Merge pull request #85 from byuflowlab/robust

juddmehr · web-flow · commit 8ab5e8703fa3 · 2025-11-05T14:01:11.000-07:00
minor naming convention change
diff --git a/README.md b/README.md
@@ -6,7 +6,7 @@
 [![Code Style: Blue](https://img.shields.io/badge/code%20style-blue-4495d1.svg)](https://github.com/invenia/BlueStyle)
 
 DuctAPE is a code for the aerodynamic evaluation of axisymmetric ducted rotors designed for incompressible (low mach) applications.
-It is strongly influenced by the underlying [theory](https://web.mit.edu/drela/Public/web/dfdc/DFDCtheory12-31.pdf) of Ducted Fan Design Code [(DFDC)](https://web.mit.edu/drela/Public/web/dfdc/), utilizing a linear axisymmetric vortex panel method for duct and center body, blade element lifting line rotor representation, and psuedo wake-screw wake model axisymmetrically smeared onto an elliptic grid for efficient computation.
+It is strongly influenced by the underlying [theory](https://web.mit.edu/drela/Public/web/dfdc/DFDCtheory12-31.pdf) of Ducted Fan Design Code [(DFDC)](https://web.mit.edu/drela/Public/web/dfdc/), utilizing a linear axisymmetric vortex panel method for duct and center body, blade element actuator line rotor representation, and psuedo wake-screw wake model axisymmetrically smeared onto an elliptic grid for efficient computation.
 
 DuctAPE has been developed specifically for applications in gradient-based optimization settings. <!-- add citations later -->
 The default solver methods have been chosen to balance code efficiency as well as robustness while simultaneously allowing for efficient automatic differentiation through DuctAPE employing [ImplicitAD.jl](https://flow.byu.edu/ImplicitAD.jl/dev/).
diff --git a/docs/latex/model_validation.tex b/docs/latex/model_validation.tex
@@ -260,7 +260,7 @@ \subsection{Verification Compared to DFDC}
      \centering
 \tikzsetnextfilename{verification/verification_geometry}
      \input{figures/verification/verification_geometry.tikz}%\hspace*{5em}
-     \caption{Single rotor verification case geometry generated by DuctAPE. Duct and center body geometry in \primary{blue}, rotor lifting line location in \secondary{red}, and approximate wake streamlines in \tertiary{green}, where markers indicate panel egdes.}
+     \caption{Single rotor verification case geometry generated by DuctAPE. Duct and center body geometry in \primary{blue}, rotor actuator line location in \secondary{red}, and approximate wake streamlines in \tertiary{green}, where markers indicate panel egdes.}
     \label{fig:singlerotorgeom}
 \end{figure}
 
diff --git a/docs/src/DuctAPE/theory_latex/ductape/vandv.tex b/docs/src/DuctAPE/theory_latex/ductape/vandv.tex
@@ -32,7 +32,7 @@ \subsection{Verification Against DFDC}
      \centering
 %\tikzsetnextfilename{verification/verification_geometry}
      \input{./ductape/figures/verification/verification_geometry.tikz}%\hspace*{5em}
-     \caption[DuctAPE verification geometry.]{Single rotor verification case geometry generated in DuctAPE. Duct and center body geometry in blue, rotor lifting line location in red, and approximate wake streamlines in green, where markers indicate panel egdes.}
+     \caption[DuctAPE verification geometry.]{Single rotor verification case geometry generated in DuctAPE. Duct and center body geometry in blue, rotor actuator line location in red, and approximate wake streamlines in green, where markers indicate panel egdes.}
     \label{fig:singlerotorgeom}
 \end{figure}
 
