README.md

aeroHS

This program computes the flow properties around NACA 4 digits airfoils. It uses the Hess-Smith method to solve the flow field.

It can solve 2 airfoils problems and ground effect problems (with both the image method and with a ground panelization method).

Code compilation steps

In order to compile the code: CMake, GNUplot, LAPACK and BLAS libraries are required.

cmake .

make 

cd bin/

./aeroHS

How to compute flow properties

Physics

The Hess-Smith method treats incompressible inviscid potential flows:

$$ \boldsymbol{\nabla} \cdot \boldsymbol{u} = 0 $$ $$ \boldsymbol{\nabla} \times \boldsymbol{u} = \boldsymbol{0} \\ $$

This brings solving the Laplace problem for the scalar function $\phi_{(x, y)}$ :

$$ \text{if} \ \boldsymbol{u} = \boldsymbol{\nabla} \phi \rightarrow \boldsymbol{\nabla} \times \boldsymbol{\nabla} \phi = \boldsymbol{0} $$

$$ \text{In order to satisfy incompressibility: } \boldsymbol{\nabla} \cdot \boldsymbol{\nabla} \phi = \boldsymbol{\Delta} \phi = 0 $$

In order to solve the problem, it is used a first order discretization for the potential $\phi$ made by source/sink and vortex distribution on airfoil's panels. The Hess-Smith method uses a constant distribution of vorticity over the panels and a variable distribution of sources/sinks. The Runge-Kutta condition is applied at the trailing edge of the airfoil(s) in order to solve the problem.

Program

Flow simulation and Cp study of NACA0012.

Once in bin/:

# launching program
./aeroHS
# selecting analysis -> 1 airfoil analysis
1 
# selecting Cp analysis
1
# selecting AOA
0
# selecting airfoil name
naca0012
# selecting chord discretization
120
# leading edge position setup
# selecting leading edge x position
0
# selecting leading edge y position 
0
# grid setup coords for flow visualization
# selecting grid initial x coord
-1 
# selecting grid final x coord
3
# selecting grid initial y coord
-0.5
# selecting grid final y coord
0.5
# flow plot with GNUplot