日光温室不通风情况下的湿度分布模型,利用流体力学原理和湍流模型实现。输入参数包括温室具体结构、位置、植物蒸腾参数、蒸发参数、墙体导热系数、土壤含水量、空气流动速度、降水量、风速、水蒸气含量等多个参数,输出湿度分布图。matlab代码实现案例
时间: 2023-10-20 15:21:57 浏览: 40
实现这个模型需要用到CFD(Computational Fluid Dynamics,计算流体动力学)模拟方法,需要一定的数学物理基础和编程能力。以下是一个简单的matlab代码实现案例,仅供参考。
```matlab
% 定义常数
Rd = 287; % 干空气气体常数
Rv = 461.5; % 水蒸气气体常数
Cp = 1005; % 空气比热容
Lv = 2.5e6; % 水蒸气潜热
g = 9.81; % 重力加速度
k = 0.4; % 湍流模型常数
% 定义参数
L = 10; % 温室长度
W = 5; % 温室宽度
H = 3; % 温室高度
dx = 0.1; % 离散网格大小
dy = 0.1;
dz = 0.1;
dt = 0.1; % 时间步长
T = 288; % 初始温度
P = 101325; % 大气压强
RH = 0.5; % 初始相对湿度
u = 0.1; % 空气流动速度
E = 0.1; % 植物蒸腾速率
Ew = 0.05; % 土壤水分蒸发速率
kw = 0.1; % 土壤导热系数
kw1 = 0.5; % 温室墙体导热系数
q = 0.1; % 降水速率
v = 5; % 风速
% 初始化网格
x = 0:dx:L;
y = 0:dy:W;
z = 0:dz:H;
T = repmat(T, length(x), length(y), length(z));
RH = repmat(RH, length(x), length(y), length(z));
u = repmat(u, length(x), length(y), length(z));
E = repmat(E, length(x), length(y), length(z));
Ew = repmat(Ew, length(x), length(y));
q = repmat(q, length(x), length(y));
v = repmat(v, length(x), length(y), length(z));
% 开始模拟
for t = 0:dt:3600
% 计算水蒸气含量
es = 6.11 * 10 ^ (7.5 * T ./ (T + 237.3)); % 饱和水蒸气压
e = RH .* es; % 实际水蒸气压
w = 0.622 * e ./ (P - e); % 水蒸气含量
% 计算空气密度
rho = P ./ (Rd * T) .* (1 + 0.61 * w);
% 计算速度场
[U, V, W] = calc_velocity(u, v, rho, dx, dy, dz, k);
% 计算湍流能
k0 = calc_k(rho, U, V, W, k);
% 计算湍流耗散率
epsilon = calc_epsilon(k0, rho, U, V, W, dx, dy, dz, k);
% 计算温度场
T = calc_temperature(T, rho, Cp, U, V, W, dx, dy, dz, kw1);
% 计算湿度场
RH = calc_humidity(w, rho, Cp, U, V, W, dx, dy, dz, E, Ew, q, kw, kw1, Lv, dt);
% 计算土壤水分含量
Ew = calc_soil_moisture(Ew, q, kw, dx, dy, dt);
% 计算风速场
v = calc_wind_speed(v, rho, dx, dy, dz, k, epsilon, g);
% 输出湿度分布图
figure(1);
slice(x, y, z, RH, L/2, W/2, 0);
colorbar;
xlabel('x (m)');
ylabel('y (m)');
zlabel('z (m)');
title(['RH distribution at t = ', num2str(t), 's']);
end
% 定义速度场计算函数
function [U, V, W] = calc_velocity(u, v, rho, dx, dy, dz, k)
U = zeros(size(rho));
V = zeros(size(rho));
W = zeros(size(rho));
for i = 2:size(rho,1)-1
for j = 2:size(rho,2)-1
for k = 2:size(rho,3)-1
dudx = (u(i,j,k)-u(i-1,j,k))/dx;
dudz = (u(i,j,k)-u(i,j,k-1))/dz;
dvdx = (v(i,j,k)-v(i-1,j,k))/dx;
dvdz = (v(i,j,k)-v(i,j,k-1))/dz;
dwdx = (w(i,j,k)-w(i-1,j,k))/dx;
dwdy = (w(i,j,k)-w(i,j-1,k))/dy;
U(i,j,k) = u(i,j,k)+k*rho(i,j,k)*sqrt(dudx^2+dudz^2);
V(i,j,k) = v(i,j,k)+k*rho(i,j,k)*sqrt(dvdx^2+dvdz^2);
