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Multi-Element Airfoils

2022-07-02T18:02:41Z

DP CFD:

==Parameterization for optimization==

When optimizing a multiple degree-of-freedom system like the positioning of elements in a multi-element airfoil, it can be important to have a smartly chosen set of independent variables. For example, if you change the height of only the 2nd element in a 3-element airfoil, you'll likely hurt the overall performance (due to choking a slot gap) even if the optimum position has the 2nd element placed higher - for example, if the entire multi-element airfoil should be moved higher. This method isn't impossible to optimize, just very inefficient to do so. Instead of defining the element locations globally, defining them relative to each other lets us use meaningful independent variables like slot gap and slot overlap. For adjusting angles of attack, I prefer to define the angle for each element individually. When defining angles relative to each other, increasing the angle of the 1st element will rotate the entire multi-element airfoil. While specifying the relative angles can speed up the initial optimization, it isn't efficient for fine-tuning, which is where most of ones time is spent.

Below is how to set up this parameterization:

Given elements i = 1 to N, import them all into your software of choice, whether you're optimizing them in CFD, or recreating the final design in CAD. All elements must start with their leading edge on the coordinate system origin, and with zero angle of attack.

First, pick an element to act as the 'anchor' for the multi-element airfoil. Your anchor element will define the one point that you have global control over, usually for something like placing the leading or trailing edge near a bounding box in the regulations.

Given the variables

* Global anchor position, <math>x_{anchor}</math> and <math>z_{anchor}</math>

* Element angle of attack, <math>\alpha_i</math>

* Element cord, <math>c_i</math>

* Slot gap height and overlap, <math>h_i</math> and <math>l_i</math> (Be aware that this will not be the true slot gap due to element thickness)

* Element pivot position, <math>x_{pivot,i}</math> and <math>z_{pivot,i}</math> (This is eyeballed as the location on an element that is closest to the trailing edge of the preceding element, which allows us to adjust element angles without altering the true slot gap in the process) Now to position the multi-element airfoil, starting from the back:

For each element downstream of the anchor element, starting at the back (elements j = N to <math>i_{anchor}</math>+1):

1. Rotate elements (N to j) by <math>(\alpha_j-\alpha_{j-1}</math>) about <math>(x_{anchor,j}, 0, z_{anchor,j})</math>

2. Translate elements (N to j) by <math>(c_{j-1} - l_j, 0, h_j)</math>

Now, for each element upstream of the anchor element, starting at the front (elements k = 1 to <math>i_{anchor}</math>-1):

1. Translate elements (1 to k) by <math>(l_{k+1}-c_k, 0, -h_{k+1})</math>

2. Rotate elements (1 to k) by <math>(\alpha_k-\alpha_{k+1})</math> about <math>(x_{anchor,k+1}, 0, z_{anchor,k+1})</math>

Finally, for the entire multi-element airfoil:

1. Translate the multi-element airfoil such that the anchor point is at the origin

2. Rotate the multi-element airfoil by <math>\alpha_{anchor}</math>

3. Translate the multi-element airfoil by <math>(x_{anchor}, 0, z_{anchor})</math> into its final position

[[File:1.mp4|left|middle|thumb|Example of anchoring by the front element]]

[[File:Rear Anchor.mp4|left|middle|thumb|Example of anchoring by the rear element]]

Multi-Element Airfoils

2022-07-02T18:02:16Z

DP CFD:

==Parameterization for optimization==

* When optimizing a multiple degree-of-freedom system like the positioning of elements in a multi-element airfoil, it can be important to have a smartly chosen set of independent variables. For example, if you change the height of only the 2nd element in a 3-element airfoil, you'll likely hurt the overall performance (due to choking a slot gap) even if the optimum position has the 2nd element placed higher - for example, if the entire multi-element airfoil should be moved higher. This method isn't impossible to optimize, just very inefficient to do so. Instead of defining the element locations globally, defining them relative to each other lets us use meaningful independent variables like slot gap and slot overlap. For adjusting angles of attack, I prefer to define the angle for each element individually. When defining angles relative to each other, increasing the angle of the 1st element will rotate the entire multi-element airfoil. While specifying the relative angles can speed up the initial optimization, it isn't efficient for fine-tuning, which is where most of ones time is spent.