@@ -129,7 +129,7 @@ \subsection{Validation with Experimental Data}
      \centering
 %\tikzsetnextfilename{validation/high_speed_validation_geometry}
      \setlength{\sidecapraise}{-2.5cm}
-     \begin{sidecaption}[DuctAPE validation geometry.]{High-speed validation case geometry generated in DuctAPE. Duct and center body geometry in blue, rotor lifting line location in red, and approximate wake streamlines in green, where markers indicate panel edges.}[fig:highspeedgeom]
+     \begin{sidecaption}[DuctAPE validation geometry.]{High-speed validation case geometry generated in DuctAPE. Duct and center body geometry in blue, rotor actuator line location in red, and approximate wake streamlines in green, where markers indicate panel edges.}[fig:highspeedgeom]
      \input{./ductape/figures/validation/high_speed_validation_geometry.tikz}%\hspace*{5em}
  \end{sidecaption}
  \vskip -3cm
@@ -140,15 +140,15 @@ \subsection{Validation with Experimental Data}
 %      \centering
 % %\tikzsetnextfilename{validation/validation_geometry}
 %      \input{ductape/figures/validation/validation_geometry.tikz}%\hspace*{5em}
-%      \caption{Low-speed validation case geometry generated in DuctAPE. Duct and center body geometry in blue, rotor lifting line location in red, and approximate wake streamlines in green, where markers indicate panel edges.}
+%      \caption{Low-speed validation case geometry generated in DuctAPE. Duct and center body geometry in blue, rotor actuator line location in red, and approximate wake streamlines in green, where markers indicate panel edges.}
 %     \label{fig:lowspeedgeom}
 % \end{figure}
 %
 % \begin{figure}[h!]
 %      \centering
 % %\tikzsetnextfilename{validation/reduced_exit_validation_geometry}
 %      \input{ductape/figures/validation/reduced_exit_validation_geometry.tikz}%\hspace*{5em}
-%      \caption{Validation case geometry generated in DuctAPE. Duct and center body geometry in blue, rotor lifting line location in red, and approximate wake streamlines in green, where markers indicate panel edges.}
+%      \caption{Validation case geometry generated in DuctAPE. Duct and center body geometry in blue, rotor actuator line location in red, and approximate wake streamlines in green, where markers indicate panel edges.}
 %     \label{fig:lowspeedgeom}
 % \end{figure}
 
diff --git a/docs/src/DuctAPE/theory_latex/rotor_wake_method/figures/absolute_reference_frame.tikz b/docs/src/DuctAPE/theory_latex/rotor_wake_method/figures/absolute_reference_frame.tikz
@@ -31,7 +31,7 @@
     \draw[secondary, thick] (Orplus)-- (Orminus);
     \draw[-{Stealth[length=2pt,width=2pt]}, secondary, thick] (O)-- (Ozplus);
 
-    % blade lifting line
+    % blade actuator line
     \coordinate (rhub) at (0.0,0.5);
     \coordinate (rtip) at (0.0,2.0);
     \draw[tertiary,ultra thick] (rhub) -- (rtip);
@@ -49,7 +49,7 @@
 
     % circulations
 
-    % blade lifting line label
+    % blade actuator line label
 
     % blade circulations label
 \end{tikzpicture}
diff --git a/docs/src/DuctAPE/theory_latex/rotor_wake_method/referece_frames.tex b/docs/src/DuctAPE/theory_latex/rotor_wake_method/referece_frames.tex
@@ -46,7 +46,7 @@ \subsection{Absolute Frame}
     \centering
    \input{./rotor_wake_method/figures/absolute_reference_frame.tikz}
     % \includegraphics[width=\textwidth]{./rotor_wake_method/figures/duct_frame}
-   \caption[Absolute reference frame.]{Meridional view showing the absolute reference frame. Example duct and center body geometry is shown in blue, the origin location is shown in red, and an example blade lifting line location is shown in green.}
+   \caption[Absolute reference frame.]{Meridional view showing the absolute reference frame. Example duct and center body geometry is shown in blue, the origin location is shown in red, and an example blade actuator line location is shown in green.}
     \label{fig:absolutecoordinatesystem}
 \end{figure}
 
@@ -64,7 +64,7 @@ \subsection{Relative Frame}
 %
 We can use this cascade view to understand the various velocity decompositions through which we can relate the absolute and relative reference frames.
 %
-The blade rotates in the positive \(\theta\) direction, and the \(m\) axis (where \(dm^2 = dz^2+dr^2\)) is along a streamline passing through the lifting line representing the blade.
+The blade rotates in the positive \(\theta\) direction, and the \(m\) axis (where \(dm^2 = dz^2+dr^2\)) is along a streamline passing through the actuator line representing the blade.
 %
 That is to say, the \(m\) axis is the meridional axis, which may or may not be orthogonal to \(r\) for a given blade element.
 
diff --git a/docs/src/DuctAPE/theory_latex/rotor_wake_method/rotor_aero.tex b/docs/src/DuctAPE/theory_latex/rotor_wake_method/rotor_aero.tex
@@ -69,12 +69,12 @@ \section{A Blade Element Model}
 \subsection{Blade Circulation}
 \label{ssec:bladecirculation}
 
