644): 439–445.

20.

Park

Shim

Lee

(2020) PIV measurement of separation bubble on an airfoil at low Reynolds numbers. Journal of Aerospace Engineering 33(1): 04019105.

21.

Phillips

(1988) Studies of friction drag and pressure drag of airfoils using the Eppler program. SAE technical paper series 881396, Warrendale. (SAE = The Engineering Society for Advanced Mobility Land, Sea, Air and Space, 400 Commonwealth Drive, Warrendale, PA, 15090, USA.)

22.

Popelka

Matejka

Simurda

, et al. (2011) Boundary layer transition, separation and flow control on airfoils, wings and bodies in CFD, wind-tunnel and in-flight studies. Technical Soaring 35(5): 108–115.

23.

Reda

(1991) Observations of dynamic stall phenomena using liquid crystal coatings. AIAA Journal 29(2): 308–310.

24.

Rethmel

(2011) Airfoil leading edge flow separation control using nanosecond pulse DBD plasma actuators. Master’s Thesis, Mechanical Engineering, The Ohio State University, Columbus, OH, USA, pp.25–30.

25.

Rinoie

Shingo

Sato

(1990) Measurements of short bubble and long bubble formed on NACA 63-009 airfoil. Journal of the Japan Society for Aeronautical and Space Sciences 38(436): 249–257.

26.

Rinoie

Takemura

(2004) Oscillating behaviour of laminar separation bubble formed on an aerofoil near stall. The Aeronautical Journal 108(1081): 153–163.

27.

Ripley

Pauley

(1993) The unsteady structure of two-dimensional steady laminar separation. Physics of Fluids A Fluid Dynamics 5: 3099–3106.

28.

Robert

(2016) Errors and problems while conducting research studies in a wind tunnel -selected examples. Transactions of the Institute of Aviation 245(4): 169–177.

29.

Schlichting

(1960) Boundary Layer Theory, 4th edn. New York, London: McGraw-Hill Book Company.

30.

Selig

Guglielmo

Broeren

, et al. (1995) Summary of Low Speed Airfoil Data, vol. I. Virginia Beach, VA: SoarTech Publications, p.2345.

31.

Spalart

Strelets

(2000) Mechanisms of transition and heat transfer in a separation bubble. Journal of Fluid Mechanics 403: 329–349.

32.

Versteeg

Malalasekera

(2007) An Introduction to Computational Fluid Dynamics: The Finite Volume Method, 2nd edn. Harlow, England: Pearson Education, pp.273–279.

33.

Walters

Cokljat

(2008) A three-eq11 eddy-viscosity model for Reynolds-averaged Navier–Stokes simulations of transitional flow. Journal of Fluids Engineering 130(12): 121401.

34.

Watmuff

(1999) Evolution of a wave packet into vortex loops in a laminar separation bubble. Journal of Fluid Mechanics 397: 119–169.

35.

Winslow

Otsuka

Govindarajan

, et al. (2018) Basic understanding of airfoil characteristics at low Reynolds numbers (10⁴–10⁵). Journal of Aircraft 55(3): 1050–1061.

36.

Zaman

KBMQ

Mckinzie

Rumsey

(1989) A natural low-frequency oscillation of the flow over an airfoil near stalling conditions. Journal of Fluid Mechanics 202: 403–442.

37.

Zhang

Hain

Kähler

(2008) Scanning PIV investigation of the laminar separation bubble on a SD7003 airfoil. Experiments in Fluids 45: 725–743.