347 lines
15 KiB
Python
347 lines
15 KiB
Python
import numpy as np
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import matplotlib.pyplot as plt
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from scipy.interpolate import CubicSpline
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from scipy.integrate import simpson
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# -----------------------------
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# 1. 材料级：PDMS光学性能计算（你的模型核心逻辑，修复变量定义错误）
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# -----------------------------
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def make_strictly_increasing(wl, n, k):
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# 去除重复点并确保波长严格递增
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unique_wl, indices = np.unique(wl, return_index=True)
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if len(unique_wl) != len(wl):
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print(f"Removed {len(wl) - len(unique_wl)} duplicate wavelength points")
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wl, n, k = wl[indices], n[indices], k[indices]
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# 确保严格递增
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is_increasing = np.diff(wl) > 0
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if not all(is_increasing):
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valid_indices = np.concatenate([[True], is_increasing])
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wl, n, k = wl[valid_indices], n[valid_indices], k[valid_indices]
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return wl, n, k
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def read_split_data(file_path):
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with open(file_path, 'r', encoding='utf-8') as f:
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lines = [line.strip() for line in f if line.strip() and not line.startswith('#')]
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split_idx = None
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for i, line in enumerate(lines):
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if line == 'wl k':
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split_idx = i
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break
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if split_idx is None:
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raise ValueError("未找到'wl k'表头，请检查数据格式！")
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n_lines = lines[1:split_idx]
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wl_n, n_list = [], []
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for line in n_lines:
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parts = line.split()
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if len(parts) != 2:
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continue # 跳过格式错误的行
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wl, n_val = parts
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wl_n.append(float(wl)), n_list.append(float(n_val))
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k_lines = lines[split_idx + 1:]
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wl_k, k_list = [], []
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for line in k_lines:
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parts = line.split()
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if len(parts) != 2:
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continue # 跳过格式错误的行
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wl, k_val = parts
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wl_k.append(float(wl)), k_list.append(float(k_val))
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# 转换为numpy数组
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wl_n, n_list = np.array(wl_n), np.array(n_list)
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wl_k, k_list = np.array(wl_k), np.array(k_list)
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# 确保n和k的波长完全一致
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assert np.allclose(wl_n, wl_k), "n和k的波长列表不一致！"
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# 排序
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sorted_idx = np.argsort(wl_n)
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return wl_n[sorted_idx], n_list[sorted_idx], k_list[sorted_idx]
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def fresnel_reflectance(n1, k1, n2, k2):
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m1, m2 = n1 + 1j * k1, n2 + 1j * k2
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return np.abs((m1 - m2) / (m1 + m2)) ** 2
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def thin_film_optical_properties(n_film, k_film, d, wl):
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"""修复denominator未定义的错误，完整计算R_total和T_total"""
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R12 = fresnel_reflectance(1.0, 0.0, n_film, k_film) # 空气→薄膜
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R23 = fresnel_reflectance(n_film, k_film, 1.0, 0.0) # 薄膜→空气
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delta = 2 * np.pi * n_film * d / wl # 干涉相位差
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alpha_abs = 4 * np.pi * k_film * d / wl # 吸收衰减系数
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# 计算分母（关键修复：补充denominator的定义）
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denominator = 1 + R12 * R23 * np.exp(-alpha_abs) + 2 * np.sqrt(R12 * R23 * np.exp(-alpha_abs)) * np.cos(2 * delta)
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# 总反射率
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numerator_R = R12 + R23 * np.exp(-alpha_abs) + 2 * np.sqrt(R12 * R23 * np.exp(-alpha_abs)) * np.cos(2 * delta)
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R_total = numerator_R / denominator
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# 总透射率（修复后）
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T_total = (1 - R12) * (1 - R23) * np.exp(-alpha_abs) / denominator
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# 吸收率=发射率（热平衡下）
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alpha_total = 1 - R_total - T_total
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return alpha_total, R_total, T_total # alpha_total即ε（发射率）
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# -----------------------------
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# 2. 数据读取与预处理
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# -----------------------------
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# 替换为你的data.txt实际路径（确保正确）
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DATA_PATH = '/Users/spasolreisa/IdeaProjects/asiaMath/data.txt'