-To get circulation for each blade element, we treat the rotor blade as a lifting line and assume that:
+To get circulation for each blade element, we treat the rotor blade as an actuator line and assume that:
 
 \begin{assumption}
 \label{asm:liftingline}
 
-    \asm{The rotor can reasonably be modeled as a lifting line such that local blade circulation can be expressed according to the Kutta-Joukowski theorem, which states:}
+    \asm{The rotor can reasonably be modeled as an actuator line such that local blade circulation can be expressed according to the Kutta-Joukowski theorem, which states:}
 
     \[ \vect{F} = \rho \vect{W} \times \vect{\Gamma} \]
 
@@ -84,7 +84,7 @@ \subsection{Blade Circulation}
 
 \end{assumption}
 
-Modeling the rotor blades as lifting lines, if we take the velocity to be the local inflow velocity magnitude, \(W=\left[W_z^2+W_\theta^2\right]^{1/2}\) at the radial point of interest, we can take the perpendicular component of the force to be lift also at the radial point of interest.
+Modeling the rotor blades as actuator lines, if we take the velocity to be the local inflow velocity magnitude, \(W=\left[W_z^2+W_\theta^2\right]^{1/2}\) at the radial point of interest, we can take the perpendicular component of the force to be lift also at the radial point of interest.
 %
 We can then rearrange the expression for the Kutta-Joukowski theorem in \cref{asm:liftingline} for the local circulation magnitude, \(\Gamma(r)\), along the blade as
 
diff --git a/docs/src/DuctAPE/theory_latex/rotor_wake_method/wake_aero.tex b/docs/src/DuctAPE/theory_latex/rotor_wake_method/wake_aero.tex
@@ -94,7 +94,7 @@ \subsection{Starting with a Standard Wake Screw}
 
     \limit{This is a simplified modeling approach that ignores the some of the flow turning of the blade.}
 
-    \why{By using this lifting line approach rather than some other approach, such as a lifting surface, we (like many of our other assumptions) simplify the model, allowing for simpler implementation and faster computation.}
+    \why{By using this actuator line approach rather than some other approach, such as a lifting surface, we (like many of our other assumptions) simplify the model, allowing for simpler implementation and faster computation.}
 
 \end{assumption}
 
@@ -160,7 +160,7 @@ \subsection{Starting with a Standard Wake Screw}
 %
 On the other hand, \(\gamma_\theta\) would only be generally applicable if we assumed that the \(\Omega r\) component of \(W_\theta\) (see \cref{eqn:relativevelocities}) was constant in the entire wake.
 %
-In actuality, we only know \(\Omega r\) right at the rotor lifting line, but not generally in the remainder of the wake.
+In actuality, we only know \(\Omega r\) right at the rotor actuator line, but not generally in the remainder of the wake.
 %
 We therefore want to develop a more general expression for \(\gamma_\theta\) based on requiring the wake to be force-free, or in other words, we demand static pressure continuity across the vortex sheets.
 %
@@ -790,7 +790,7 @@ \subsection{Piece 4: Disk and Sheet Jumps}
     \Delta h_{\text{disk}} = w_c = \Omega \Delta(r C_\theta).
 \end{equation}
 
-\noindent We can relate the jump in enthalpy to the circulation by applying our lifting line assumption (\cref{asm:liftingline}),
+\noindent We can relate the jump in enthalpy to the circulation by applying our actuator line assumption (\cref{asm:liftingline}),
 which means that there is no radial deviation in flow across the blade, as well as substituting in for \(C_\theta\) from \cref{eqn:vtheta} (for a single disk).
 
 % \begin{equation}
diff --git a/docs/src/DuctAPE/theory_latex/rotor_wake_method/wake_geometry.tex b/docs/src/DuctAPE/theory_latex/rotor_wake_method/wake_geometry.tex
@@ -11,7 +11,7 @@ \section{A Streamlined Elliptic Grid}
 %
 By so doing, we complete a large portion of the computation related to the wake outside of the iterative solver, greatly reducing computational cost.
 %
-We utilize a method from \citeauthor{thompson_1974} to determine approximate streamline locations based on the duct and centerbody geometries and blade element positions along the rotor lifting line.
+We utilize a method from \citeauthor{thompson_1974} to determine approximate streamline locations based on the duct and centerbody geometries and blade element positions along the rotor actuator line.
 
