|
| 1 | +""" pyplots.ai |
| 2 | +psychrometric-basic: Psychrometric Chart for HVAC |
| 3 | +Library: letsplot 4.9.0 | Python 3.14.3 |
| 4 | +Quality: 81/100 | Created: 2026-03-15 |
| 5 | +""" |
| 6 | + |
| 7 | +import numpy as np |
| 8 | +import pandas as pd |
| 9 | +from lets_plot import ( |
| 10 | + LetsPlot, |
| 11 | + aes, |
| 12 | + element_blank, |
| 13 | + element_line, |
| 14 | + element_rect, |
| 15 | + element_text, |
| 16 | + geom_line, |
| 17 | + geom_path, |
| 18 | + geom_point, |
| 19 | + geom_polygon, |
| 20 | + geom_segment, |
| 21 | + geom_text, |
| 22 | + ggplot, |
| 23 | + ggsize, |
| 24 | + labs, |
| 25 | + scale_color_identity, |
| 26 | + scale_fill_identity, |
| 27 | + scale_x_continuous, |
| 28 | + scale_y_continuous, |
| 29 | + theme, |
| 30 | + theme_minimal, |
| 31 | +) |
| 32 | +from lets_plot.export import ggsave |
| 33 | + |
| 34 | + |
| 35 | +LetsPlot.setup_html() |
| 36 | + |
| 37 | +# Constants |
| 38 | +P_ATM = 101325.0 # Pa, standard atmospheric pressure |
| 39 | + |
| 40 | +# Colorblind-safe palette (no red-green) |
| 41 | +COLOR_SATURATION = "#306998" # Python blue for 100% RH |
| 42 | +COLOR_WET_BULB = "#0072B2" # Blue (colorblind-safe) |
| 43 | +COLOR_ENTHALPY = "#D55E00" # Vermillion (colorblind-safe) |
| 44 | +COLOR_VOLUME = "#9467bd" # Purple |
| 45 | +COLOR_COMFORT = "#306998" # Python blue |
| 46 | +COLOR_PROCESS = "#e67e22" # Orange |
| 47 | + |
| 48 | + |
| 49 | +# Psychrometric equations (ASHRAE-based) |
| 50 | +def saturation_pressure(t): |
| 51 | + t_k = t + 273.15 |
| 52 | + if t >= 0: |
| 53 | + ln_ps = ( |
| 54 | + -5.8002206e3 / t_k |
| 55 | + + 1.3914993 |
| 56 | + - 4.8640239e-2 * t_k |
| 57 | + + 4.1764768e-5 * t_k**2 |
| 58 | + - 1.4452093e-8 * t_k**3 |
| 59 | + + 6.5459673 * np.log(t_k) |
| 60 | + ) |
| 61 | + else: |
| 62 | + ln_ps = ( |
| 63 | + -5.6745359e3 / t_k |
| 64 | + + 6.3925247 |
| 65 | + - 9.677843e-3 * t_k |
| 66 | + + 6.2215701e-7 * t_k**2 |
| 67 | + + 2.0747825e-9 * t_k**3 |
| 68 | + - 9.484024e-13 * t_k**4 |
| 69 | + + 4.1635019 * np.log(t_k) |
| 70 | + ) |
| 71 | + return np.exp(ln_ps) |
| 72 | + |
| 73 | + |
| 74 | +def humidity_ratio(t_db, rh): |
| 75 | + p_s = saturation_pressure(t_db) |
| 76 | + p_w = rh * p_s |
| 77 | + return 0.621945 * p_w / (P_ATM - p_w) |
| 78 | + |
| 79 | + |
| 80 | +def wet_bulb_line(t_wb, t_db_range): |
| 81 | + w_sat = humidity_ratio(t_wb, 1.0) |
| 82 | + h_fg = 2501.0 |
| 83 | + cp_a = 1.006 |
| 84 | + cp_w = 1.86 |
| 85 | + w_values = [] |
| 86 | + for t_db in t_db_range: |
| 87 | + w = (h_fg * w_sat - cp_a * (t_db - t_wb)) / (h_fg + cp_w * t_db - cp_a * t_wb + (cp_w - cp_a) * t_wb) |
| 88 | + w_values.append(max(w, 0)) |
| 89 | + return np.array(w_values) |
| 90 | + |
| 91 | + |
