Turn a string into a windmill

JavaScript (ES6), 291 bytes

r=a=>{w.textContent=a.map(a=>a.join``).join`
`;for(i=j=h=a.length>>1;j++,i--;){t=a[i][i];a[i][i]=a[h][i];a[h][i]=a[j][i];a[j][i]=a[j][h];a[j][h]=a[j][j];a[j][j]=a[h][j];a[h][j]=a[i][j];a[i][j]=a[i][h];a[i][h]=t}}
s=w=>{a=[...w=[...w]].map(_=>w.map(_=>' '));a[w.length>>1]=w;setInterval(r,1000,a)}
s("windmills")

<pre id=w>

MATL, 35 33 21 bytes

jtn2/kYaG1$Xd`wtD3X!T

The following will animate the windmill (26 bytes)

jtn2/kYaG1$Xd`wtXxDlY.3X!T

Online Demo

In this version , the Xx specifies to clear the display and the 1Y. is a 1-second pause.

Explanation

The basic idea is that we want to create two versions of the input. An "orthogonal" version

+-----+
|     |       
|     |
|abcde|
|     |
|     |
+-----+

And a "diagonal" version

+-----+
|a    |
| b   |
|  c  |
|   d |
|    e|
+-----+

We push these two versions onto the stack. Each time through the loop, we switch the order of stack and rotate the top one clockwise.

j       % Grab the input as a string
t       % Duplicate the input

%--- Create the "orthogonal" version ---%

n2/     % Determine numel(input) / 2
k       % Round down to nearest integer
Ya      % Pad the input string with floor(numel(input)/2) rows above and below 

%--- Create the "diagonal" version ---%

G       % Grab the input again
1$Xd    % Place the input along the diagonal of a matrix    

`       % do...while loop   
  w     % Flip the order of the first two elements on the stack
  t     % Duplicate the top of the stack
  
  %--- OCTAVE ONLY (converts NULL to space chars) ---%

  O       % Create a scalar zero
  32      % Number literal (ASCII code for ' ')
  XE      % Replaces 0 elements in our 3D array with 32 (' ')

  %--- END OCTAVE ONLY ---%
  
  D     % Display the element     
  3X!   % Rotate this element 90 degrees counter-clockwise 3 times (clockwise)
  T     % Explicit TRUE to create an infinite loop
        % Implicit end of while loop
        

05AB1E, 88 53 bytes

Code:

¹VYg;ïU[2FX¶×DYsJ,YvNð×y¶J?}YvðX×yJ,}Yv¹gN>-ð×yJ,}YRV

Try it online!. Make sure to hit the kill button right after you run it, because it goes into an infinite loop.