NACA 2412 翼型面元法 MATLAB 程序：考虑尾缘库塔条件

以下是一个考虑尾缘库塔条件的 MATLAB 孤立翼型面元法程序示例，针对 NACA 2412 翼型：

% 孤立翼型面元法（考虑尾缘库塔条件）MATLAB 程序示例

% 翼型几何形状定义
% 以 NACA 2412 翼型为例
c = 1; % 翼弦长
m = 0.02; % 最大弯度位置参数
p = 0.4; % 最大弯度厚度参数
t = 0.12; % 最大弯度厚度比
n = 100; % 离散点数

% 生成翼型上表面坐标
x_upper = linspace(0, c, n);
yt_upper = 5 * t * (0.2969 * sqrt(x_upper/c) - 0.126 * (x_upper/c) - 0.3516 * (x_upper/c).^2 + 0.2843 * (x_upper/c).^3 - 0.1015 * (x_upper/c).^4);
xc_upper = x_upper - yt_upper .* sin(atan(2 * m * (x_upper/c - p)/(p^2)));
yc_upper = yt_upper .* cos(atan(2 * m * (x_upper/c - p)/(p^2)));

% 生成翼型下表面坐标
x_lower = linspace(c, 0, n);
yt_lower = -yt_upper;
xc_lower = x_lower - yt_lower .* sin(atan(2 * m * (x_lower/c - p)/(p^2))) + c;
yc_lower = yt_lower .* cos(atan(2 * m * (x_lower/c - p)/(p^2)));

% 合并上下表面坐标
x = [x_upper, x_lower(2:end-1)];
yc = [yc_upper, yc_lower(2:end-1)];

% 创建面元
numPanels = length(x) - 1;
panels = zeros(numPanels, 4); % 每个面元的坐标 [x1, y1, x2, y2]
for i = 1:numPanels
    panels(i, :) = [x(i), yc(i), x(i+1), yc(i+1)];
end

% 边界条件定义
V_inf = 1; % 无穷远处的远场速度
alpha = 5; % 迎角
alpha_rad = deg2rad(alpha);
U_inf = V_inf * cos(alpha_rad);
W_inf = V_inf * sin(alpha_rad);

% 形成影响系数矩阵和右侧项
A = zeros(numPanels+1);
b = zeros(numPanels+1, 1);

% 构建面元影响系数矩阵
for i = 1:numPanels
    for j = 1:numPanels
        if i == j
            A(i,j) = -pi;
        else
            A(i,j) = calcInfluenceCoeff(panels(i,:), panels(j,:));
        end
    end
    A(i,numPanels+1) = 1;
    b(i) = -U_inf * cos(alpha_rad) - W_inf * sin(alpha_rad);
end

% 构建尾缘库塔条件的影响系数矩阵项
for j = 1:numPanels
    A(numPanels+1,j) = 0;
end
A(numPanels+1,numPanels+1) = 1;

% 构建尾缘库塔条件的右侧项
b(numPanels+1) = 0;

% 解线性方程组并得到面元强度
gamma = A\b;

% 计算速度分布和压力分布
x_plot = linspace(0, c, 100); % 用于绘制速度和压力分布的点
V = zeros(size(x_plot));
cp = zeros(size(x_plot));
for i = 1:length(x_plot)
    V(i) = calcVelocity(x_plot(i), alpha_rad, gamma, panels);
    cp(i) = 1 - (V(i)/V_inf)^2;
end

% 绘制速度分布曲线
figure
plot(x_plot, V)
xlabel('x')
ylabel('Velocity')
title('Velocity Distribution around NACA 2412 Airfoil')

% 绘制压力分布曲线
figure
plot(x_plot, cp)
xlabel('x')
ylabel('Cp')
title('Pressure Coefficient Distribution around NACA 2412 Airfoil')


% 计算面元对点的影响系数函数
function A_ij = calcInfluenceCoeff(Panel_i, Panel_j)
    x1_i = Panel_i(1);
    y1_i = Panel_i(2);
    x2_i = Panel_i(3);
    y2_i = Panel_i(4);

    x1_j = Panel_j(1);
    y1_j = Panel_j(2);
    x2_j = Panel_j(3);
    y2_j = Panel_j(4);

    A_ij = -0.5 * (log(dist(x1_i, y1_i, x2_i, y2_i) / dist(x1_j, y1_j, x2_j, y2_j)) / (2 * pi));
end

% 计算点的速度函数
function V = calcVelocity(x, alpha, gamma, panels)
    V = 0;
    for i = 1:length(panels)
        V = V + (gamma(i) / (2 * pi)) * calcLift(x, panels(i,:)) * cos(alpha);
    end
end

% 计算面元的升力函数
function L = calcLift(x, panel)
    x1 = panel(1);
    y1 = panel(2);
    x2 = panel(3);
    y2 = panel(4);

    dx = x2 - x1;
    dy = y2 - y1;

    L = dx * (x - x1) + dy * (y - y1);
end

% 计算两点之间的距离函数
function d = dist(x1, y1, x2, y2)
    d = sqrt((x2 - x1)^2 + (y2 - y1)^2);
end

请注意，此示例程序仅考虑了 NACA 2412 翼型，并假设了一些参数和条件。对于其他翼型，您需要相应地调整翼型参数和生成坐标的方法。此外，此程序还是一个简化版本，可能无法适应所有情况，并且还有一些细节需要根据您的具体需求进行调整。

希望这个示例能够帮助您编写考虑尾缘库塔条件的孤立翼型面元法的 MATLAB 程序！如有任何进一步的问题，请随时提问。