| 92 | +# Data - Generate psychrometric curves |
| 93 | +t_db_fine = np.linspace(-10, 50, 300) |
| 94 | + |
| 95 | +all_frames = [] |
| 96 | + |
| 97 | +# Relative humidity curves (10% to 100%) |
| 98 | +rh_colors = { |
| 99 | + 0.1: "#b0b0b0", |
| 100 | + 0.2: "#a0a0a0", |
| 101 | + 0.3: "#909090", |
| 102 | + 0.4: "#808080", |
| 103 | + 0.5: "#707070", |
| 104 | + 0.6: "#606060", |
| 105 | + 0.7: "#505050", |
| 106 | + 0.8: "#404040", |
| 107 | + 0.9: "#303030", |
| 108 | + 1.0: "#306998", |
| 109 | +} |
| 110 | + |
| 111 | +for rh_val in np.arange(0.1, 1.05, 0.1): |
| 112 | + rh_val = round(rh_val, 1) |
| 113 | + w_values = [] |
| 114 | + t_valid = [] |
| 115 | + for t in t_db_fine: |
| 116 | + w = humidity_ratio(t, rh_val) * 1000 # convert to g/kg |
| 117 | + if 0 <= w <= 30: |
| 118 | + w_values.append(w) |
| 119 | + t_valid.append(t) |
| 120 | + df_rh = pd.DataFrame( |
| 121 | + { |
| 122 | + "t_db": t_valid, |
| 123 | + "w": w_values, |
| 124 | + "group": f"RH {int(rh_val * 100)}%", |
| 125 | + "color": rh_colors[rh_val], |
| 126 | + "line_type": "rh", |
| 127 | + } |
| 128 | + ) |
| 129 | + all_frames.append(df_rh) |
| 130 | + |
| 131 | +df_rh_all = pd.concat(all_frames, ignore_index=True) |
| 132 | + |
| 133 | +# Wet-bulb temperature lines |
| 134 | +wb_frames = [] |
| 135 | +wb_temps = [0, 5, 10, 15, 20, 25, 30, 35] |
| 136 | + |
| 137 | +for t_wb in wb_temps: |
| 138 | + t_range = np.linspace(t_wb, min(t_wb + 30, 50), 100) |
| 139 | + w_vals = wet_bulb_line(t_wb, t_range) * 1000 # g/kg |
| 140 | + mask = (w_vals >= 0) & (w_vals <= 30) |
| 141 | + df_wb = pd.DataFrame( |
| 142 | + {"t_db": t_range[mask], "w": w_vals[mask], "group": f"WB {t_wb}°C", "color": COLOR_WET_BULB, "line_type": "wb"} |
| 143 | + ) |
| 144 | + wb_frames.append(df_wb) |
| 145 | + |
| 146 | +df_wb_all = pd.concat(wb_frames, ignore_index=True) |
| 147 | + |
| 148 | +# Enthalpy lines |
| 149 | +enth_frames = [] |
| 150 | +enthalpy_values_list = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110] |
| 151 | + |
| 152 | +for h_target in enthalpy_values_list: |
| 153 | + t_points = [] |
| 154 | + w_points = [] |
| 155 | + for t in np.linspace(-10, 50, 200): |
| 156 | + w = (h_target - 1.006 * t) / (2501.0 + 1.86 * t) |
| 157 | + w_gkg = w * 1000 |
| 158 | + if 0 <= w_gkg <= 30 and -10 <= t <= 50: |
| 159 | + t_points.append(t) |
| 160 | + w_points.append(w_gkg) |
| 161 | + if len(t_points) > 1: |
| 162 | + df_h = pd.DataFrame( |
| 163 | + { |
| 164 | + "t_db": t_points, |
| 165 | + "w": w_points, |
| 166 | + "group": f"h={h_target}", |
| 167 | + "color": COLOR_ENTHALPY, |
| 168 | + "line_type": "enthalpy", |
| 169 | + } |
| 170 | + ) |
| 171 | + enth_frames.append(df_h) |
| 172 | + |
