Multi-Element Airfoils - Revision history

Emilyanthony at 22:06, 30 May 2024

2024-05-30T22:06:40Z

DP CFD at 18:02, 2 July 2022

2022-07-02T18:02:41Z

DP CFD at 18:02, 2 July 2022

2022-07-02T18:02:16Z

DP CFD at 17:58, 2 July 2022

2022-07-02T17:58:57Z

DP CFD at 17:54, 2 July 2022

2022-07-02T17:54:59Z

DP CFD at 17:46, 2 July 2022

2022-07-02T17:46:37Z

DP CFD at 17:45, 2 July 2022

2022-07-02T17:45:11Z

DP CFD at 17:43, 2 July 2022

2022-07-02T17:43:10Z

DP CFD at 17:40, 2 July 2022

2022-07-02T17:40:26Z

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..."

2022-07-02T17:38:12Z

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..."

New page

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}

← Older revision		Revision as of 22:06, 30 May 2024
Line 68:		Line 68:

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

@@ Line 1: / Line 1: @@
 ==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.
+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:
@@ Line 11: / Line 11: @@
 Given the variables
-- Global anchor position, <math>x_{anchor}</math> and <math>z_{anchor}</math>
+* Global anchor position, <math>x_{anchor}</math> and <math>z_{anchor}</math>
-- Element angle of attack, <math>\alpha_i</math>
+* Element angle of attack, <math>\alpha_i</math>
-- Element cord, <math>c_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)
+* 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)<br />Now to position the multi-element airfoil, starting from the back:
+* 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)<br />Now to position the multi-element airfoil, starting from the back:

@@ Line 1: / Line 1: @@
 ==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:

@@ Line 18: / Line 18: @@
 - 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)<br /
+- 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)<br />Now to position the multi-element airfoil, starting from the back:
@@ Line 47: / Line 45: @@
 . Translate the multi-element airfoil by <math>(x_{anchor}, 0, z_{anchor})</math> into its final position
-Example gif for anchoring by the rear airfoil https://imgur.com/FEJzkjI
+[[File:Rear Anchor.mp4|left|middle|thumb|Example of anchoring by the rear element]]

@@ Line 10: / Line 10: @@
 Given the variables
-- Global anchor position, <math>x_{anchor}</math>and <span><math></math></span><span><math>z_{anchor}</math></span><span><math></math></span><span><math></math></span><span><math></math></span><span><math></math></span>z_anchor<br />- Element angle of attack, <math></math><math></math>α_i<br />- Element cord, c_i<math></math><br />- 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)<br />- 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)<br />Now to position the multi-element airfoil, starting from the back:
+- Global anchor position, <math>x_{anchor}</math> and <math>z_{anchor}</math>
-For each element downstream of the anchor element, starting at the back (elements j = N to  i_anchor+1):
+- Element cord, <math>c_i</math>
-. Rotate elements (N to j) by (α\_j-α_{j-1}) about (x_anchor,j, 0,  z_anchor,j)<br />2. Translate elements (N to j) by (c_{j-1} - l_j, 0, h_j)
+- 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)<br /
-. Translate elements (1 to k) by (l\_{k+1}-c\_k, 0, -h_{k+1})<br />2. Rotate elements (1 to k) by (α\_k-α\_{k+1}) about (x\_{anchor,k+1}, 0, z_{anchor,k+1})
@@ Line 28: / Line 42: @@
-. Translate the multi-element airfoil such that the anchor point is at the origin<br />2. Rotate the multi-element airfoil by α_anchor<br />3. Translate the multi-element airfoil by (x_anchor, 0, z_anchor) into its final position
+. Translate the multi-element airfoil such that the anchor point is at the origin
-[Example gif for anchoring by the front airfoil](https://imgur.com/H45nLKj)
+Example gif for anchoring by the front airfoil https://imgur.com/H45nLKj
-[Example gif for anchoring by the rear airfoil](https://imgur.com/FEJzkjI)
+Example gif for anchoring by the rear airfoil https://imgur.com/FEJzkjI

← Older revision		Revision as of 17:46, 2 July 2022
Line 10:		Line 10:
	Given the variables		Given the variables

−	- Global anchor position, <math>~~x_anchor~~</math>and <span><math></math></span><span><math></math></span><span><math></math></span><span><math></math></span><span><math></math></span><span><math></math></span>z_anchor<br />- Element angle of attack, <math></math><math></math>α_i<br />- Element cord, c_i<math></math><br />- 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)<br />- 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)<br />Now to position the multi-element airfoil, starting from the back:	+	- Global anchor position, <math>x_{anchor}</math>and <span><math></math></span><span><math>z_{anchor}</math></span><span><math></math></span><span><math></math></span><span><math></math></span><span><math></math></span>z_anchor<br />- Element angle of attack, <math></math><math></math>α_i<br />- Element cord, c_i<math></math><br />- 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)<br />- 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)<br />Now to position the multi-element airfoil, starting from the back:

← Older revision		Revision as of 17:45, 2 July 2022
Line 10:		Line 10:
	Given the variables		Given the variables

−	- Global anchor position, x_anchor and z_anchor<br />- Element angle of attack, α_i<br />- Element cord, c_i<br />- 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)<br />- 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)<br />Now to position the multi-element airfoil, starting from the back:	+	- Global anchor position, <math>x_anchor</math>and <span><math></math></span><span><math></math></span><span><math></math></span><span><math></math></span><span><math></math></span><span><math></math></span>z_anchor<br />- Element angle of attack, <math></math><math></math>α_i<br />- Element cord, c_i<math></math><br />- 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)<br />- 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)<br />Now to position the multi-element airfoil, starting from the back:

@@ Line 1: / Line 1: @@
 ==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.
+Below is how to set up this parameterization:
-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.
@@ Line 11: / Line 10: @@
 Given the variables
-\begin{itemize}
+- Global anchor position, x_anchor and z_anchor<br />- Element angle of attack, α_i<br />- Element cord, c_i<br />- 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)<br />- 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)<br />Now to position the multi-element airfoil, starting from the back:
-  \item Global anchor position, $x\textsubscript{anchor}$ and $z\textsubscript{anchor}$
-  \item Element angle of attack, $\alpha\textsubscript{i}$
-  \item Element cord, $c\textsubscript{i}$
+For each element downstream of the anchor element, starting at the back (elements j = N to  i_anchor+1):
-  \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
+. Rotate elements (N to j) by (α\_j-α_{j-1}) about (x_anchor,j, 0,  z_anchor,j)<br />2. Translate elements (N to j) by (c_{j-1} - l_j, 0, h_j)
-For each element downstream of the anchor element, starting at the back (elements $j = N$ to  $i\textsubscript{anchor}+1$):
+Now, for each element upstream of the anchor element, starting at the front (elements k = 1 to  i_anchor-1):
-Now, for each element upstream of the anchor element, starting at the front (elements $k = 1$ to  $i\textsubscript{anchor}-1$):
+. Translate elements (1 to k) by (l\_{k+1}-c\_k, 0, -h_{k+1})<br />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:
-\begin{enumerate}
-  \item Translate the multi-element airfoil such that the anchor point is at the origin
+. Translate the multi-element airfoil such that the anchor point is at the origin<br />2. Rotate the multi-element airfoil by α_anchor<br />3. Translate the multi-element airfoil by (x_anchor, 0, z_anchor) into its final position
-  \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}
+[Example gif for anchoring by the front airfoil](https://imgur.com/H45nLKj)

← Older revision		Revision as of 17:40, 2 July 2022
Line 1:		Line 1:
−	Parameterization for optimization	+	==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.		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.