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wl_all, n_all, k_all = read_split_data(DATA_PATH)
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wl_all, n_all, k_all = make_strictly_increasing(wl_all, n_all, k_all)
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print(f"数据读取成功：波长范围 {wl_all.min():.2f}–{wl_all.max():.2f} μm，共{len(wl_all)}个数据点")
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# 三次样条插值
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cs_n = CubicSpline(wl_all, n_all)
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cs_k = CubicSpline(wl_all, k_all)
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# 定义PDMS厚度和计算波长范围
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thicknesses = [0.5, 1.0, 1.5, 2.0]
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wl_fine = np.linspace(wl_all.min(), wl_all.max(), 500) # 细化解析度
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# -----------------------------
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# 3. 预计算材料级关键参数（ε和α）
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# -----------------------------
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# 存储平均发射率（8-13μm，黑体辐射加权）和平均太阳吸收率（0.3-2.5μm，太阳光谱加权）
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avg_eps_dict = {} # 平均发射率 ε_avg
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avg_alpha_dict = {} # 平均太阳吸收率 α_avg
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# 定义权重光谱（辐射冷却+太阳吸收关键波段）
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def planck_spectrum(wl, T):
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"""普朗克黑体光谱（8-13μm波段权重）"""
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wl_m = wl * 1e-6 # 转换为米
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c1 = 3.7418e8 # 第一辐射常数 (W·μm⁴/m²)
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c2 = 14388 # 第二辐射常数 (μm·K)
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return c1 / (wl_m ** 5 * (np.exp(c2 / (wl * T)) - 1))
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def solar_spectrum_am15(wl):
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"""AM1.5太阳光谱（0.3-2.5μm波段权重）"""
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spectrum = np.zeros_like(wl)
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mask = (wl >= 0.3) & (wl <= 2.5)
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wl_masked = wl[mask]
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# 经验拟合AM1.5标准光谱
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spectrum[mask] = np.where(
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wl_masked < 0.5, 800 + 400 * wl_masked,
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np.where(wl_masked < 1.0, 1000 - 200 * (wl_masked - 0.5),
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np.where(wl_masked < 1.5, 900 - 100 * (wl_masked - 1.0),
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750 - 200 * (wl_masked - 1.5)))
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)
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return spectrum
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# 计算各厚度的平均ε和α
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for d in thicknesses:
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print(f"\n正在计算厚度 {d} μm 的光学性能...")
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# -----------------------------
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# 计算平均发射率 ε_avg（8-13μm，黑体辐射加权）
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# -----------------------------
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if wl_all.min() <= 13 and wl_all.max() >= 8:
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wl_rad = np.linspace(8, 13, 300) # 辐射冷却核心波段
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n_rad = cs_n(wl_rad)
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k_rad = cs_k(wl_rad)
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eps_rad, _, _ = thin_film_optical_properties(n_rad, k_rad, d, wl_rad)
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planck_weight = planck_spectrum(wl_rad, T=298) # 25℃黑体光谱权重
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# 加权平均
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eps_avg = simpson(eps_rad * planck_weight, wl_rad) / simpson(planck_weight, wl_rad)
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else:
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print(f"警告：数据未覆盖8-13μm波段，使用全波段平均发射率替代")
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n_film = cs_n(wl_fine)
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k_film = cs_k(wl_fine)
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eps_full, _, _ = thin_film_optical_properties(n_film, k_film, d, wl_fine)
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eps_avg = np.mean(eps_full)
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avg_eps_dict[d] = eps_avg
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# -----------------------------
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# 计算平均太阳吸收率 α_avg（0.3-2.5μm，太阳光谱加权）
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# -----------------------------
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if wl_all.min() <= 2.5 and wl_all.max() >= 0.3:
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wl_solar = np.linspace(0.3, 2.5, 300) # 太阳光谱波段
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n_solar = cs_n(wl_solar)
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k_solar = cs_k(wl_solar)
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alpha_solar, _, _ = thin_film_optical_properties(n_solar, k_solar, d, wl_solar)
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solar_weight = solar_spectrum_am15(wl_solar) # AM1.5太阳光谱权重
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# 加权平均
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alpha_avg = simpson(alpha_solar * solar_weight, wl_solar) / simpson(solar_weight, wl_solar)
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else:
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print(f"警告：数据未覆盖0.3-2.5μm太阳波段，使用PDMS典型值α=0.08")
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alpha_avg = 0.08 # PDMS在太阳波段的典型吸收率（低吸收）
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avg_alpha_dict[d] = alpha_avg
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# -----------------------------
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# 4. 系统级：净冷却功率计算（解答思路核心逻辑）
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# -----------------------------
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# 系统物理参数（可根据实际场景调整）
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sigma = 5.67e-8 # 斯特藩-玻尔兹曼常数 (W/m²·K⁴)