Below is how to set up this parameterization:

Given elements i = 1 to N, import them all into your software of choice, whether you're optimizing them in CFD, or recreating the final design in CAD. All elements must start with their leading edge on the coordinate system origin, and with zero angle of attack.

First, pick an element to act as the 'anchor' for the multi-element airfoil. Your anchor element will define the one point that you have global control over, usually for something like placing the leading or trailing edge near a bounding box in the regulations.

Given the variables

- Global anchor position, <math>x_{anchor}</math> and <math>z_{anchor}</math>

- Element angle of attack, <math>\alpha_i</math>

- Element cord, <math>c_i</math>

- item Slot gap height and overlap, <math>h_i</math> and <math>l_i</math> (Be aware that this will not be the true slot gap due to element thickness)

- Element pivot position, <math>x_{pivot,i}</math> and <math>z_{pivot,i}</math> (This is eyeballed as the location on an element that is closest to the trailing edge of the preceding element, which allows us to adjust element angles without altering the true slot gap in the process) Now to position the multi-element airfoil, starting from the back:

For each element downstream of the anchor element, starting at the back (elements j = N to <math>i_{anchor}</math>+1):

1. Rotate elements (N to j) by <math>(\alpha_j-\alpha_{j-1}</math>) about <math>(x_{anchor,j}, 0, z_{anchor,j})</math>

2. Translate elements (N to j) by <math>(c_{j-1} - l_j, 0, h_j)</math>

Now, for each element upstream of the anchor element, starting at the front (elements k = 1 to <math>i_{anchor}</math>-1):

1. Translate elements (1 to k) by <math>(l_{k+1}-c_k, 0, -h_{k+1})</math>

2. Rotate elements (1 to k) by <math>(\alpha_k-\alpha_{k+1})</math> about <math>(x_{anchor,k+1}, 0, z_{anchor,k+1})</math>

Finally, for the entire multi-element airfoil:

1. Translate the multi-element airfoil such that the anchor point is at the origin

2. Rotate the multi-element airfoil by <math>\alpha_{anchor}</math>

3. Translate the multi-element airfoil by <math>(x_{anchor}, 0, z_{anchor})</math> into its final position

[[File:1.mp4|left|middle|thumb|Example of anchoring by the front element]]

[[File:Rear Anchor.mp4|left|middle|thumb|Example of anchoring by the rear element]]

Multi-Element Airfoils

2022-07-02T17:58:57Z

DP CFD:

==Parameterization for optimization==
When optimizing a multiple degree-of-freedom system like the positioning of elements in a multi-element airfoil, it can be important to have a smartly chosen set of independent variables. For example, if you change the height of only the 2nd element in a 3-element airfoil, you'll likely hurt the overall performance (due to choking a slot gap) even if the optimum position has the 2nd element placed higher - for example, if the entire multi-element airfoil should be moved higher. This method isn't impossible to optimize, just very inefficient to do so. Instead of defining the element locations globally, defining them relative to each other lets us use meaningful independent variables like slot gap and slot overlap. For adjusting angles of attack, I prefer to define the angle for each element individually. When defining angles relative to each other, increasing the angle of the 1st element will rotate the entire multi-element airfoil. While specifying the relative angles can speed up the initial optimization, it isn't efficient for fine-tuning, which is where most of ones time is spent.

Below is how to set up this parameterization:

Given elements i = 1 to N, import them all into your software of choice, whether you're optimizing them in CFD, or recreating the final design in CAD. All elements must start with their leading edge on the coordinate system origin, and with zero angle of attack.

First, pick an element to act as the 'anchor' for the multi-element airfoil. Your anchor element will define the one point that you have global control over, usually for something like placing the leading or trailing edge near a bounding box in the regulations.

