# ----------------------------- # Question 2: Comprehensive Evaluation of PDMS Thin Film Radiative Cooling Performance # ----------------------------- import numpy as np import matplotlib.pyplot as plt from scipy.integrate import simpson from scipy.optimize import fsolve import pandas as pd from org.use.q1_2 import cs_n, cs_k # Use previously defined core functions # from first_question_core import read_split_data, make_strictly_increasing, thin_film_emissivity, cs_n, cs_k # ========================== # Improved Physical Parameters and Environmental Conditions # ========================== class EnvironmentalConditions: """Environmental conditions parameters class""" def __init__(self): # Basic environmental parameters self.T_amb = 25 + 273.15 # Ambient temperature (K) self.rh = 0.6 # Relative humidity (60%) self.wind_speed = 1.0 # Wind speed (m/s) self.cloud_cover = 0.1 # Cloud cover (0-1) # Solar radiation parameters self.G_sun_total = 1000 # Total solar irradiance (W/m²) self.T_sun = 5778 # Sun surface temperature (K) # Convective heat transfer coefficient (based on wind speed) self.h_conv = 5 + 3.8 * self.wind_speed # Convective heat transfer coefficient (W/m²·K) # ========================== # Improved Radiation Models # ========================== def planck_blackbody(wl, T): """Planck blackbody spectral radiance (W/(m²·μm·sr))""" h = 6.62607015e-34 c = 299792458 k = 1.380649e-23 wl_m = wl * 1e-6 numerator = 2 * h * c ** 2 / (wl_m ** 5) denominator = np.exp(h * c / (wl_m * k * T)) - 1 return numerator / 1e6 def load_AM15_spectrum(wl): """Load standard AM1.5 solar spectrum (approximate implementation)""" solar_spec = np.zeros_like(wl) # Main characteristics of solar spectrum (simplified model) mask_visible = (wl >= 0.3) & (wl <= 0.78) mask_nir = (wl > 0.78) & (wl <= 2.5) # Visible band (peak at 0.5μm) if np.any(mask_visible): wl_vis = wl[mask_visible] solar_spec[mask_visible] = 1.0 * np.exp(-((wl_vis - 0.5) / 0.2) ** 2) # Near-infrared band if np.any(mask_nir): wl_nir = wl[mask_nir] solar_spec[mask_nir] = 0.7 * np.exp(-((wl_nir - 1.0) / 0.5) ** 2) # Normalize to 1000 W/m² total_power = simpson(solar_spec, wl) solar_spec = solar_spec * 1000 / total_power return solar_spec def atmospheric_transmittance(wl, humidity=0.6): """Improved atmospheric transmittance model""" tau = np.ones_like(wl) # Atmospheric window 8-13μm (high transmittance with fluctuations) window_mask = (wl >= 8) & (wl <= 13) if np.any(window_mask): wl_window = wl[window_mask] # Fluctuations within the window, not fixed values tau_window = 0.85 + 0.1 * np.sin(2 * np.pi * (wl_window - 8) / 2.5) tau[window_mask] = np.clip(tau_window, 0.7, 0.95) # Water vapor absorption bands h2o_bands = [(5.5, 7.5, 0.3), (13.5, 16, 0.4), (16, 20, 0.2)] for band_start, band_end, absorption in h2o_bands: band_mask = (wl >= band_start) & (wl <= band_end) if np.any(band_mask): tau[band_mask] = tau[band_mask] * (1 - absorption * humidity) # CO2 absorption band (15μm) co2_mask = (wl >= 14) & (wl <= 16) if np.any(co2_mask): tau[co2_mask] = tau[co2_mask] * 0.3 # O3 absorption band (9.6μm) o3_mask = (wl >= 9.3) & (wl <= 9.9) if np.any(o3_mask): tau[o3_mask] = tau[o3_mask] * 0.5 return tau def atmospheric_downward_radiation(wl, T_atm, humidity=0.6): """Improved atmospheric downward radiation model""" planck_atm = planck_blackbody(wl, T_atm) tau_atm = atmospheric_transmittance(wl, humidity) # Atmospheric emissivity = 1 - transmittance epsilon_atm = 1 - tau_atm return planck_atm * epsilon_atm # ========================== # Core Cooling Performance Evaluation # ========================== def calculate_comprehensive_cooling_metrics(d, env_conditions): """Comprehensive