| 173 | +df_enth_all = pd.concat(enth_frames, ignore_index=True) |
| 174 | + |
| 175 | +# Specific volume lines |
| 176 | +vol_frames = [] |
| 177 | +vol_values = [0.78, 0.80, 0.82, 0.84, 0.86, 0.88, 0.90, 0.92, 0.94] |
| 178 | + |
| 179 | +for v_target in vol_values: |
| 180 | + t_points = [] |
| 181 | + w_points = [] |
| 182 | + for t in np.linspace(-10, 50, 200): |
| 183 | + w = (v_target * (P_ATM / 1000) / (0.287042 * (t + 273.15)) - 1) / 1.6078 |
| 184 | + w_gkg = w * 1000 |
| 185 | + if 0 <= w_gkg <= 30 and -10 <= t <= 50: |
| 186 | + t_points.append(t) |
| 187 | + w_points.append(w_gkg) |
| 188 | + if len(t_points) > 1: |
| 189 | + df_v = pd.DataFrame( |
| 190 | + {"t_db": t_points, "w": w_points, "group": f"v={v_target}", "color": COLOR_VOLUME, "line_type": "volume"} |
| 191 | + ) |
| 192 | + vol_frames.append(df_v) |
| 193 | + |
| 194 | +df_vol_all = pd.concat(vol_frames, ignore_index=True) |
| 195 | + |
| 196 | +# Comfort zone polygon (20-26°C, humidity ratio at 30-60% RH) |
| 197 | +comfort_t = [20, 26, 26, 20, 20] |
| 198 | +comfort_w = [ |
| 199 | + humidity_ratio(20, 0.3) * 1000, |
| 200 | + humidity_ratio(26, 0.3) * 1000, |
| 201 | + humidity_ratio(26, 0.6) * 1000, |
| 202 | + humidity_ratio(20, 0.6) * 1000, |
| 203 | + humidity_ratio(20, 0.3) * 1000, |
| 204 | +] |
| 205 | +df_comfort = pd.DataFrame({"t_db": comfort_t, "w": comfort_w}) |
| 206 | + |
| 207 | +# HVAC process path: cooling and dehumidification (32°C, 50% RH → 24°C, 50% RH) |
| 208 | +state1_t, state1_rh = 32, 0.50 |
| 209 | +state2_t, state2_rh = 24, 0.50 |
| 210 | +state1_w = humidity_ratio(state1_t, state1_rh) * 1000 |
| 211 | +state2_w = humidity_ratio(state2_t, state2_rh) * 1000 |
| 212 | + |
| 213 | +df_process = pd.DataFrame({"t_db": [state1_t, state2_t], "w": [state1_w, state2_w]}) |
| 214 | + |
| 215 | +# RH label positions (staggered to avoid overlap) |
| 216 | +rh_label_frames = [] |
| 217 | +for rh_val in np.arange(0.1, 1.05, 0.1): |
| 218 | + rh_val = round(rh_val, 1) |
| 219 | + t_label = ( |
| 220 | + 44 |
| 221 | + if rh_val <= 0.2 |
| 222 | + else ( |
| 223 | + 40 |
| 224 | + if rh_val == 0.3 |
| 225 | + else ( |
| 226 | + 34 |
| 227 | + if rh_val == 0.4 |
| 228 | + else ( |
| 229 | + 30 |
| 230 | + if rh_val <= 0.6 |
| 231 | + else (24 if rh_val == 0.7 else (22 if rh_val == 0.8 else (17 if rh_val == 0.9 else 14))) |
| 232 | + ) |
| 233 | + ) |
| 234 | + ) |
| 235 | + ) |
| 236 | + w_label = humidity_ratio(t_label, rh_val) * 1000 |
| 237 | + if w_label <= 28: |
| 238 | + rh_label_frames.append({"t_db": t_label, "w": w_label, "label": f"{int(rh_val * 100)}%"}) |
| 239 | + |
| 240 | +df_rh_labels = pd.DataFrame(rh_label_frames) |
| 241 | + |
| 242 | +# Wet-bulb labels (offset from saturation curve to avoid RH label collision) |