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G_sun_list = [500, 700, 900, 1100] # 不同太阳辐照强度（对应多云到晴天）
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T_amb_list = np.linspace(293, 318, 6) # 环境温度（20-45℃，转换为开尔文）
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v_wind = 1.5 # 风速 (m/s)
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h_conv = 5.6 + 3.1 * v_wind # 对流换热系数（经验公式，W/m²·K）
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def net_cooling_power(eps, alpha, T_s, T_amb, G_sun, h_conv, sigma):
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"""净冷却功率公式：P_net = 辐射散热 - 太阳吸收热 - 对流换热损失"""
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# 辐射散热（向宇宙太空）
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rad散热 = eps * sigma * T_s ** 4
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# 太阳吸收热（从太阳光获取的热量）
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solar吸热 = alpha * G_sun
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# 对流换热损失（向环境散热/吸热）
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conv损失 = h_conv * (T_s - T_amb)
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# 环境辐射吸收（从环境获取的辐射热）
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amb_rad吸热 = eps * sigma * T_amb ** 4
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# 净冷却功率（正值表示主动冷却，负值表示吸热）
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return rad散热 - solar吸热 - conv损失 - amb_rad吸热
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def solve_surface_temperature(eps, alpha, T_amb, G_sun, h_conv, sigma):
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"""迭代求解PDMS薄膜表面温度T_s（净冷却功率=0时的热平衡温度）"""
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T_s_guess = T_amb - 5 # 初始猜测（比环境低5℃）
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tol = 1e-3 # 收敛精度
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max_iter = 100 # 最大迭代次数
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for _ in range(max_iter):
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P_net = net_cooling_power(eps, alpha, T_s_guess, T_amb, G_sun, h_conv, sigma)
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# 数值微分求导（牛顿迭代法，确保收敛）
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dP_dT = (net_cooling_power(eps, alpha, T_s_guess + 1e-4, T_amb, G_sun, h_conv, sigma) -
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net_cooling_power(eps, alpha, T_s_guess - 1e-4, T_amb, G_sun, h_conv, sigma)) / (2e-4)
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if abs(dP_dT) < 1e-6:
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break # 避免除以零
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# 更新猜测值
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T_s_new = T_s_guess - P_net / dP_dT
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# 限制温度范围（物理合理值）
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T_s_new = max(250, min(T_amb + 5, T_s_new))
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# 检查收敛
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if abs(T_s_new - T_s_guess) < tol:
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return T_s_new
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T_s_guess = T_s_new
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return T_s_guess # 若未收敛，返回最后一次猜测值
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# -----------------------------
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# 5. 全链条分析：材料性能→系统冷却性能
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# -----------------------------
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# 存储各厚度的系统级结果
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system_results = {}
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for d in thicknesses:
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eps = avg_eps_dict[d]
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alpha = avg_alpha_dict[d]
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# 初始化结果矩阵（太阳辐照×环境温度）
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P_net_matrix = np.zeros((len(G_sun_list), len(T_amb_list)))
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T_s_matrix = np.zeros((len(G_sun_list), len(T_amb_list)))
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# 遍历所有太阳辐照和环境温度组合
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for i, G_sun in enumerate(G_sun_list):
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for j, T_amb in enumerate(T_amb_list):
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# 求解表面温度
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T_s = solve_surface_temperature(eps, alpha, T_amb, G_sun, h_conv, sigma)
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T_s_matrix[i, j] = T_s
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# 计算净冷却功率
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P_net = net_cooling_power(eps, alpha, T_s, T_amb, G_sun, h_conv, sigma)
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P_net_matrix[i, j] = P_net
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# 存储结果
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system_results[d] = {
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"eps_avg": eps,
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"alpha_avg": alpha,
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"P_net": P_net_matrix,
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"T_s": T_s_matrix
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}
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# -----------------------------
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# 6. 结果可视化（全链条分析图表）
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# -----------------------------
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plt.rcParams['font.sans-serif'] = ['Arial'] # 统一字体
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plt.rcParams['axes.unicode_minus'] = False # 支持负号
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# 图1：材料级性能（平均ε和α随厚度变化）
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fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5))
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thicknesses_arr = np.array(thicknesses)
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# 平均发射率
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ax1.bar(thicknesses_arr - 0.08, [system_results[d]["eps_avg"] for d in thicknesses],
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width=0.15, label='Avg Emissivity (8-13μm)', color='darkred', alpha=0.8)
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ax1.set_xlabel('PDMS Thickness (μm)', fontsize=12)
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ax1.set_ylabel('Emissivity', fontsize=12)
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ax1.set_title('Average Emissivity (Radiative Cooling Window)', fontsize=14, fontweight='bold')