cooling performance evaluation""" # Define calculation wavelength range wl_calc = np.linspace(0.3, 20, 2000) # Get material optical properties n_film = cs_n(wl_calc) k_film = cs_k(wl_calc) epsilon = thin_film_emissivity(n_film, k_film, d, wl_calc) alpha = epsilon # Kirchhoff's law # Calculate energy components # 1. Solar radiation absorption solar_spec = load_AM15_spectrum(wl_calc) P_sun = simpson(alpha * solar_spec, wl_calc) # 2. Atmospheric radiation absorption atm_spec = atmospheric_downward_radiation(wl_calc, env_conditions.T_amb, env_conditions.rh) P_atm = simpson(alpha * atm_spec, wl_calc) def radiative_cooling_power(T_film): planck_film = planck_blackbody(wl_calc, T_film) # 应该乘以立体角π（对半球积分），不是乘以π return simpson(epsilon * planck_film, wl_calc) * np.pi # 4. Initial net cooling power (T_film = T_amb) P_rad_initial = radiative_cooling_power(env_conditions.T_amb) P_net_initial = P_rad_initial - (P_sun + P_atm) # 5. Solve equilibrium temperature def net_power_balance(T_film): P_rad = radiative_cooling_power(T_film) # 表面向外辐射 P_atm_absorb = P_atm # 大气辐射吸收（在环境温度下计算） P_sun_absorb = P_sun # 太阳辐射吸收 P_conv = env_conditions.h_conv * (T_film - env_conditions.T_amb) # 能量平衡：辐射冷却功率 = 吸收的大气辐射 + 吸收的太阳辐射 + 对流换热 return P_rad - P_atm_absorb - P_sun_absorb - P_conv try: T_eq = fsolve(net_power_balance, env_conditions.T_amb - 10)[0] delta_T = T_eq - env_conditions.T_amb # Temperature change (K) except: T_eq = env_conditions.T_amb delta_T = 0 # 6. Calculate maximum cooling power (at lower temperatures) T_test = np.linspace(env_conditions.T_amb - 50, env_conditions.T_amb, 100) P_net_values = [net_power_balance(T) for T in T_test] P_cooling_max = max(P_net_values) if P_net_values else 0 # 7. Calculate atmospheric window utilization wl_window = np.linspace(8, 13, 200) epsilon_window = thin_film_emissivity(cs_n(wl_window), cs_k(wl_window), d, wl_window) window_efficiency = np.mean(epsilon_window) # 8. Solar reflectance (visible band) wl_visible = np.linspace(0.38, 0.78, 100) alpha_visible = thin_film_emissivity(cs_n(wl_visible), cs_k(wl_visible), d, wl_visible) solar_reflectance = 1 - np.mean(alpha_visible) return { 'Thickness_μm': d, 'Net_Cooling_Power_Wm2': P_net_initial, 'Max_Cooling_Power_Wm2': P_cooling_max, 'Equilibrium_Temp_C': T_eq - 273.15, 'Temperature_Reduction_C': delta_T, 'Solar_Absorption_Wm2': P_sun, 'Atmospheric_Absorption_Wm2': P_atm, 'Window_Efficiency': window_efficiency, 'Solar_Reflectance': solar_reflectance, 'Convection_Coefficient_Wm2K': env_conditions.h_conv } # ========================== # Multi-Environment Analysis # ========================== def analyze_environmental_impact(d): """Analyze performance under different environmental conditions""" environments = { 'Standard': EnvironmentalConditions(), 'High_Humidity': EnvironmentalConditions(), 'Windy': EnvironmentalConditions(), 'Cloudy': EnvironmentalConditions() } # Set different environmental parameters environments['High_Humidity'].rh = 0.9 environments['Windy'].wind_speed = 5.0 environments['Windy'].h_conv = 5 + 3.8 * 5.0 environments['Cloudy'].cloud_cover = 0.8 environments['Cloudy'].G_sun_total = 200 # Reduced solar radiation on cloudy days results = {} for name, env in environments.items(): results[name] = calculate_comprehensive_cooling_metrics(d, env) return results # ========================== # Main Execution # ========================== def main(): print("=== Question 2: Comprehensive Evaluation of PDMS Thin Film Radiative Cooling Performance ===") # Define thickness range thicknesses = [0.5, 1.0, 1.5, 2.0, 2.5, 3.0] env_std = EnvironmentalConditions() # Calculate performance for all