Uniform Flow
Uniform Flow
Modeling a Submarine Using Potential Flow Analysis
Modeling a Submarine Using Potential Flow Analysis
Potential flow analysis can be used to model a variety of objects and how they interact with fluid flows.
June 21, 2017—Kaleb Alekel
The most basic potential flow regime is a uniform stream in the x direction.
Let’s model a stream with velocity U=5:
In[]:=
U=5;
The following are the stream function and velocity potential, respectively:
In[]:=
ψuniform[y_]=Uy;ϕuniform[x_]=Ux;
Finding the x and y components of the velocity is trivial in this case, but it will help with understanding a more complex flow later.
To find the x component of the velocity of the stream, we take the derivative of the velocity potential with respect to x:
In[]:=
u=D[ϕuniform[x],x]
Out[]=
5
To find the y component, we take the negative derivative of the stream function with respect to y:
In[]:=
v=-D[ψuniform[x],y]
Out[]=
0
Now let’s plot the streamlines of the flow:
In[]:=
StreamPlot[{u,v},{x,-6,6},{y,-6,6},StreamScaleFull,FrameLabel{x,y},StreamStyle{Arrowheads[.03],Black}]
Out[]=
Source or Sink at the Origin
Source or Sink at the Origin
Rankine Half-Body
Rankine Half-Body
FURTHER EXPLORATIONS
Try modeling a symmetrical airfoil using a series of sinks and sources in a uniform flow.
Try modeling an airfoil in a uniform stream near the ground by using an image airfoil.
AUTHORSHIP INFORMATION
Kaleb Alekel
6/21/17