Given the variables

- Global anchor position, <math>x_{anchor}</math> and <math>z_{anchor}</math>

- Element angle of attack, <math>\alpha_i</math>

- Element cord, <math>c_i</math>

- item Slot gap height and overlap, <math>h_i</math> and <math>l_i</math> (Be aware that this will not be the true slot gap due to element thickness)

- Element pivot position, <math>x_{pivot,i}</math> and <math>z_{pivot,i}</math> (This is eyeballed as the location on an element that is closest to the trailing edge of the preceding element, which allows us to adjust element angles without altering the true slot gap in the process) Now to position the multi-element airfoil, starting from the back:

For each element downstream of the anchor element, starting at the back (elements j = N to <math>i_{anchor}</math>+1):

1. Rotate elements (N to j) by <math>(\alpha_j-\alpha_{j-1}</math>) about <math>(x_{anchor,j}, 0, z_{anchor,j})</math>

2. Translate elements (N to j) by <math>(c_{j-1} - l_j, 0, h_j)</math>

Now, for each element upstream of the anchor element, starting at the front (elements k = 1 to <math>i_{anchor}</math>-1):

1. Translate elements (1 to k) by <math>(l_{k+1}-c_k, 0, -h_{k+1})</math>

2. Rotate elements (1 to k) by <math>(\alpha_k-\alpha_{k+1})</math> about <math>(x_{anchor,k+1}, 0, z_{anchor,k+1})</math>

Finally, for the entire multi-element airfoil:

1. Translate the multi-element airfoil such that the anchor point is at the origin

2. Rotate the multi-element airfoil by <math>\alpha_{anchor}</math>

3. Translate the multi-element airfoil by <math>(x_{anchor}, 0, z_{anchor})</math> into its final position

[[File:1.mp4|left|middle|thumb|Example of anchoring by the front element]]

[[File:Rear Anchor.mp4|left|middle|thumb|Example of anchoring by the rear element]]

File:Rear Anchor.mp4

2022-07-02T17:58:33Z

DP CFD:

File:1.mp4

2022-07-02T17:56:04Z

DP CFD:

Multi-Element Airfoils

2022-07-02T17:54:59Z

DP CFD:

==Parameterization for optimization==
When optimizing a multiple degree-of-freedom system like the positioning of elements in a multi-element airfoil, it can be important to have a smartly chosen set of independent variables. For example, if you change the height of only the 2nd element in a 3-element airfoil, you'll likely hurt the overall performance (due to choking a slot gap) even if the optimum position has the 2nd element placed higher - for example, if the entire multi-element airfoil should be moved higher. This method isn't impossible to optimize, just very inefficient to do so. Instead of defining the element locations globally, defining them relative to each other lets us use meaningful independent variables like slot gap and slot overlap. For adjusting angles of attack, I prefer to define the angle for each element individually. When defining angles relative to each other, increasing the angle of the 1st element will rotate the entire multi-element airfoil. While specifying the relative angles can speed up the initial optimization, it isn't efficient for fine-tuning, which is where most of ones time is spent.

Below is how to set up this parameterization:

Given elements i = 1 to N, import them all into your software of choice, whether you're optimizing them in CFD, or recreating the final design in CAD. All elements must start with their leading edge on the coordinate system origin, and with zero angle of attack.

First, pick an element to act as the 'anchor' for the multi-element airfoil. Your anchor element will define the one point that you have global control over, usually for something like placing the leading or trailing edge near a bounding box in the regulations.