thicknesses all_results = [] for d in thicknesses: result = calculate_comprehensive_cooling_metrics(d, env_std) all_results.append(result) # Convert to DataFrame for analysis df_results = pd.DataFrame(all_results) # Output detailed results print("\n=== Cooling Performance Comparison of Different PDMS Film Thicknesses ===") print(df_results.round(3)) # Find optimal thickness best_cooling_idx = df_results['Net_Cooling_Power_Wm2'].idxmax() best_temp_idx = df_results['Temperature_Reduction_C'].idxmin() best_cooling = df_results.iloc[best_cooling_idx] best_temp = df_results.iloc[best_temp_idx] print(f"\n=== Optimal Performance Analysis ===") print( f"Maximum net cooling power: {best_cooling['Thickness_μm']}μm, Power: {best_cooling['Net_Cooling_Power_Wm2']:.2f} W/m²") print( f"Lowest equilibrium temperature: {best_temp['Thickness_μm']}μm, Temperature: {best_temp['Equilibrium_Temp_C']:.2f}°C") print(f"Maximum temperature reduction: {abs(best_temp['Temperature_Reduction_C']):.2f}°C") # Environmental sensitivity analysis (using optimal thickness) optimal_thickness = best_cooling['Thickness_μm'] print(f"\n=== Environmental Sensitivity Analysis (Thickness: {optimal_thickness}μm) ===") env_results = analyze_environmental_impact(optimal_thickness) for env_name, result in env_results.items(): print(f"{env_name}: Net cooling power = {result['Net_Cooling_Power_Wm2']:.2f} W/m², " f"Equilibrium temperature = {result['Equilibrium_Temp_C']:.2f}°C") # Visualize results plot_comprehensive_results(df_results, env_results) # Output technical recommendations provide_technical_recommendations(df_results, env_results, optimal_thickness) def plot_comprehensive_results(df_results, env_results): """Plot comprehensive results""" fig, axes = plt.subplots(2, 3, figsize=(18, 12)) # Subplot 1: Net cooling power vs thickness axes[0, 0].plot(df_results['Thickness_μm'], df_results['Net_Cooling_Power_Wm2'], 'o-', linewidth=3, markersize=8) axes[0, 0].set_xlabel('Film Thickness (μm)') axes[0, 0].set_ylabel('Net Cooling Power (W/m²)') axes[0, 0].set_title('Net Cooling Power vs Thickness') axes[0, 0].grid(True, alpha=0.3) axes[0, 0].axhline(y=0, color='red', linestyle='--', alpha=0.7) # Subplot 2: Equilibrium temperature vs thickness axes[0, 1].plot(df_results['Thickness_μm'], df_results['Equilibrium_Temp_C'], 's-', linewidth=3, markersize=8, color='orange') axes[0, 1].set_xlabel('Film Thickness (μm)') axes[0, 1].set_ylabel('Equilibrium Temperature (°C)') axes[0, 1].set_title('Equilibrium Temperature vs Thickness') axes[0, 1].grid(True, alpha=0.3) axes[0, 1].axhline(y=25, color='red', linestyle='--', alpha=0.7, label='Ambient Temp') # Subplot 3: Atmospheric window utilization axes[0, 2].plot(df_results['Thickness_μm'], df_results['Window_Efficiency'], '^-', linewidth=3, markersize=8, color='green') axes[0, 2].set_xlabel('Film Thickness (μm)') axes[0, 2].set_ylabel('Atmospheric Window Efficiency') axes[0, 2].set_title('8-13μm Atmospheric Window Emissivity') axes[0, 2].grid(True, alpha=0.3) # Subplot 4: Solar reflectance axes[1, 0].plot(df_results['Thickness_μm'], df_results['Solar_Reflectance'], 'd-', linewidth=3, markersize=8, color='purple') axes[1, 0].set_xlabel('Film Thickness (μm)') axes[1, 0].set_ylabel('Visible Light Reflectance') axes[1, 0].set_title('Solar Reflectance vs Thickness') axes[1, 0].grid(True, alpha=0.3) # Subplot 5: Environmental sensitivity env_names = list(env_results.keys()) cooling_powers = [env_results[name]['Net_Cooling_Power_Wm2'] for name in env_names] axes[1, 1].bar(env_names, cooling_powers, color=['blue', 'green', 'orange', 'red'], alpha=0.7) axes[1, 1].set_ylabel('Net Cooling Power (W/m²)') axes[1, 1].set_title('Cooling Performance under Different Conditions') axes[1, 1].tick_params(axis='x', rotation=45) axes[1, 1].axhline(y=0, color='black', linestyle='--', alpha=0.5) # Subplot 6: Energy component breakdown (optimal thickness) best_idx = df_results['Net_Cooling_Power_Wm2'].idxmax() best_result = df_results.iloc[best_idx] components = ['Radiative Cooling', 'Solar Absorption', 'Atmospheric Absorption'] values = [best_result['Net_Cooling_Power_Wm2'] + best_result['Solar_Absorption_Wm2'] + best_result[ 'Atmospheric_Absorption_Wm2'], -best_result['Solar_Absorption_Wm2'], -best_result['Atmospheric_Absorption_Wm2']] colors = ['green', 'red', 'orange'] axes[1, 2].bar(components, values, color=colors, alpha=0.7) axes[1, 2].set_ylabel('Power (W/m²)') axes[1, 2].set_title(f'Energy Balance Breakdown (Thickness: {best_result["Thickness_μm"]}μm)') axes[1, 2].axhline(y=0, color='black', linestyle='-', alpha=0.8) plt.tight_layout() plt.savefig('PDMS_comprehensive_cooling_analysis.png', dpi=300, bbox_inches='tight') plt.show() def provide_technical_recommendations(df_results, env_results, optimal_thickness): """Provide detailed technical recommendations""" print("\n" + "=" * 80) print("=== Radiative Cooling Technology Development and Application Recommendations ===") print("=" * 80) best_result = df_results[df_results['Thickness_μm'] == optimal_thickness].iloc[0] print("1. Optimal Thickness Selection:") print(f" • Recommended thickness: {optimal_thickness} μm") print(f" • Performance metrics: Net cooling power {best_result['Net_Cooling_Power_Wm2']:.2f} W/m², " f"Equilibrium temperature {best_result['Equilibrium_Temp_C']:.2f} °C") print(f" • Technical advantages: Atmospheric window efficiency {best_result['Window_Efficiency']:.3f}, " f"Solar reflectance {best_result['Solar_Reflectance']:.3f}") print("\n2. Environmental Adaptability Analysis:") for env_name, result in env_results.items(): power = result['Net_Cooling_Power_Wm2'] temp = result['Equilibrium_Temp_C'] print(f" • {env_name}: Net power {power:.2f} W/m², Equilibrium temperature {temp:.2f} °C") print("\n3. Technical Improvement Directions:") print( " • Optical performance optimization: Enhance 8-13μm emissivity through surface microstructure or nanoparticle doping") print(" • Solar reflection enhancement: Add visible light reflection layers to reduce solar absorption") print(" • Environmental robustness: Develop composite materials adaptable to high humidity and cloudy conditions") print("\n4. Application Scenarios:") print( " • Building energy efficiency: Building facades, roof coatings, expected to reduce AC energy consumption by 15-25%") print(" • Electronic device cooling: Server rooms, photovoltaic panel cooling") print(" • Personal thermal management: Smart textiles, wearable devices") print(" • Special applications: Cold chain logistics, agricultural greenhouse cooling") print("\n5. Industrialization Development Path:") print(" • Short-term (1-2 years): Optimize PDMS film fabrication process, reduce costs") print(" • Medium-term (2-3 years): Develop multilayer composite structures, improve performance") print(" • Long-term (3-5 years): Achieve integration of intelligent radiative cooling systems") # ========================== # Mock core functions for testing (replace with actual implementations) # ========================== def thin_film_emissivity(n_film, k_film, d, wl): """Mock implementation - replace with actual function""" # Simplified implementation for testing R = 0.1 # Approximate reflectance alpha = 4 * np.pi * k_film * d / wl T = np.exp(-alpha) return 1 - R - T if __name__ == "__main__": main()