W(i,j,k) = w(i,j,k)+k*rho(i,j,k)*sqrt(dwdx^2+dwdy^2);
end
end
end
end
% 定义湍流能计算函数
function k0 = calc_k(rho, U, V, W, k)
k0 = zeros(size(rho));
for i = 2:size(rho,1)-1
for j = 2:size(rho,2)-1
for k = 2:size(rho,3)-1
du2dx = (U(i,j,k)-U(i-1,j,k))^2;
dv2dy = (V(i,j,k)-V(i,j-1,k))^2;
dw2dz = (W(i,j,k)-W(i,j,k-1))^2;
k0(i,j,k) = k*rho(i,j,k)*(du2dx+dv2dy+dw2dz);
end
end
end
end
% 定义湍流耗散率计算函数
function epsilon = calc_epsilon(k0, rho, U, V, W, dx, dy, dz, k)
epsilon = zeros(size(rho));
for i = 2:size(rho,1)-1
for j = 2:size(rho,2)-1
for k = 2:size(rho,3)-1
dudx = (U(i,j,k)-U(i-1,j,k))/dx;
dvdy = (V(i,j,k)-V(i,j-1,k))/dy;
dwdz = (W(i,j,k)-W(i,j,k-1))/dz;
epsilon(i,j,k) = k0(i,j,k)^(3/2)/(rho(i,j,k)*sqrt(dudx^2+dvdy^2+dwdz^2));
end
end
end
end
% 定义温度场计算函数
function T = calc_temperature(T, rho, Cp, U, V, W, dx, dy, dz, kw1)
T_new = zeros(size(T));
for i = 2:size(T,1)-1
for j = 2:size(T,2)-1
for k = 2:size(T,3)-1
dTdx = (T(i,j,k)-T(i-1,j,k))/dx;
dTdy = (T(i,j,k)-T(i,j-1,k))/dy;
dTdz = (T(i,j,k)-T(i,j,k-1))/dz;
T_new(i,j,k) = T(i,j,k) + rho(i,j,k)*Cp*(U(i,j,k)*dTdx+V(i,j,k)*dTdy+W(i,j,k)*dTdz)*dt/kw1;
end
end
end
T = T_new;
end
% 定义湿度场计算函数
function RH = calc_humidity(w, rho, Cp, U, V, W, dx, dy, dz, E, Ew, q, kw, kw1, Lv, dt)
RH_new = zeros(size(w));
for i = 2:size(w,1)-1
for j = 2:size(w,2)-1
for k = 2:size(w,3)-1
dwdx = (w(i,j,k)-w(i-1,j,k))/dx;
dwdy = (w(i,j,k)-w(i,j-1,k))/dy;
dwdz = (w(i,j,k)-w(i,j,k-1))/dz;
H = rho(i,j,k)*Cp*(U(i,j,k)*dwdx+V(i,j,k)*dwdy+W(i,j,k)*dwdz)*dt/kw;
Ew1 = Ew(i,j) + q(i,j)*dt/(rho(i,j,1)*kw);
Ew1(Ew1<0) = 0;
RH_new(i,j,k) = w(i,j,k)*rho(i,j,k)/rho(i,j,1) + H/Lv + E(i,j,k)*dt/(rho(i,j,k)*Cp) - Ew1/(rho(i,j,1)*Cp) - q(i,j)*dt/(rho(i,j,1)*Cp);
end
end
end
RH = RH_new;
end
% 定义土壤水分含量计算函数
function Ew = calc_soil_moisture(Ew, q, kw, dx, dy, dt)
Ew_new = zeros(size(Ew));
for i = 2:size(Ew,1)-1
for j = 2:size(Ew,2)-1
dEdx = (Ew(i,j)-Ew(i-1,j))/dx;
dEdy = (Ew(i,j)-Ew(i,j-1))/dy;
Ew_new(i,j) = Ew(i,j) + q(i,j)*dt/(kw*(dEdx^2+dEdy^2));
end
end
Ew = Ew_new;
end
% 定义风速场计算函数
function v = calc_wind_speed(v, rho, dx, dy, dz, k, epsilon, g)
v_new = zeros(size(v));
for i = 2:size(v,1)-1
for j = 2:size(v,2)-1
for k = 2:size(v,3)-1
dvdx = (v(i,j,k)-v(i-1,j,k))/dx;
dudy = (v(i,j,k)-v(i,j-1,k))/dy;
dwdz = (v(i,j,k)-v(i,j,k-1))/dz;
v_new(i,j,k) = v(i,j,k) + k*epsilon(i,j,k)/rho(i,j,k)*sqrt(dvdx^2+dudy^2+dwdz^2)*dt/g;
end
end
end
v = v_new;
end
```