Given the variables

- Global anchor position, <math>x_{anchor}</math> and <math>z_{anchor}</math>

- Element angle of attack, <math>\alpha_i</math>

- Element cord, <math>c_i</math>

- item Slot gap height and overlap, <math>h_i</math> and <math>l_i</math> (Be aware that this will not be the true slot gap due to element thickness)

- Element pivot position, <math>x_{pivot,i}</math> and <math>z_{pivot,i}</math> (This is eyeballed as the location on an element that is closest to the trailing edge of the preceding element, which allows us to adjust element angles without altering the true slot gap in the process) i_{anchor}</math>+1):

1. Rotate elements (N to j) by <math>(\alpha_j-\alpha_{j-1}</math>) about <math>(x_{anchor,j}, 0, z_{anchor,j})</math>

2. Translate elements (N to j) by <math>(c_{j-1} - l_j, 0, h_j)</math>

Now, for each element upstream of the anchor element, starting at the front (elements k = 1 to <math>i_{anchor}</math>-1):

1. Translate elements (1 to k) by <math>(l_{k+1}-c_k, 0, -h_{k+1})</math>

2. Rotate elements (1 to k) by <math>(\alpha_k-\alpha_{k+1})</math> about <math>(x_{anchor,k+1}, 0, z_{anchor,k+1})</math>

Finally, for the entire multi-element airfoil:

1. Translate the multi-element airfoil such that the anchor point is at the origin

2. Rotate the multi-element airfoil by <math>\alpha_{anchor}</math>

3. Translate the multi-element airfoil by <math>(x_{anchor}, 0, z_{anchor})</math> into its final position

Example gif for anchoring by the front airfoil https://imgur.com/H45nLKj

Example gif for anchoring by the rear airfoil https://imgur.com/FEJzkjI

Multi-Element Airfoils

2022-07-02T17:46:37Z

DP CFD:

==Parameterization for optimization==
When optimizing a multiple degree-of-freedom system like the positioning of elements in a multi-element airfoil, it can be important to have a smartly chosen set of independent variables. For example, if you change the height of only the 2nd element in a 3-element airfoil, you'll likely hurt the overall performance (due to choking a slot gap) even if the optimum position has the 2nd element placed higher - for example, if the entire multi-element airfoil should be moved higher. This method isn't impossible to optimize, just very inefficient to do so. Instead of defining the element locations globally, defining them relative to each other lets us use meaningful independent variables like slot gap and slot overlap. For adjusting angles of attack, I prefer to define the angle for each element individually. When defining angles relative to each other, increasing the angle of the 1st element will rotate the entire multi-element airfoil. While specifying the relative angles can speed up the initial optimization, it isn't efficient for fine-tuning, which is where most of ones time is spent.

Below is how to set up this parameterization:

Given elements i = 1 to N, import them all into your software of choice, whether you're optimizing them in CFD, or recreating the final design in CAD. All elements must start with their leading edge on the coordinate system origin, and with zero angle of attack.

First, pick an element to act as the 'anchor' for the multi-element airfoil. Your anchor element will define the one point that you have global control over, usually for something like placing the leading or trailing edge near a bounding box in the regulations.

Given the variables

- Global anchor position, <math>x_{anchor}</math>and <math></math><math>z_{anchor}</math><math></math><math></math><math></math><math></math>z_anchor - Element angle of attack, <math></math><math></math>α_i - Element cord, c_i<math></math> - item Slot gap height and overlap, h_i and l_i (Be aware that this will not be the true slot gap due to element thickness) - Element pivot position, x_pivot,i and z_pivot,i (This is eyeballed as the location on an element that is closest to the trailing edge of the preceding element, which allows us to adjust element angles without altering the true slot gap in the process) Now to position the multi-element airfoil, starting from the back:

For each element downstream of the anchor element, starting at the back (elements j = N to i_anchor+1):

1. Rotate elements (N to j) by (α\_j-α_{j-1}) about (x_anchor,j, 0, z_anchor,j) 2. Translate elements (N to j) by (c_{j-1} - l_j, 0, h_j)

Now, for each element upstream of the anchor element, starting at the front (elements k = 1 to i_anchor-1):

1. Translate elements (1 to k) by (l\_{k+1}-c\_k, 0, -h_{k+1}) 2. Rotate elements (1 to k) by (α\_k-α\_{k+1}) about (x\_{anchor,k+1}, 0, z_{anchor,k+1})

