High Reynolds Number Flow around Airfoil in Deep Stall

Flows Around Bodies

Underlying Flow Regime 2-11

Test Case Study

Brief Description of the Test Case

The following presents a precise description of the primary test case, the NACA0021 airfoil at 60° angle of attack.

A visual impression of the geometry and flow has been shown in Figure 1. The experiments were carried out in the wind tunnel of Monash University (see Figure 2). The width of the experimental section is 7.2 airfoil chord lengths, c, and its height is 16c.

Figure 2: NACA0021 airfoil in wind tunnel (left) and a plan view of wind tunnel (right) [ ]
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The airfoil geometry normalized with the chord length, c, is defined by:

{y=\pm {\frac {0.21}{0.2}}\left(0.2969\ {\sqrt {x}}-0.126\ x-0.3516\ x^{2}+0.2846\ x^{3}-0.1015\ x^{4}\right)}

Experimental flow parameters, needed to set up appropriate numerical simulations, are presented in Table 2.

**Table 2:** Flow parameters
Parameter	Notation	Value
Reynolds number	${Re=U_{\infty }c/\nu }$	2.7×10⁵
Chord length	$\left.c\right.$	0.125 m
Angle of attack	$\left.\alpha \right.$	60°
Free stream Mach number	$\left.M\right.$	0.1
Free stream streamwise turbulence intensity	$\left.l_{u}\right.$	0.6%

The flow parameters measured in the experiments are as follows:

Time-averaged pressure coefficient distribution over the airfoil surface, ${C_{p}(x)={\frac {p-p_{\infty }}{{\frac {1}{2}}\rho U_{\infty }^{2}c}}}$ , where $\left.p_{\infty }\right.$ is the reference pressure from the undisturbed far-field flow and $\left.\rho \right.$ is the fluid density.

Time-averaged sectional drag and lift coefficients, $\left.C_{d},\ C_{l}\right.$ integrated from pressure at individual spanwise locations near the spanwise mid-point: ${C_{d}={\frac {d}{{\frac {1}{2}}\rho U_{\infty }^{2}c}},\ C_{l}={\frac {l}{{\frac {1}{2}}\rho U_{\infty }^{2}c}}}$ , where $\left.d\right.$ and $\left.l\right.$ are the sectional pressure drag and lift forces, respectively.

Time histories of the sectional lift and drag coefficients (32,000 points total over the time interval T≈9000 (c/U₀)).

These data are available on the web site of the DESider EU project [‌5] in digital form: http://cfd.mace.manchester.ac.uk/desider/

Test Case Experiments

A detailed description of the test facility and measurement techniques used in the experiments is given in [‌27, 28]. So here we present only concise information about these aspects of the test case.

As already mentioned, the width of the experimental section is 7.2 airfoil chord lengths c and its height is 16c.The two-dimensionality of the flow over the NACA0021 model was improved by the use of the endplates (see Figure 2). It was found that the free-stream flow has a turbulence intensity of 0.6% and variations of the velocity over the central 0.3m×0.3m area of the test section are less than 3%. During the runs the dynamic pressure was determined by a Pitot upstream of and above the model. This allowed the coefficient of pressure to be determined for each sample. Although the flow decelerates over the distance from the Pitot to the section containing the model, an error in velocity caused by this was less than 6% and was not corrected for.

The aspect ratio of the model was equal to 7.2, which ensured a low value of blockage (6.25% at α = 90°) and is sufficient to minimize possible effects of the finite span on the unsteady flow characteristics [‌27].

The time-averaged pressure coefficient distribution over the airfoil surface was measured with the use of multiple pressure taps arranged in five rows along the model span. In the streamwise direction the taps were concentrated towards the leading edge, which allowed a better resolution of the high pressure gradients in this area. The model was aligned to zero angle of attack by equalizing the pressure on its top and bottom surface. During the runs each tap was sampled at 1000 Hz for 35 seconds and measured pressure signals were corrected for the amplitude and phase response of the tubing. The corrected pressure measurements were fitted with a spline function across the surface for integration of the forces.

The lift and drag were computed from the measured pressures for each time step and then analyzed for frequency content, which resulted in the sectional PSD of the forces. Thus both mean and time-dependent forces are available.

CFD Methods

During the DESider project the considered test case was computed by 8 partners (see Table 3). All the partners used their own flow solvers. Other than that, the difference between the simulations included different grids, somewhat different computational set-ups (e.g. span- sizes of the computational domain), boundary conditions in the span- direction (slip walls or periodic ones), and simulation approaches (DES with different background RANS turbulence models, X-LES [8], SAS based on the k – ω SST model [12] and k – ω TRRANS model [30]). All results were obtained from fully-turbulent computations and the force coefficients were integrated over a single spanwise position (as in the experiment).

Contributed by: Charles Mockett; Misha Strelets — CFD Software GmbH and Technische Universitaet Berlin; New Technologies and Services LLC (NTS) and Saint-Petersburg State University