 In the method of \citeauthor{thompson_1974} a transformation is defined between rectangular and arbitrary shaped regions, with the arbitrary shaped region lying on a physical plane.\scite{thompson_1974}
 %
@@ -437,7 +437,7 @@ \subsection{Discretizing the Wake into Panels}
 % %
 % By Helmholtz` theorems, we cannot just have the vortex filaments of the wake (smeared or otherwise) simply end.
 % %
-% On the rotor blades, we have lines of circulation [(reference one of the figures)] from which the wake filaments are shed (as would be expected from a lifting line method).
+% On the rotor blades, we have lines of circulation [(reference one of the figures)] from which the wake filaments are shed (as would be expected from an actuator line method).
 % %
 % We have not, however, defined those shed wake filaments to be semi-infinite, but rather to be discretized into smeared vortex panels.
 % %
diff --git a/docs/src/index.md b/docs/src/index.md
@@ -6,7 +6,7 @@
 [![Code Style: Blue](https://img.shields.io/badge/code%20style-blue-4495d1.svg)](https://github.com/invenia/BlueStyle)
 
 DuctAPE is a code for the aerodynamic evaluation of axisymmetric ducted rotors designed for incompressible (low mach) applications.
-It is strongly influenced by the underlying [theory](https://web.mit.edu/drela/Public/web/dfdc/DFDCtheory12-31.pdf) of Ducted Fan Design Code [(DFDC)](https://web.mit.edu/drela/Public/web/dfdc/), utilizing a linear axisymmetric vortex panel method for duct and center body, blade element lifting line rotor representation, and psuedo wake-screw wake model axisymmetrically smeared onto an elliptic grid for efficient computation.
+It is strongly influenced by the underlying [theory](https://web.mit.edu/drela/Public/web/dfdc/DFDCtheory12-31.pdf) of Ducted Fan Design Code [(DFDC)](https://web.mit.edu/drela/Public/web/dfdc/), utilizing a linear axisymmetric vortex panel method for duct and center body, blade element actuator line rotor representation, and psuedo wake-screw wake model axisymmetrically smeared onto an elliptic grid for efficient computation.
 
 DuctAPE has been developed specifically for applications in gradient-based optimization settings.
 The default solver methods have been chosen to balance code efficiency as well as robustness while simultaneously allowing for efficient automatic differentiation through DuctAPE employing [ImplicitAD.jl](https://flow.byu.edu/ImplicitAD.jl/dev/).
diff --git a/src/preprocess/geometry/body_geometry.jl b/src/preprocess/geometry/body_geometry.jl
@@ -81,7 +81,10 @@ function reinterpolate_bodies!(
 
     # repaneled casing inlet nodes
     casing_inlet_z = scaled_cosine_spacing(
-        num_duct_inlet_panels + 1, 2 * duct_inlet_length, duct_le_coordinates[1]; mypi=pi / 2.0
+        num_duct_inlet_panels + 1,
+        2 * duct_inlet_length,
+        duct_le_coordinates[1];
+        mypi=pi / 2.0,
     )
     casing_inlet_r = finterp(casing_z, casing_r, casing_inlet_z)
 
@@ -98,7 +101,10 @@ function reinterpolate_bodies!(
 
     # repaneled nacelle inlet nodes
     nacelle_inlet_z = scaled_cosine_spacing(
-        num_duct_inlet_panels + 1, 2 * duct_inlet_length, duct_le_coordinates[1]; mypi=pi / 2.0
+        num_duct_inlet_panels + 1,
+        2 * duct_inlet_length,
+        duct_le_coordinates[1];
+        mypi=pi / 2.0,
     )
     nacelle_inlet_r = finterp(nacelle_z, nacelle_r, nacelle_inlet_z)
 
@@ -114,11 +120,26 @@ function reinterpolate_bodies!(
 
     center_body_inlet_length = center_body_in_wake_z[1] - center_body_z[1]
     center_body_inlet_z = scaled_cosine_spacing(
-        num_center_body_inlet_panels + 1, 2 * center_body_inlet_length, center_body_z[1]; mypi=pi / 2.0
+        num_center_body_inlet_panels + 1,
+        2 * center_body_inlet_length,
+        center_body_z[1];
+        mypi=pi / 2.0,
     )
     center_body_inlet_r = finterp(center_body_z, center_body_r, center_body_inlet_z)
 