Finally, for the entire multi-element airfoil:

1. Translate the multi-element airfoil such that the anchor point is at the origin 2. Rotate the multi-element airfoil by α_anchor 3. Translate the multi-element airfoil by (x_anchor, 0, z_anchor) into its final position

[Example gif for anchoring by the front airfoil](https://imgur.com/H45nLKj)

[Example gif for anchoring by the rear airfoil](https://imgur.com/FEJzkjI)

Multi-Element Airfoils

2022-07-02T17:45:11Z

DP CFD:

==Parameterization for optimization==
When optimizing a multiple degree-of-freedom system like the positioning of elements in a multi-element airfoil, it can be important to have a smartly chosen set of independent variables. For example, if you change the height of only the 2nd element in a 3-element airfoil, you'll likely hurt the overall performance (due to choking a slot gap) even if the optimum position has the 2nd element placed higher - for example, if the entire multi-element airfoil should be moved higher. This method isn't impossible to optimize, just very inefficient to do so. Instead of defining the element locations globally, defining them relative to each other lets us use meaningful independent variables like slot gap and slot overlap. For adjusting angles of attack, I prefer to define the angle for each element individually. When defining angles relative to each other, increasing the angle of the 1st element will rotate the entire multi-element airfoil. While specifying the relative angles can speed up the initial optimization, it isn't efficient for fine-tuning, which is where most of ones time is spent.

Below is how to set up this parameterization:

Given elements i = 1 to N, import them all into your software of choice, whether you're optimizing them in CFD, or recreating the final design in CAD. All elements must start with their leading edge on the coordinate system origin, and with zero angle of attack.

First, pick an element to act as the 'anchor' for the multi-element airfoil. Your anchor element will define the one point that you have global control over, usually for something like placing the leading or trailing edge near a bounding box in the regulations.

Given the variables

- Global anchor position, <math>x_anchor</math>and <math></math><math></math><math></math><math></math><math></math><math></math>z_anchor - Element angle of attack, <math></math><math></math>α_i - Element cord, c_i<math></math> - item Slot gap height and overlap, h_i and l_i (Be aware that this will not be the true slot gap due to element thickness) - Element pivot position, x_pivot,i and z_pivot,i (This is eyeballed as the location on an element that is closest to the trailing edge of the preceding element, which allows us to adjust element angles without altering the true slot gap in the process) Now to position the multi-element airfoil, starting from the back:

For each element downstream of the anchor element, starting at the back (elements j = N to i_anchor+1):

1. Rotate elements (N to j) by (α\_j-α_{j-1}) about (x_anchor,j, 0, z_anchor,j) 2. Translate elements (N to j) by (c_{j-1} - l_j, 0, h_j)

Now, for each element upstream of the anchor element, starting at the front (elements k = 1 to i_anchor-1):

1. Translate elements (1 to k) by (l\_{k+1}-c\_k, 0, -h_{k+1}) 2. Rotate elements (1 to k) by (α\_k-α\_{k+1}) about (x\_{anchor,k+1}, 0, z_{anchor,k+1})

Finally, for the entire multi-element airfoil:

1. Translate the multi-element airfoil such that the anchor point is at the origin 2. Rotate the multi-element airfoil by α_anchor 3. Translate the multi-element airfoil by (x_anchor, 0, z_anchor) into its final position

[Example gif for anchoring by the front airfoil](https://imgur.com/H45nLKj)

[Example gif for anchoring by the rear airfoil](https://imgur.com/FEJzkjI)

Multi-Element Airfoils

2022-07-02T17:43:10Z

DP CFD:

==Parameterization for optimization==
When optimizing a multiple degree-of-freedom system like the positioning of elements in a multi-element airfoil, it can be important to have a smartly chosen set of independent variables. For example, if you change the height of only the 2nd element in a 3-element airfoil, you'll likely hurt the overall performance (due to choking a slot gap) even if the optimum position has the 2nd element placed higher - for example, if the entire multi-element airfoil should be moved higher. This method isn't impossible to optimize, just very inefficient to do so. Instead of defining the element locations globally, defining them relative to each other lets us use meaningful independent variables like slot gap and slot overlap. For adjusting angles of attack, I prefer to define the angle for each element individually. When defining angles relative to each other, increasing the angle of the 1st element will rotate the entire multi-element airfoil. While specifying the relative angles can speed up the initial optimization, it isn't efficient for fine-tuning, which is where most of ones time is spent.

