Difference between revisions of "Dynamic stall NACA0012 Michael Alletto"

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  &alpha;(t) = &alpha;<sub>0</sub> + A sin(&omega; t)
 
  &alpha;(t) = &alpha;<sub>0</sub> + A sin(&omega; t)
  
The mean inflow angle can be achieved by either inclining the airfoil or the inflow velocity. In our case we chose to incline the inflow velocity with a mean pitching angle of zero. This results in a velocity vector at the inflow plane of $u = (1.33 \ 0 0.23)$.
+
The mean inflow angle can be achieved by either inclining the airfoil or the inflow velocity. In our case we chose to incline the inflow velocity with a mean pitching angle of zero. This results in a velocity vector at the inflow plane of u = (1.33 0   0.23).
 
The airfoils is pitching around an axis located at a quarter chord length from the leading edge at the symmetry axis of the airfoil.  
 
The airfoils is pitching around an axis located at a quarter chord length from the leading edge at the symmetry axis of the airfoil.  
  
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Regarding the inflow condition for the turbulent quantities the suggestion reported in https://www.openfoam.com/documentation/guides/latest/doc/guide-turbulence-ras-k-omega-sst.html and in https://www.openfoam.com/documentation/guides/latest/doc/guide-turbulence-ras-k-omega-sst-lm.html are applied. For the turbulent dissipation rate $\omega$ a reference length scale $L = 1$ m is chosen. A sensitivity analysis of the latter quantity has shown little influence of the flow on $L$ at the inflow. Together wit an inflow turbulent intensity $I = 0.08$\% of the reference experiment \cite{lee2004} we get following values $k = 1.7 \times 10^{-6} \frac{m^2}{s^2}$, $\omega = 0.0024 \frac{1}{s}$, $Re_\theta = 1190$. At the wall we chose a nutkWallfunction were the turbulent viscosity at the wall is calculated using a binomial blending between the values obtained applying the laws in the viscose sublayer and the one in the logarithmic wall layer. For details see https://www.openfoam.com/documentation/guides/latest/doc/guide-bcs-wall-turbulence-nutkWallFunction.html.
+
Regarding the inflow condition for the turbulent quantities the suggestion reported in https://www.openfoam.com/documentation/guides/latest/doc/guide-turbulence-ras-k-omega-sst.html and in https://www.openfoam.com/documentation/guides/latest/doc/guide-turbulence-ras-k-omega-sst-lm.html are applied. For the turbulent dissipation rate $\omega$ a reference length scale L = 1 m is chosen. A sensitivity analysis of the latter quantity has shown little influence of the flow on L at the inflow. Together wit an inflow turbulent intensity I = 0.08% of the reference experiment [2] we get following values k = 1.7 x 10<sup>-6</sup> </sup> m<sup>2</sup>/s<sup>2</sup>, $\omega = 0.0024 \frac{1}{s}$, $Re_\theta = 1190$. At the wall we chose a nutkWallfunction were the turbulent viscosity at the wall is calculated using a binomial blending between the values obtained applying the laws in the viscose sublayer and the one in the logarithmic wall layer. For details see https://www.openfoam.com/documentation/guides/latest/doc/guide-bcs-wall-turbulence-nutkWallFunction.html.
  
 
==References==
 
==References==

Revision as of 10:10, 8 January 2022

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You can download the case file https://gitlab.com/mAlletto/openfoamtutorials/-/tree/master/dynamicStall] here.

Introduction

In this tutorial we will look at the simulation of the dynamic stall of a periodically pitching NACA0012 airfoil in an incompressbile flow. We will compare 2D RANS simulations with the experiments by [2]. The periodically pitching motion is achieved by an arbitrary mesh interphase (AMI). The same periodically pitching motion can be achieved also using the morphing mesh approach or using the overset mesh method. Unfortunately a few test with the morphing mesh lead to a deterioration of the mesh due to the large deformation of the mesh for the present case. Regarding the overset mesh such problem do not occur since the mesh topology is not changed. A few test however, lead to a much higher computational time compared to the AMI strategy. For this reason the AMI is chosen. The same method shown in this tutorial, could be also applied to the pitching motion of the wings of a wind turbines or a helicopters. Dynamic stall is a phenomena occurring in many technical application like vertical axis turbines (see [4]), airfoils under the influence of gusts, ma- neuvering aircraft and also horizontal axis wind turbines (see [3]). Dynamic stall on a periodically pitching airfoil is characterized by the increase of the lift coefficient Cl and the drag coefficient Cd well beyond the maximum values obtained for a static airfoil. The stall angel αs is also much higher for pitching airfoils compared to static airfoils (see [2]). Main cause of the increased lift and drag coefficient is the development of a large attached dynamic stall vertex (DSV) developing on the suction side of the airfoil as the angle of attach increases. This vortex is swept towards the trailing edge causing the pressure minima to move towards the trailing edge. This causes a strong nose down moment (see [3]). As the angle of attach decreases the flow becomes attached again with a large hysteresis in the lift. The strong variation of the lift and drag leads to large oscillatory forces and the change in the moment coefficient Cm leads to large torsion of the airfoil. Since this large forces and moment can severely damage the structure, it is a must to have numerical tools which can accurately predict this phenomena.