     # assemble new duct coordinates
+
+    @assert (
+        size(rp_duct_coordinates) == size(
+            hcat(
+                [reverse(casing_in_wake_z)'; reverse(casing_in_wake_r)'],
+                [reverse(casing_inlet_z)[2:end]'; reverse(casing_inlet_r)[2:end]'],
+                [nacelle_inlet_z[2:end]'; nacelle_inlet_r[2:end]'],
+                [nacelle_in_wake_z[2:end]'; nacelle_in_wake_r[2:end]'],
+            ),
+        )
+    ) "Duct Repaneling Error: check that the 'dte_minus_cbte' and `num_panels` inputs in the `paneling_constants` are correct"
+
     rp_duct_coordinates .= hcat(
         [reverse(casing_in_wake_z)'; reverse(casing_in_wake_r)'],
         [reverse(casing_inlet_z)[2:end]'; reverse(casing_inlet_r)[2:end]'],
diff --git a/src/preprocess/geometry/rotor_geometry.jl b/src/preprocess/geometry/rotor_geometry.jl
@@ -199,7 +199,7 @@ Obtain rotor hub and tip radii based on duct and center_body geometry.
 - `rp_duct_coordinates::Matrix{Float}` : re-paneled duct coordinates
 - `rp_center_body_coordinates::Matrix{Float}` : re-paneled center_body coordinates
 - `tip_gaps::Vector{Float}` : gaps between blade tips and duct surface (MUST BE ZEROS for now)
-- `rotor_axial_position::Vector{Float}` : rotor lifting line axial positions.
+- `rotor_axial_position::Vector{Float}` : rotor actuator line axial positions.
 
 # Returns
 - `Rtips::Vector{Float}` : rotor tip radii
@@ -319,7 +319,7 @@ end
 Generate rotor panel objects.
 
 # Arguments
-- `rotor_axial_position::Vector{Float}` : rotor lifting line axial position
+- `rotor_axial_position::Vector{Float}` : rotor actuator line axial position
 - `wake_grid::Array{Float,3}` : wake elliptic grid axial and radial locations
 - `rotor_indices_in_wake::Vector{Int}` : indices of where along wake the rotors are placed
 - `num_wake_sheets::Int` : number of wake sheets
diff --git a/src/preprocess/preprocess.jl b/src/preprocess/preprocess.jl
@@ -242,7 +242,7 @@ Function that calls all of the various panel generation functions are returns a
 - `rp_center_body_coordinates::Matrix{Float}` : matrix containing the re-paneled center_body coordinates
 - `num_wake_sheets::Int` : number of wake sheets
 - `rotor_indices_in_wake::Vector{Int}` : vector containing the indices of where in the wake the rotors reside (used later to define the rotor panel edges).
-- `rotor_axial_position:Vector{Float}` : axial locations of rotor lifting lines (contained in Rotor)
+- `rotor_axial_position:Vector{Float}` : axial locations of rotor actuator lines (contained in Rotor)
 - `wake_grid::Array{Float}` : array containig the z and r elliptic grid points defning the wake geometry.
 
