-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathmain.m
182 lines (130 loc) · 7.31 KB
/
main.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
%% INTRO
clc;
clear;
close all;
%% PROBLEM DEFINITION
run("profili.m")
nacapane_1 = nacapane_slat;
N1 = N_slat;
nacapane_2 = nacapane_main;
N2 = N_main;
nacapane_3 = nacapane_flap;
N3 = N_flap;
u_inf = [50;
0]; % ASINTOTIC VELOCITY [m/s]
%% FOIL PANELISATION PLOT
% figure;
axis equal;
hold on;
grid on;
plot(nacapane_1.x_pane, nacapane_1.y_pane, '-'); % FOIL 1 RAPRESENTATION
plot(nacapane_2.x_pane, nacapane_2.y_pane, '-'); % FOIL 2 RAPRESENTATION
plot(nacapane_3.x_pane, nacapane_3.y_pane, '-'); % FOIL 2 RAPRESENTATION
plot(nacapane_1.x_pane_m, nacapane_1.y_pane_m, '-'); % FOIL 1 RAPRESENTATION
plot(nacapane_2.x_pane_m, nacapane_2.y_pane_m, '-'); % FOIL 2 RAPRESENTATION
plot(nacapane_3.x_pane_m, nacapane_3.y_pane_m, '-'); % FOIL 2 RAPRESENTATION
% plot(center_1(:, 1), center_1(:, 2), 'o'); % CENTERS 1
% plot(center_2(:, 1), center_2(:, 2), 'o'); % CENTERS 2
% plot(center_3(:, 1), center_3(:, 2), 'o'); % CENTERS 2
title("Foil panelisation", 'Interpreter', 'latex')
legend('slat', 'main', 'flap')
%% LINEAR SISTEM
[A, b, center_1, center_2, center_3] = Matrix_definition(nacapane_1, nacapane_2, nacapane_3, N1, N2, N3, u_inf);
x = A\b; % COMPUTATION OF LINEAR SISTEM SOLUTION
q_1 = x(1:N1); % INTENSITIES OF SURCES FOIL 1
q_2 = x(N1+1:N1+N2); % INTENSITIES OF SURCES FOIL 2
q_3 = x(N1+N2+1:end-3); % INTENSITIES OF SURCES FOIL 3
gamma_1 = x(end-2); % INTENSITY OF VORTEX FOIL 1
gamma_2 = x(end-1); % INTENSITY OF VORTEX FOIL 2
gamma_3 = x(end); % INTENSITY OF VORTEX FOIL 3
u_tot = @(x, y) TotalVelocity_groundX3 (q_1, q_2, q_3, gamma_1, gamma_2, ...
gamma_3, u_inf, x, y, nacapane_1, nacapane_2, ...
nacapane_3, N1, N2, N3);
%% plot y-component of velocity
Nfx = 100;
Nfy = 100;
xx = linspace(-1,4,Nfx);
V_y_field = zeros(1, Nfy);
for i = 1:Nfx
u_aux = TotalVelocity_groundX3 (q_1, q_2, q_3,gamma_1, gamma_2, ...
gamma_3, u_inf, xx(i), 0, ...
nacapane_1, nacapane_2, ...
nacapane_3, N1, N2, N3);
V_y_field(i) = u_aux'*[0;1];
end
figure;
plot(xx, V_y_field);
%% COEFFICIENTS COMPUTATION
Cp_1 = zeros(N1, 1); % MEMORY ALLOCATION
Cp_2 = zeros(N2, 1); % MEMORY ALLOCATION
Cp_3 = zeros(N3, 1); % MEMORY ALLOCATION
Circ_1 = 0; % VARIABLE INITIALIZATION
Circ_2 = 0; % VARIABLE INITIALIZATION
Circ_3 = 0; % VARIABLE INITIALIZATION
% 1
for i = 1 : N1
Estremo_1 = [nacapane_1.x_pane(i); nacapane_1.y_pane(i)]; % DEFINITION OF COORDINATES OF FIRST POINT OF PANEL i
Estremo_2 = [nacapane_1.x_pane(i+1); nacapane_1.y_pane(i+1)]; % DEFINITION OF COORDINATES OF LAST POINT OF PANEL i
[~, tau] = versors (Estremo_1, Estremo_2); % DEFINITION OF TANGENT VERSOR OF PANEL i
aux = u_tot(center_1(i,1),center_1(i,2))'*tau;
Cp_1(i) = 1 - aux^2/(norm(u_inf))^2; % PRESSURE COEFFICIENT COMPUTATION