Setup

The next figure shows the setup of the simulation. In the experiment by [2] a Reynolds number based on the chord length c of Re = Uoo c / v = 1.35 x 105 was investigated. Uoo is the velocity upstream and v the kinematic viscosity. Three reduced frequency κ = \frac{ω c }{2 Uoo} = 0.1, 0.05, 0.025 from the experiment are investigated. ω is the pitching frequency. In order to compare the measurements and the simulation, both have to have the same non-dimensional parameters. For the simulation a chord length of c = 1 m and a kinematic viscosity of v = 1.0 x 105 m2/s2. From the specification of these two parameters we get a velocity of Uoo = $ 1.35 m/s. Based on the aforementioned parameters we get following frequencies ω 0.27 0.135 0.0675 rad/s for the three reduced frequencies κ = 0.1, 0.05, 0.025. For the considered case we have a mean inflow angle of α0 = 10° and an amplitude A = 15°. The periodic pitching movement is defined as:

α(t) = α0 + A sin(ω t)

The mean inflow angle can be achieved by either inclining the airfoil or the inflow velocity. In our case we chose to incline the inflow velocity with a mean pitching angle of zero. This results in a velocity vector at the inflow plane of u = (1.33 0 0.23). The airfoils is pitching around an axis located at a quarter chord length from the leading edge at the symmetry axis of the airfoil.



Regarding the inflow condition for the turbulent quantities the suggestion reported in https://www.openfoam.com/documentation/guides/latest/doc/guide-turbulence-ras-k-omega-sst.html and in https://www.openfoam.com/documentation/guides/latest/doc/guide-turbulence-ras-k-omega-sst-lm.html are applied. For the turbulent dissipation rate $\omega$ a reference length scale L = 1 m is chosen. A sensitivity analysis of the latter quantity has shown little influence of the flow on L at the inflow. Together wit an inflow turbulent intensity I = 0.08% of the reference experiment [2] we get following values k = 1.7 x 10-6 m2/s2, $\omega = 0.0024 \frac{1}{s}$, $Re_\theta = 1190$. At the wall we chose a nutkWallfunction were the turbulent viscosity at the wall is calculated using a binomial blending between the values obtained applying the laws in the viscose sublayer and the one in the logarithmic wall layer. For details see https://www.openfoam.com/documentation/guides/latest/doc/guide-bcs-wall-turbulence-nutkWallFunction.html.

References

[1] SI Benton and MR Visbal. The onset of dynamic stall at a high, transi- tional reynolds number. Journal of Fluid Mechanics, 861:860–885, 2019.

[2] T Lee and P Gerontakos. Investigation of flow over an oscillating airfoil. Journal of Fluid Mechanics, 512:313–341, 2004.

[3] Miguel R Visbal and Daniel J Garmann. Analysis of dynamic stall on a pitching airfoil using high-fidelity large-eddy simulations. AIAA Journal, 56(1):46–63, 2018.

[4] Shengyi Wang, Derek B Ingham, Lin Ma, Mohamed Pourkashanian, and Zhi Tao. Numerical investigations on dynamic stall of low reynolds number flow around oscillating airfoils. Computers & fluids, 39(9):1529– 1541, 2010.

[5] Shengyi Wang, Derek B Ingham, Lin Ma, Mohamed Pourkashanian, and Zhi Tao. Turbulence modeling of deep dynamic stall at relatively low reynolds number. Journal of Fluids and Structures, 33:191–209, 2012.

[6] Yan Zhang. Effects of distributed leading-edge roughness on aerody- namic performance of a low-reynolds-number airfoil: an experimental study. Theoretical and Applied Mechanics Letters, 8(3):201–207, 2018.