# Numerical Investigation of Flow Control Feasibility with a Trailing Edge Flap

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1 Journal of Physics: Conference Series OPEN ACCESS Numerical Investigation of Flow Control Feasibility with a Trailing Edge Flap To cite this article: W J Zhu et al 2014 J. Phys.: Conf. Ser View the article online for updates and enhancements. Related content - Aerodynamic behavior of an airfoil with morphing trailing edge for wind turbine applications T Wolff, B Ernst and J R Seume - Synthetic jet actuation for load control H de Vries, E T A van der Weide and H W M Hoeijmakers - Experimental and simulated control of lift using trailing edge devices A Cooperman, M Blaylock and C P van Dam This content was downloaded from IP address on 25/01/2018 at 07:38

4 2. Numerical method The numerical code used for the present study is the incompressible flow solver EllipSys2D [24,25,26]. The solver was developed at Technical University of Denmark (DTU) since 1990s. It is a general-purpose Navier-Stokes code based on a second-order multi-block finite volume method. The code solves the velocity-pressure coupled flow equations employing the SIMPLE/SIMPLEC/PISO methods and a multi-grid strategy. To treat moving boundary problems, the IB method is implemented in the EllipSys code. This technique is used in the present work to simulate flow over a deformable TEF. The first procedure for implementing an IB method is to identify and tag the cells inside the solid body. The rest of the cells represent flow fields. The neighbouring cells that connect the inside and outside cells of the body are identified and tagged, such that they represent the solid boundary. Figure 1 is a sketch showing how the cells are tagged. The dashed line represents part of the solid boundary. The solid dots are the forcing cells which will be treated as an external forcing. The velocities at the forcing cells are linearly or bilinearly interpolated based on the local wall geometry. To represent the body, forcing terms are introduced to the governing equations. The modified incompressible Navier- Stokes (NS) equations read: uu uu+ fρ + = p + μδ (1) t u= 0 (2) where the body force f creates the desired velocity field along the solid boundary; p is the pressure, ρ is the density of air, u denotes the velocity components and µ is the dynamic viscosity. During each time step while solving the general NS equations, the forcing term f is determined from a time discretization of equation (1), such that n uu+ 1 n fn+ 1/ 2 n+ 1/ 2 = RHS + Δt (3) where RHS results from the discretization of the convective, viscous and pressure-gradient terms at time level n+1/2. The notation of f at n+1/2 means direct forcing, i.e. the forcing term is being computed before the velocity but at the same time step. From Eq. (2), the volume force f which yields +1 the desired velocity nvreads, fvun+ 1 n n+ 1/ 2 n+ 1/2 = RHS +. Δt (4) Solving the flow equation with the forcing term determines the velocity on the wall represented by the +1 IB. The velocity nvon the forcing cells is determined by linear or bilinear interpolation between the wall surface and the neighbouring grid points. 3

5 Figure 1. Definition of the solid boundary, the cells inside of the solid boundary and the forcing cells. It is a limitation and a challenge to apply the IB method for high Reynolds number turbulent flows. In principle, IB method can be directly combined with most turbulence models or Direct Numerical Simulations (DNS). However, special treatments of turbulence models are usually required to improve the solution accuracy. The present work is focused on the Reynolds averaged Navier-Stokes (RANS) equations for industrial relevant flows at high Reynolds numbers. The chosen turbulence closure is the k-ω SST model [27]. A rewritten scheme using direct forcing approach was implemented in the finite volume flow solver. Besides this, the boundary conditions in the SST turbulence model are changed, such that 60 k w = 0, ω ib =. (5) ρ β Δy ( ) 2 As in the standard k-ω procedure, the normal distance to the wall is computed. In the IB method, the normal distance to the immersed boundary, Δ yib, is also computed, Δ yib as shown in equation (5). Note that the value of the normal distance changes for problems with moving boundary. More details about numerical implementations can be found in Zhu et al. [23]. ib 3. Implementation of the TE Control System Sections 3.1. Geometrical setup In order to control the fluctuating lift, a NACA airfoil is designed with a deformable TE. As an example, a ±10 TE deformation is shown in Figure 2. As sketched in the figure, the TE is fixed at points a and b, where the last 15% of the airfoil is flexible. Denoting the x-value of the i th point on the IB surface as x i ib (n), the new x-position at the time step n+1 is calculated from the following formula, p i xib n x i i i a b xib n xib n uib n t ( ), ( + 1) = ( ) + ( ) Δ (6) xc x a, b 4

6 Similarly, the new y-position is given as In the above equations, y i ib i u ib and i ib i xib n x i i a b n yib n vib n t ( ), ( + 1) = ( ) + ( ) Δ (7) xc x a, b v are the prescribed velocities at the i th IB point in the x- and y- directions, which are calculated from the flap angular velocity β (t). The notation ( ) a,b refers to the upper and lower surfaces according to the two fixed points a and b, and the point c is fixed in the x- direction, see Figure 2. It is seen that the flap is subject to a rigid movement for p = 1. In the present case the exponent p = 2 is used, resulting in the elastically deformed shape as shown in Figure 2. Note that the velocity introduced by the TE curvature change is considered in the flow simulation. p Figure 2. Sketch of a NACA airfoil with a 15%-chord deformable trailing edge flap Control setup A classic PID algorithm is implemented in the numerical flow solver for controlling the flap. The airfoil lift coefficient is obtained from the integrated force through the CFD computation. The use of the numerically integrated lift [5] as control objective serves in general as a reference for control strategies, using e.g. inflow sensors [7], pressure differences [9] or hinge moments [28]. The control law can be written as t β = K Pe( t) + K I e( t) dt + K De ( t) (8) where β is the TE defection angle, K P is the proportional gain, K I is the integration gain and K D is the derivative gain. The error signal used here is the difference of the dynamic lift coefficient and the static lift coefficient, such as e( t) = C ( t) C ( t) (9) l The static lift is averaged after the flow is fully developed. Using the RANS approach, the static lift is a constant in case of attached flow. A deflection angle β is selected to reduce the lift oscillations about 0 l 5