Circ_1 = Circ_1 + norm(Estremo_2 - Estremo_1)*gamma_1; % CIRCOLATION COMPUTATION
end
Cl_1 = 2*Circ_1/(norm(u_inf)*chord_slat); % LIFT COEFFICIENT COMPUTATION
% 2
for i = 1 : N2
Estremo_1 = [nacapane_2.x_pane(i); nacapane_2.y_pane(i)]; % DEFINITION OF COORDINATES OF FIRST POINT OF PANEL i
Estremo_2 = [nacapane_2.x_pane(i+1); nacapane_2.y_pane(i+1)]; % DEFINITION OF COORDINATES OF LAST POINT OF PANEL i
[~, tau] = versors (Estremo_1, Estremo_2); % DEFINITION OF TANGENT VERSOR OF PANEL i
aux = u_tot(center_2(i,1),center_2(i,2))'*tau;
Cp_2(i) = 1 - aux^2/(norm(u_inf))^2; % PRESSURE COEFFICIENT COMPUTATION
Circ_2 = Circ_2 + norm(Estremo_2 - Estremo_1)*gamma_2; % CIRCOLATION COMPUTATION
end
Cl_2 = 2*Circ_2/(norm(u_inf)*chord_main); % LIFT COEFFICIENT COMPUTATION
% 3
for i = 1 : N3
Estremo_1 = [nacapane_3.x_pane(i); nacapane_3.y_pane(i)]; % DEFINITION OF COORDINATES OF FIRST POINT OF PANEL i
Estremo_2 = [nacapane_3.x_pane(i+1); nacapane_3.y_pane(i+1)]; % DEFINITION OF COORDINATES OF LAST POINT OF PANEL i
[~, tau] = versors (Estremo_1, Estremo_2); % DEFINITION OF TANGENT VERSOR OF PANEL i
aux = u_tot(center_3(i,1),center_3(i,2))'*tau;
Cp_3(i) = 1 - aux^2/(norm(u_inf))^2; % PRESSURE COEFFICIENT COMPUTATION
Circ_3 = Circ_3 + norm(Estremo_2 - Estremo_1)*gamma_3; % CIRCOLATION COMPUTATION
end
Cl_3 = 2*Circ_3/(norm(u_inf)*chord_flap); % LIFT COEFFICIENT COMPUTATION
rho = 1.225;
L = rho*norm(u_inf)*(Circ_1+Circ_2+Circ_3);
Cl = L/(0.5*rho*norm(u_inf)^2*(chord_main+chord_slat+chord_flap));
%% PRESSURE COEFFICIENT PLOT
figure;
hold on;
grid on;
xplot = linspace(0,1,N1/2+1);
xplot_meno = linspace(1,0,N1/2);
plot(xplot_meno,-Cp_1(1:N1/2), 'b-', 'LineWidth', 1.5)
plot(xplot,-Cp_1(N1/2:N1), 'b--', 'LineWidth', 1.5)
plot(xplot_meno,-Cp_2(1:N1/2), 'r-', 'LineWidth', 1.5)
plot(xplot,-Cp_2(N2/2:N2), 'r--', 'LineWidth', 1.5)
plot(xplot_meno,-Cp_3(1:N3/2), 'g-', 'LineWidth', 1.5)
plot(xplot,-Cp_3(N3/2:N3), 'g--', 'LineWidth', 1.5)
legend('bottom airfoil 1', 'top airfoil 1', ...
'bottom airfoil 2', 'top airfoil 2', ...
'bottom airfoil 3', 'top airfoil 3')
xlabel('$x$', 'Interpreter', 'latex')
ylabel('$C_p$','Interpreter', 'latex')
figure
hold on
grid on
plot(nacapane_1.x_pane(1:N1/2),-Cp_1(1:N1/2), 'b-', 'LineWidth', 1.5)
plot(nacapane_1.x_pane(N1/2:N1),-Cp_1(N1/2:N1), 'b--', 'LineWidth', 1.5)
plot(nacapane_2.x_pane(1:N2/2) ,-Cp_2(1:N2/2), 'r-', 'LineWidth', 1.5)
plot(nacapane_2.x_pane(N2/2:N2) ,-Cp_2(N2/2:N2), 'r--', 'LineWidth', 1.5)
plot(nacapane_3.x_pane(1:N3/2) ,-Cp_3(1:N3/2), 'g-', 'LineWidth', 1.5)
plot(nacapane_3.x_pane(N3/2:N3) ,-Cp_3(N3/2:N3), 'g--', 'LineWidth', 1.5)
%% FIELD PLOT
x_lim = [-1, 2];
y_lim = [0, h_main+1];
Nfx = 50;
Nfy = 50;
Velocity_Plot(Nfx, Nfy, x_lim, y_lim, q_1, q_2, q_3, gamma_1, gamma_2, ...
gamma_3, nacapane_1, nacapane_2, nacapane_3, N1, N2, N3, ...
u_inf, 'A_Field');