| 243 | +wb_label_frames = [] |
| 244 | +for t_wb in wb_temps: |
| 245 | + w_at_sat = humidity_ratio(t_wb, 1.0) * 1000 |
| 246 | + if w_at_sat <= 28: |
| 247 | + wb_label_frames.append({"t_db": t_wb + 2.5, "w": w_at_sat + 1.0, "label": f"{t_wb}°C"}) |
| 248 | + |
| 249 | +df_wb_labels = pd.DataFrame(wb_label_frames) |
| 250 | + |
| 251 | +# Enthalpy labels (with units) |
| 252 | +enth_label_frames = [] |
| 253 | +for h_target in enthalpy_values_list: |
| 254 | + w_at_zero = (h_target - 1.006 * (-5)) / (2501.0 + 1.86 * (-5)) |
| 255 | + w_gkg = w_at_zero * 1000 |
| 256 | + if 0 < w_gkg <= 28: |
| 257 | + enth_label_frames.append({"t_db": -8, "w": w_gkg, "label": f"{h_target} kJ/kg"}) |
| 258 | + |
| 259 | +df_enth_labels = pd.DataFrame(enth_label_frames) |
| 260 | + |
| 261 | +# Volume labels (with units) |
| 262 | +vol_label_frames = [] |
| 263 | +for v_target in vol_values: |
| 264 | + w_at_45 = (v_target * (P_ATM / 1000) / (0.287042 * (45 + 273.15)) - 1) / 1.6078 |
| 265 | + w_gkg = w_at_45 * 1000 |
| 266 | + if 0 < w_gkg <= 28: |
| 267 | + vol_label_frames.append({"t_db": 46, "w": w_gkg, "label": f"{v_target} m³/kg"}) |
| 268 | + |
| 269 | +df_vol_labels = pd.DataFrame(vol_label_frames) |
| 270 | + |
| 271 | +# Plot |
| 272 | +plot = ( |
| 273 | + ggplot() |
| 274 | + # Comfort zone |
| 275 | + + geom_polygon( |
| 276 | + data=df_comfort, |
| 277 | + mapping=aes(x="t_db", y="w"), |
| 278 | + fill=COLOR_COMFORT, |
| 279 | + alpha=0.10, |
| 280 | + color=COLOR_COMFORT, |
| 281 | + size=1.0, |
| 282 | + linetype="dashed", |
| 283 | + ) |
| 284 | + # RH curves |
| 285 | + + geom_line(data=df_rh_all, mapping=aes(x="t_db", y="w", group="group", color="color"), size=1.0) |
| 286 | + # Wet-bulb lines (colorblind-safe blue) |
| 287 | + + geom_line(data=df_wb_all, mapping=aes(x="t_db", y="w", group="group"), color=COLOR_WET_BULB, size=0.6, alpha=0.55) |
| 288 | + # Enthalpy lines (colorblind-safe vermillion) |
| 289 | + + geom_line( |
| 290 | + data=df_enth_all, mapping=aes(x="t_db", y="w", group="group"), color=COLOR_ENTHALPY, size=0.5, alpha=0.45 |
| 291 | + ) |
| 292 | + # Specific volume lines |
| 293 | + + geom_line(data=df_vol_all, mapping=aes(x="t_db", y="w", group="group"), color=COLOR_VOLUME, size=0.5, alpha=0.45) |
| 294 | + # HVAC process path with arrow |
| 295 | + + geom_path( |
| 296 | + data=df_process, |
| 297 | + mapping=aes(x="t_db", y="w"), |
| 298 | + color=COLOR_PROCESS, |
| 299 | + size=2.5, |
| 300 | + arrow={"type": "closed", "length": 12}, |
| 301 | + ) |
| 302 | + # State points |
| 303 | + + geom_point(data=df_process, mapping=aes(x="t_db", y="w"), color=COLOR_PROCESS, size=5, shape=16) |
| 304 | + # RH labels |