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ax1.grid(True, alpha=0.3)
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ax1.set_ylim(0, 1.05)
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# 平均太阳吸收率
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ax2.bar(thicknesses_arr - 0.08, [system_results[d]["alpha_avg"] for d in thicknesses],
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width=0.15, label='Avg Solar Absorptivity (0.3-2.5μm)', color='darkblue', alpha=0.8)
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ax2.set_xlabel('PDMS Thickness (μm)', fontsize=12)
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ax2.set_ylabel('Absorptivity', fontsize=12)
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ax2.set_title('Average Solar Absorptivity', fontsize=14, fontweight='bold')
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ax2.grid(True, alpha=0.3)
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ax2.set_ylim(0, 0.2) # 限制范围，更清晰
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plt.tight_layout()
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plt.savefig('material_performance.png', dpi=300, bbox_inches='tight')
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# 图2：系统级性能（净冷却功率随环境温度变化，选最优厚度）
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# 最优厚度：ε/α比值最大（平衡高发射和低吸收）
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optimal_d = max(thicknesses, key=lambda x: system_results[x]["eps_avg"] / (system_results[x]["alpha_avg"] + 0.01))
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print(
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f"\n最优厚度：{optimal_d} μm（ε={system_results[optimal_d]['eps_avg']:.4f}, α={system_results[optimal_d]['alpha_avg']:.4f}）")
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fig, ax = plt.subplots(figsize=(12, 6))
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T_amb_c = T_amb_list - 273.15 # 转换为摄氏度
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colors = ['red', 'orange', 'green', 'blue']
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for i, G_sun in enumerate(G_sun_list):
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P_net = system_results[optimal_d]["P_net"][i, :]
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ax.plot(T_amb_c, P_net, marker='o', markersize=6, linewidth=2,
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color=colors[i], label=f'Solar Irradiance = {G_sun} W/m²')
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ax.set_xlabel('Ambient Temperature (°C)', fontsize=12)
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ax.set_ylabel('Net Cooling Power (W/m²)', fontsize=12)
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ax.set_title(f'Net Cooling Power vs Ambient Temperature (PDMS Thickness = {optimal_d} μm)',
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fontsize=14, fontweight='bold')
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ax.grid(True, alpha=0.3)
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ax.legend(fontsize=11)
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# 添加零线（区分冷却/吸热）
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ax.axhline(y=0, color='black', linestyle='--', alpha=0.5, label='Zero Cooling Power')
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plt.tight_layout()
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plt.savefig('net_cooling_power.png', dpi=300, bbox_inches='tight')
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# 图3：表面温度随环境温度变化
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fig, ax = plt.subplots(figsize=(12, 6))
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for i, G_sun in enumerate(G_sun_list):
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T_s = system_results[optimal_d]["T_s"][i, :] - 273.15 # 转换为摄氏度
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ax.plot(T_amb_c, T_s, marker='s', markersize=6, linewidth=2,
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color=colors[i], label=f'Solar Irradiance = {G_sun} W/m²')
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ax.set_xlabel('Ambient Temperature (°C)', fontsize=12)
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ax.set_ylabel('PDMS Surface Temperature (°C)', fontsize=12)
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ax.set_title(f'Surface Temperature vs Ambient Temperature (PDMS Thickness = {optimal_d} μm)',
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fontsize=14, fontweight='bold')
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ax.grid(True, alpha=0.3)
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ax.legend(fontsize=11)
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# 添加环境温度参考线（y=x）
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ax.plot(T_amb_c, T_amb_c, color='black', linestyle='--', alpha=0.5, label='Ambient Temperature')
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plt.tight_layout()
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plt.savefig('surface_temperature.png', dpi=300, bbox_inches='tight')
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plt.show()
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# -----------------------------
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# 7. 关键结果输出（量化分析）
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# -----------------------------
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print("\n" + "=" * 60)
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print("材料-系统全链条关键结果")
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print("=" * 60)
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for d in thicknesses:
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print(f"\n厚度 {d} μm:")
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print(f" - 平均发射率（8-13μm）: {system_results[d]['eps_avg']:.4f}")
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print(f" - 平均太阳吸收率（0.3-2.5μm）: {system_results[d]['alpha_avg']:.4f}")
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print(f" - 最优工况净冷却功率（T_amb=30℃, G_sun=900 W/m²）: {system_results[d]['P_net'][2, 2]:.2f} W/m²")
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print(f" - 对应表面温度: {system_results[d]['T_s'][2, 2] - 273.15:.2f} ℃")
|
||
|
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print("\n" + "=" * 60)
|
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print("结论：PDMS薄膜的最优厚度为 {} μm，在典型工况下（30℃环境、900 W/m²太阳辐照）".format(optimal_d))
|
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print("可实现 {:.2f} W/m² 的净冷却功率，表面温度比环境低 {:.2f} ℃".format(
|
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system_results[optimal_d]['P_net'][2, 2],
|
||
30 - (system_results[optimal_d]['T_s'][2, 2] - 273.15)
|
||
))
|
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print("=" * 60) |