% Aero ** Laplace Eq Solution for Streamlines ***

% *** by K. Chen ***********

% Case B: Uniform flow between two plates, An inlet on the ceiling ***

% u(=Vx)and density at x=0:

u=1;

den=1;

% Channel length and height ***

L=1;

H=0.5;

% x and y increments of FD mesh **

dx=0.05;

dy=dx;

nx=L/dx;

ny=H/dy;

nx1=nx+1;

ny1=ny+1;

% initial condition **

for i=1:nx1

for j=1:ny1

s(i,j)=0; % stream function (psi) values

end

end

% BCs ***

% (1) channel floor

for i=1:nx1

s(i,1)=0;

end

% (2) channel ceiling: an opening of width 0.1 at x = 0.2-0.3(i=5-7)

% with Vy = V_open

V_open=-1 % in the negative y-dir

for i=1:5

s(i,ny1)=den*u*H;

end

s(6,ny1)=s(5,ny1)-V_open*dx

s(7,ny1)=s(6,ny1)-V_open*dx

for i=8:nx1

s(i,ny1)=s(7,ny1);

end

% (3) inlet and exit

for j=2:ny

s(1,j)=den*u*dx*(j-1); % at x = 0

s(nx1,j)=(s(nx1,ny1)y)*(j-1);% psi increases linearly at x = L

end

% Iteration starts here. NI = # of iterations

NI=700;

for N=1:NI

for i=2:nx

for j=2:ny

s(i,j)=(s(i+1,j)+s(i-1,j)+s(i,j+1)+s(i,j-1))/4;

end

end

end

xx=0:dx:L;

yy=0:dy:H;

% Must do s tranpose before CONTOUR

st=s';

% C=contour(xx,yy,st,9);

C=contour(xx,yy,st,21);

clabel(C)

1. (20 points) Revise Matlab code "Stream" for the flow over a triangular airfoil shown below: Uniform flow, u=1m/s Uniform flow, u 1 m/s H=0.5 m The apexes of the triangle are at (x, y)-(0.35, 0.15), (0.45, 0.25) and (0.55, 0.15). -0 aty=0. Try = 0.12, 0.15 and 0.18 on the airfoil surface to decide which flow pattern satisfies the Kutta condition at the trailing edge (Fig. 4.19). 1. (20 points) Revise Matlab code "Stream" for the flow over a triangular airfoil shown below: Uniform flow, u=1m/s Uniform flow, u 1 m/s H=0.5 m The apexes of the triangle are at (x, y)-(0.35, 0.15), (0.45, 0.25) and (0.55, 0.15). -0 aty=0. Try = 0.12, 0.15 and 0.18 on the airfoil surface to decide which flow pattern satisfies the Kutta condition at the trailing edge (Fig. 4.19)