| 305 | + + geom_text(data=df_rh_labels, mapping=aes(x="t_db", y="w", label="label"), size=8, color="#505050") |
| 306 | + # Wet-bulb labels |
| 307 | + + geom_text(data=df_wb_labels, mapping=aes(x="t_db", y="w", label="label"), size=7, color=COLOR_WET_BULB) |
| 308 | + # Enthalpy labels (with units, on left edge) |
| 309 | + + geom_text(data=df_enth_labels, mapping=aes(x="t_db", y="w", label="label"), size=7, color=COLOR_ENTHALPY, hjust=1) |
| 310 | + # Volume labels (with units, on right edge) |
| 311 | + + geom_text(data=df_vol_labels, mapping=aes(x="t_db", y="w", label="label"), size=7, color=COLOR_VOLUME, hjust=0) |
| 312 | + # Comfort zone label |
| 313 | + + geom_text( |
| 314 | + data=pd.DataFrame({"t_db": [23], "w": [7.5], "label": ["Comfort\nZone"]}), |
| 315 | + mapping=aes(x="t_db", y="w", label="label"), |
| 316 | + size=10, |
| 317 | + color=COLOR_COMFORT, |
| 318 | + fontface="bold", |
| 319 | + ) |
| 320 | + # Process label (positioned clear of RH labels) |
| 321 | + + geom_text( |
| 322 | + data=pd.DataFrame({"t_db": [40], "w": [16.0], "label": ["Cooling &\nDehumidification"]}), |
| 323 | + mapping=aes(x="t_db", y="w", label="label"), |
| 324 | + size=9, |
| 325 | + color=COLOR_PROCESS, |
| 326 | + fontface="bold", |
| 327 | + ) |
| 328 | + # Arrow annotation connecting label to process path |
| 329 | + + geom_segment( |
| 330 | + data=pd.DataFrame({"x": [38], "xend": [33], "y": [15.5], "yend": [14.0]}), |
| 331 | + mapping=aes(x="x", y="y", xend="xend", yend="yend"), |
| 332 | + color=COLOR_PROCESS, |
| 333 | + size=0.5, |
| 334 | + alpha=0.6, |
| 335 | + ) |
| 336 | + + scale_color_identity() |
| 337 | + + scale_fill_identity() |
| 338 | + + scale_x_continuous(limits=[-10, 50], breaks=list(range(-10, 55, 5))) |
| 339 | + + scale_y_continuous(limits=[0, 30], breaks=list(range(0, 35, 5))) |
| 340 | + + labs( |
| 341 | + x="Dry-Bulb Temperature (°C)", y="Humidity Ratio (g/kg)", title="psychrometric-basic · letsplot · pyplots.ai" |
| 342 | + ) |
| 343 | + + theme_minimal() |
| 344 | + + theme( |
| 345 | + plot_title=element_text(size=24, face="bold", color="#1a1a1a"), |
| 346 | + axis_title=element_text(size=20, color="#333333"), |
| 347 | + axis_text=element_text(size=16, color="#555555"), |
| 348 | + legend_position="none", |
| 349 | + panel_grid_major=element_line(color="#e8e8e8", size=0.3), |
| 350 | + panel_grid_minor=element_blank(), |
| 351 | + plot_background=element_rect(fill="white", color="white"), |
| 352 | + panel_background=element_rect(fill="#fafafa"), |
| 353 | + ) |
| 354 | + + ggsize(1600, 900) |
| 355 | +) |
| 356 | + |
| 357 | +# Save |
| 358 | +ggsave(plot, "plot.png", path=".", scale=3) |
| 359 | +ggsave(plot, "plot.html", path=".") |
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