 # Keyword Arguments

Original file line number	Diff line number	Diff line change
`@@ -46,7 +46,7 @@ \subsection{Absolute Frame}`
`46`	`46`	`\centering`
`47`	`47`	`\input{./rotor_wake_method/figures/absolute_reference_frame.tikz}`
`48`	`48`	`% \includegraphics[width=\textwidth]{./rotor_wake_method/figures/duct_frame}`
`49`		`- \caption[Absolute reference frame.]{Meridional view showing the absolute reference frame. Example duct and center body geometry is shown in blue, the origin location is shown in red, and an example blade lifting line location is shown in green.}`
	`49`	`+ \caption[Absolute reference frame.]{Meridional view showing the absolute reference frame. Example duct and center body geometry is shown in blue, the origin location is shown in red, and an example blade actuator line location is shown in green.}`
`50`	`50`	`\label{fig:absolutecoordinatesystem}`
`51`	`51`	`\end{figure}`
`52`	`52`
`@@ -64,7 +64,7 @@ \subsection{Relative Frame}`
`64`	`64`	`%`
`65`	`65`	`We can use this cascade view to understand the various velocity decompositions through which we can relate the absolute and relative reference frames.`
`66`	`66`	`%`
`67`		`-The blade rotates in the positive \(\theta\) direction, and the \(m\) axis (where \(dm^2 = dz^2+dr^2\)) is along a streamline passing through the lifting line representing the blade.`
	`67`	`+The blade rotates in the positive \(\theta\) direction, and the \(m\) axis (where \(dm^2 = dz^2+dr^2\)) is along a streamline passing through the actuator line representing the blade.`
`68`	`68`	`%`
`69`	`69`	`That is to say, the \(m\) axis is the meridional axis, which may or may not be orthogonal to \(r\) for a given blade element.`
`70`	`70`
Original file line number	Diff line number	Diff line change
`@@ -94,7 +94,7 @@ \subsection{Starting with a Standard Wake Screw}`
`94`	`94`
`95`	`95`	`\limit{This is a simplified modeling approach that ignores the some of the flow turning of the blade.}`
`96`	`96`
`97`		`- \why{By using this lifting line approach rather than some other approach, such as a lifting surface, we (like many of our other assumptions) simplify the model, allowing for simpler implementation and faster computation.}`
	`97`	`+ \why{By using this actuator line approach rather than some other approach, such as a lifting surface, we (like many of our other assumptions) simplify the model, allowing for simpler implementation and faster computation.}`
`98`	`98`
`99`	`99`	`\end{assumption}`
`100`	`100`
`@@ -160,7 +160,7 @@ \subsection{Starting with a Standard Wake Screw}`
`160`	`160`	`%`
`161`	`161`	`On the other hand, \(\gamma_\theta\) would only be generally applicable if we assumed that the \(\Omega r\) component of \(W_\theta\) (see \cref{eqn:relativevelocities}) was constant in the entire wake.`
`162`	`162`	`%`
`163`		`-In actuality, we only know \(\Omega r\) right at the rotor lifting line, but not generally in the remainder of the wake.`
	`163`	`+In actuality, we only know \(\Omega r\) right at the rotor actuator line, but not generally in the remainder of the wake.`
`164`	`164`	`%`
`165`	`165`	`We therefore want to develop a more general expression for \(\gamma_\theta\) based on requiring the wake to be force-free, or in other words, we demand static pressure continuity across the vortex sheets.`
`166`	`166`	`%`
`@@ -790,7 +790,7 @@ \subsection{Piece 4: Disk and Sheet Jumps}`
`790`	`790`	`\Delta h_{\text{disk}} = w_c = \Omega \Delta(r C_\theta).`
`791`	`791`	`\end{equation}`
`792`	`792`
`793`		`-\noindent We can relate the jump in enthalpy to the circulation by applying our lifting line assumption (\cref{asm:liftingline}),`
	`793`	`+\noindent We can relate the jump in enthalpy to the circulation by applying our actuator line assumption (\cref{asm:liftingline}),`
`794`	`794`	`which means that there is no radial deviation in flow across the blade, as well as substituting in for \(C_\theta\) from \cref{eqn:vtheta} (for a single disk).`
`795`	`795`
`796`	`796`	`% \begin{equation}`
Original file line number	Diff line number	Diff line change
`@@ -11,7 +11,7 @@ \section{A Streamlined Elliptic Grid}`
`11`	`11`	`%`
`12`	`12`	`By so doing, we complete a large portion of the computation related to the wake outside of the iterative solver, greatly reducing computational cost.`
`13`	`13`	`%`
`14`		`-We utilize a method from \citeauthor{thompson_1974} to determine approximate streamline locations based on the duct and centerbody geometries and blade element positions along the rotor lifting line.`
	`14`	`+We utilize a method from \citeauthor{thompson_1974} to determine approximate streamline locations based on the duct and centerbody geometries and blade element positions along the rotor actuator line.`
`15`	`15`
`16`	`16`	`In the method of \citeauthor{thompson_1974} a transformation is defined between rectangular and arbitrary shaped regions, with the arbitrary shaped region lying on a physical plane.\scite{thompson_1974}`
`17`	`17`	`%`
`@@ -437,7 +437,7 @@ \subsection{Discretizing the Wake into Panels}`
`437`	`437`	`% %`
`438`	`438`	% By Helmholtz` theorems, we cannot just have the vortex filaments of the wake (smeared or otherwise) simply end.
`439`	`439`	`% %`
`440`		`-% On the rotor blades, we have lines of circulation [(reference one of the figures)] from which the wake filaments are shed (as would be expected from a lifting line method).`
	`440`	`+% On the rotor blades, we have lines of circulation [(reference one of the figures)] from which the wake filaments are shed (as would be expected from an actuator line method).`
`441`	`441`	`% %`
`442`	`442`	`% We have not, however, defined those shed wake filaments to be semi-infinite, but rather to be discretized into smeared vortex panels.`
`443`	`443`	`% %`