Aerofoil Kinematics Computational Fluid Dynamics (Update: 01)

This post is about a 2D NACA 0010 aerofoil undergoing various forms of forced kinematics i.e. pure heaving and pitching and a combination of two known as flapping.

Heaving motion is achieved by changing the angle of attack on the aerofoil based on the Eqn. 1.

α_e = arctan[2*π*St_a*cos(2*π*f_h*t)] + α_i               Eqn. 1

The pitching motion is achieved by employing the sliding mesh with the rotational velocity governed by Eqn. 2.

ω = 2*π*f_h*ϑ*cos(2*π*f_h*t)                                 Eqn. 2

w.r.t. Eqn. 1-2 α_e is the effective angle of attack, St_a is Strouhal number (defined as (f_h*h0/U∞)), f_h is the frequency of oscillations, while ω, t and ϑ represent rotational velocity, instantaneous time and pitching angle. h0 is the heaving amplitude and U∞ is the free stream velocity.

The flapping motion is achieved by a combination of the heaving and pitching. In this particular simulation, the aerofoil is in the power extraction mode, meaning the feathering parameter χ is greater in magnitude than 1.0. Feathering parameter is defined by Eqn. 3.

χ = ϑ/arctan(h0*2*π*f_h/U∞)                                  Eqn. 3

The boundary conditions employed for the set of simulations are at Re 50,000, St_a 0.0149, h0 = aerofoil chord length, χ = 1.1 and f_h = 0.5 Hz. The animation of the velocity contours superimposed with streamlines is shown in Fig. 1. The velocity scale ranges from 0 to 7 m/s. Pressure distribution around the aerofoils in various forms of motion, after five complete cycles is shown in Fig. 2.

Fig. 1, Flow animation, fluid flow direction is from left to right

Fig. 2, Fluid flow is from left to right

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