Below is how to set up this parameterization:

Given elements i = 1 to N, import them all into your software of choice, whether you're optimizing them in CFD, or recreating the final design in CAD. All elements must start with their leading edge on the coordinate system origin, and with zero angle of attack.

First, pick an element to act as the 'anchor' for the multi-element airfoil. Your anchor element will define the one point that you have global control over, usually for something like placing the leading or trailing edge near a bounding box in the regulations.

Given the variables

- Global anchor position, x_anchor and z_anchor - Element angle of attack, α_i - Element cord, c_i - item Slot gap height and overlap, h_i and l_i (Be aware that this will not be the true slot gap due to element thickness) - Element pivot position, x_pivot,i and z_pivot,i (This is eyeballed as the location on an element that is closest to the trailing edge of the preceding element, which allows us to adjust element angles without altering the true slot gap in the process) Now to position the multi-element airfoil, starting from the back:

For each element downstream of the anchor element, starting at the back (elements j = N to i_anchor+1):

1. Rotate elements (N to j) by (α\_j-α_{j-1}) about (x_anchor,j, 0, z_anchor,j) 2. Translate elements (N to j) by (c_{j-1} - l_j, 0, h_j)

Now, for each element upstream of the anchor element, starting at the front (elements k = 1 to i_anchor-1):

1. Translate elements (1 to k) by (l\_{k+1}-c\_k, 0, -h_{k+1}) 2. Rotate elements (1 to k) by (α\_k-α\_{k+1}) about (x\_{anchor,k+1}, 0, z_{anchor,k+1})

Finally, for the entire multi-element airfoil:

1. Translate the multi-element airfoil such that the anchor point is at the origin 2. Rotate the multi-element airfoil by α_anchor 3. Translate the multi-element airfoil by (x_anchor, 0, z_anchor) into its final position

[Example gif for anchoring by the front airfoil](https://imgur.com/H45nLKj)

[Example gif for anchoring by the rear airfoil](https://imgur.com/FEJzkjI)

Multi-Element Airfoils

2022-07-02T17:40:26Z

DP CFD:

==Parameterization for optimization==

When optimizing a multiple degree-of-freedom system like the positioning of elements in a multi-element airfoil, it can be important to have a smartly chosen set of independent variables. For example, if you change the height of only the 2nd element in a 3-element airfoil, you'll likely hurt the overall performance (due to choking a slot gap) even if the optimum position has the 2nd element placed higher - for example, if the entire multi-element airfoil should be moved higher. This method isn't impossible to optimize, just very inefficient to do so. Instead of defining the element locations globally, defining them relative to each other lets us use meaningful independent variables like slot gap and slot overlap. For adjusting angles of attack, I prefer to define the angle for each element individually. When defining angles relative to each other, increasing the angle of the 1st element will rotate the entire multi-element airfoil. While specifying the relative angles can speed up the initial optimization, I feel it isn't efficient for fine-tuning, which is where most of ones time is spent.

Setting up this parameterization can be a bit of a geometric brainteaser, which is why I'm sharing it:

Given elements $i = 1$ to $N$, import them all into your software of choice, whether you're optimizing them in CFD, or recreating the final design in CAD. All elements must start with their leading edge on the coordinate system origin, and with zero angle of attack.

First, pick an element to act as the 'anchor' for the multi-element airfoil. Your anchor element will define the one point that you have global control over, usually for something like placing the leading or trailing edge near a bounding box in the regulations.

