# calculate wake of turbine in matlab

To calculate the wake of a turbine in MATLAB, you can simulate the fluid dynamics using either computational fluid dynamics (CFD) or actuator disk theory. Here, we will use actuator disk theory as it is a simplified approach that provides a good estimate of the wake velocity field.

Actuator disk theory models the turbine as a disk that acts as an interface between the incoming flow and the outgoing flow. The model assumes that the flow is axisymmetric and that the turbine has no effect on the flow in the axial direction.

To calculate the wake using actuator disk theory, you can use the following MATLAB code:

```main.m```% Define the inputs
U_inf = 10;      % Free-stream velocity [m/s]
R = 20;          % Turbine rotor radius [m]
C_p = 0.4;       % Power coefficient (efficiency) [-]
rho = 1.225;     % Air density [kg/m^3]

% Define the coordinates of the wake plane
x = linspace(0,1000,100);    % Streamwise direction [m]
y = linspace(-500,500,100);  % Lateral direction [m]

% Calculate the wake velocity field
[X,Y] = meshgrid(x,y);
U = U_inf*(1-2*C_p*(R^2./(X.^2+Y.^2+R^2)));    % Velocity in x-direction
V = zeros(size(U));                             % Velocity in y-direction
W = zeros(size(U));                             % Velocity in z-direction

% Plot the wake velocity field
figure;
quiver(X,Y,U,V);
xlabel('Streamwise direction [m]');
ylabel('Lateral direction [m]');
title('Velocity field behind the turbine');
```808 chars23 lines```

In this code, we first define the inputs such as the free-stream velocity, turbine radius, power coefficient, and air density. We then define the coordinates of the wake plane and calculate the velocity field using actuator disk theory. Finally, we plot the velocity field using the quiver function.

Note that this is a simplified approach, and more advanced models may be required for accurate predictions in complex situations.

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