7 a mean lift value under unstable wind conditions. The change of the β angle is synchronized with the flow solver, e.g., the airfoil shape at the last 15% is continuously changing during each time step. 4. Results and discussions 4.1. Mesh configuration The computational mesh, shown in Figure 3, consists of 56 mesh blocks of cells. The thickness of a laminar boundary layer at a Reynolds number of is estimated as δ/c Re -0.5 = Grid lines around the IB surface are clustered into the TE region. A grid dependency study was performed in previous work [23] where 2 and 4 blocks are applied in region of the TE. To ensure better accuracy in the current study, 8 blocks are focused in the area around the TE. Figure 3. Mesh configuration of a NACA airfoil with a truncated trailing edge Periodic inflow The case to be considered here is the periodic inflow over a NACA airfoil with a 15% chord adaptive trailing edge. The motivation for this simulation is to demonstrate the feasibility of using TEF to control gust induced lift force. Similar experiments [5] were carried out at the DTU/MEK wind tunnel with the same airfoil and TEF. To follow the experimental setup, the numerical simulation uses the same geometric configuration as it is used in the experiments. The main airfoil geometry, the TEF and the two pitching wings can be seen in Figure 4. In the experimental work [5], the velocity at the inlet is V = 30 m/s, the test section has dimension of 0.5mx0.5m, the airfoil chord is 0.25m and the trailing edge flap is 15% of the chord. This is equivalent to a Reynolds number of 5x10 5. To harmonically oscillate the inflow, two small airfoils are placed in front of the main airfoil. The small airfoils have a chord of 0.1 m and they are located at the positions of A (-0.1, 0.1) and B (-0.1, -0.1) as depicted in Figure 4. The task of these two small wings is to continuously pitch the inflow and therefore change the angle of attack at the main airfoil. During the numerical simulations, the two pitching wings are modeled by adding two lift forces in the momentum equations Such that equation (1) becomes L = 0.5sin(2πft). (10) 6

8 uu uuf+ Lρ + = p + μδ +. (11) t By applying such a prescribed force at point A and B, the desired velocity field is obtained which yields the change of angle of attack at the main airfoil. A reduced frequency of is selected for the pitching wings as it was also used in the experiment [5]. Figure 4. Sketch of the collective pitching wings and the main wing with a trailing edge flap. To control the unsteady flow via the TEF device, the unsteady C l, the time averaged value C l and the time derivative C l are computed at each time iteration and they form the input to the control system, as shown in equation (8). The flow vorticity is shown in Figure 5 at a mean angle of attack of zero and the effect from the two virtual forcing points is observed. The inflow oscillation can be observed in Figure 5(a) where the vorticity field changes periodically along the streamwise direction. Without pitching the two small airfoils, a steady lift is achieved at C l = As the small wings start to oscillate, the main airfoil attempts to maintain the steady lift around C l = As the effect from TE control system, the TE will start flapping to balance the inflow oscillation. The standard PID-control algorithm is applied to adjust the flap angle, referred to as the β angle. The lift coefficient and the position of the β angle are shown in Figure 6 as a function of non-dimensional time. The amplitude of the lift coefficient attains a value of about 0.1 which is the same as designed in [5]. It is seen that flow is quickly stabilized at around C l = when the TE control system is activated, as shown in Figure 6(a). The TE deforms as described in equations (6) and (7). The amplitude of the TE deflection angle is around 3 for downward movement and 3.5 for upward movement, as shown in Figure 6(b). A maximum load reduction over 95% is achieved from the present numerical study where a value of 80% was observed experimentally [5]. The results indicate that a standard PID-controller is sufficient for maintaining the main airfoil at the desired lift value in the gusty inflow case. Since the numerical study is not constrained by any time hysteresis from mechanical system and controllers, the load reduction is higher than what can be achieved in practice. 7

9 The Science of Making Torque from Wind 2014 (TORQUE 2014) Figure 5 (a) Illustration of vorticity field affected by upstream pitching wings. Figure 5 (b) Zoom of the pitching wings, the main airfoil and the trailing edge flap Pitching Inflow TE-Control Cl β (degrees) Deflection Angle T T Figure 6 (a) Change of Cl with inflow change and TE-control. Figure 6 (b) Change of the TE deflection angle during the control of Cl. 5. Conclusions It has been demonstrated that active control of a TE-flap has the potential of stabilizing the aerodynamic lift induced by unsteady inflow. The IB method has shown the advantage of dealing with the complex TE elastically motion. Unsteady 2D RANS simulations provide accurate flow solutions where the time dependent integrated aerodynamic lift is used to generate the error signal. The controlled TE deflection angle is generated after each time step and thus the new flow field is obtained in the next time step. Results have shown that a basic PID control strategy is able to achieve the target of load alleviation. For the periodic inflow case, the alleviation of the lift fluctuation is nearly perfect. To eliminate a ΔCl of 0.1, the maximum flap deflection is around 3.5. This is in the practical range of 8

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