Given the variables

\begin{itemize}
\item Global anchor position, $x\textsubscript{anchor}$ and $z\textsubscript{anchor}$
\item Element angle of attack, $\alpha\textsubscript{i}$
\item Element cord, $c\textsubscript{i}$
\item Slot gap height and overlap, $h\textsubscript{i}$ and $l\textsubscript{i}$
\begin{itemize}
\item Be aware that this will not be the true slot gap due to element thickness
\end{itemize}
\item Element pivot position, $x\textsubscript{pivot,i}$ and $z\textsubscript{pivot,i}$
\begin{itemize}
\item This is eyeballed as the location on an element that is closest to the trailing edge of the preceding element, which allows us to adjust element angles without altering the true slot gap in the process.
\end{itemize}
\end{itemize}

Now to position the multi-element airfoil, starting from the back:

For each element downstream of the anchor element, starting at the back (elements $j = N$ to $i\textsubscript{anchor}+1$):

\begin{enumerate}
\item Rotate elements ($N$ to $j$) by $(\alpha\textsubscript{j}-\alpha\textsubscript{j-1})$ about $(x\textsubscript{anchor,j}, 0, z\textsubscript{anchor,j})$
\item Translate elements ($N$ to $j$) by $(c\textsubscript{j-1} - l\textsubscript{j}, 0, h\textsubscript{j})$
\end{enumerate}

Now, for each element upstream of the anchor element, starting at the front (elements $k = 1$ to $i\textsubscript{anchor}-1$):

\begin{enumerate}
\item Translate elements ($1$ to $k$) by $(l\textsubscript{k+1}-c\textsubscript{k}, 0, -h\textsubscript{k+1})$
\item Rotate elements ($1$ to $k$) by ($\alpha\textsubscript{k}$-$\alpha\textsubscript{k+1}$) about $(x\textsubscript{anchor,k+1}, 0, z\textsubscript{anchor,k+1})$
\end{enumerate}

Finally, for the entire multi-element airfoil:

\begin{enumerate}
\item Translate the multi-element airfoil such that the anchor point is at the origin
\item Rotate the multi-element airfoil by $\alpha\textsubscript{anchor}$
\item Translate the multi-element airfoil by ($x\textsubscript{anchor}, 0, z\textsubscript{anchor}$) into its final position
\end{enumerate}

Multi-Element Airfoils

2022-07-02T17:38:12Z

DP CFD: Created page with "Parameterization for optimization When optimizing a multiple degree-of-freedom system like the positioning of elements in a multi-element airfoil, it can be important to have..."

Parameterization for optimization

When optimizing a multiple degree-of-freedom system like the positioning of elements in a multi-element airfoil, it can be important to have a smartly chosen set of independent variables. For example, if you change the height of only the 2nd element in a 3-element airfoil, you'll likely hurt the overall performance (due to choking a slot gap) even if the optimum position has the 2nd element placed higher - for example, if the entire multi-element airfoil should be moved higher. This method isn't impossible to optimize, just very inefficient to do so. Instead of defining the element locations globally, defining them relative to each other lets us use meaningful independent variables like slot gap and slot overlap. For adjusting angles of attack, I prefer to define the angle for each element individually. When defining angles relative to each other, increasing the angle of the 1st element will rotate the entire multi-element airfoil. While specifying the relative angles can speed up the initial optimization, I feel it isn't efficient for fine-tuning, which is where most of ones time is spent.

Setting up this parameterization can be a bit of a geometric brainteaser, which is why I'm sharing it:

Given elements $i = 1$ to $N$, import them all into your software of choice, whether you're optimizing them in CFD, or recreating the final design in CAD. All elements must start with their leading edge on the coordinate system origin, and with zero angle of attack.

First, pick an element to act as the 'anchor' for the multi-element airfoil. Your anchor element will define the one point that you have global control over, usually for something like placing the leading or trailing edge near a bounding box in the regulations.

Given the variables

\begin{itemize}
\item Global anchor position, $x\textsubscript{anchor}$ and $z\textsubscript{anchor}$
\item Element angle of attack, $\alpha\textsubscript{i}$
\item Element cord, $c\textsubscript{i}$
\item Slot gap height and overlap, $h\textsubscript{i}$ and $l\textsubscript{i}$
\begin{itemize}
\item Be aware that this will not be the true slot gap due to element thickness
\end{itemize}
\item Element pivot position, $x\textsubscript{pivot,i}$ and $z\textsubscript{pivot,i}$
\begin{itemize}
\item This is eyeballed as the location on an element that is closest to the trailing edge of the preceding element, which allows us to adjust element angles without altering the true slot gap in the process.
\end{itemize}
\end{itemize}

Now to position the multi-element airfoil, starting from the back:

For each element downstream of the anchor element, starting at the back (elements $j = N$ to $i\textsubscript{anchor}+1$):

\begin{enumerate}
\item Rotate elements ($N$ to $j$) by $(\alpha\textsubscript{j}-\alpha\textsubscript{j-1})$ about $(x\textsubscript{anchor,j}, 0, z\textsubscript{anchor,j})$
\item Translate elements ($N$ to $j$) by $(c\textsubscript{j-1} - l\textsubscript{j}, 0, h\textsubscript{j})$
\end{enumerate}

Now, for each element upstream of the anchor element, starting at the front (elements $k = 1$ to $i\textsubscript{anchor}-1$):

\begin{enumerate}
\item Translate elements ($1$ to $k$) by $(l\textsubscript{k+1}-c\textsubscript{k}, 0, -h\textsubscript{k+1})$
\item Rotate elements ($1$ to $k$) by ($\alpha\textsubscript{k}$-$\alpha\textsubscript{k+1}$) about $(x\textsubscript{anchor,k+1}, 0, z\textsubscript{anchor,k+1})$
\end{enumerate}

Finally, for the entire multi-element airfoil:

\begin{enumerate}
\item Translate the multi-element airfoil such that the anchor point is at the origin
\item Rotate the multi-element airfoil by $\alpha\textsubscript{anchor}$
\item Translate the multi-element airfoil by ($x\textsubscript{anchor}, 0, z\textsubscript{anchor}$) into its final position
\end{enumerate}

User:Rocher

2020-05-24T02:45:42Z

DP CFD:

File:Nicelandscapingbitch.png

2020-05-24T02:44:28Z

DP CFD:

User:Rocher

2020-05-24T02:43:45Z

DP CFD:

User:DP CFD

2020-05-22T23:39:58Z

DP CFD:

"Have you heard of DP, the CFD god?" - some guy in the library

^ I did not write this, but that's based on a true story. A friend in my Machine Design project group told me he was sitting in the library and overheard this guy saying something along the lines of "yeah there's this guy in undergrad who's really good at CFD, I think his name's like David Penner or something?". I didn't know the guy, my friend didn't know the guy, so I don't know how they knew about me. -DP

User:Rocher

2020-05-22T23:19:01Z

DP CFD:

Carbon vinyl wrapped carbon

Has a Reddit account

User:DP CFD

2020-05-22T23:16:46Z

DP CFD:

"Have you heard of DP, the CFD god?" - some guy in the library

^ I did not write this, but that's based on a true story. A friend in my capstone group told me he was sitting in the library and overheard this guy saying something along the lines of "yeah there's this guy in undergrad who's really good at CFD, I think his name's like David Penner or something?". I didn't know the guy, my friend didn't know the guy, so I don't know how they knew about me. -DP

Computational Fluid Dynamics

2020-05-16T02:56:37Z

DP CFD:

Rainbow air

[[Category:Body and Aero]]
[[Category:Internal Combustion]]

Computational Fluid Dynamics

2020-05-16T02:56:05Z

DP CFD:

[[Category:Body and Aero]]
[[Category:Internal Combustion]]

Rainbow air