Thermodynamics, Industrial Chiller Engineering & Vapor-Compression Cycles
Vapor-Compression Liquid Subcooling, NRE & Mass-Flow Formula
Calculate Vapor-Compression Chiller Subcooled Net Refrigerating Effect NRE (kJ/kg), Liquid Subcooling Capacity Gain %, Required Refrigerant Mass Flow Rate m_dot (kg/s), and Cycle Cooling COP from State-Point Enthalpies.
Boost Net Refrigerating Effect (NRE) and stop expansion-valve flash gas with liquid subcooling!
In a vapor-compression chiller or supermarket rack, condenser saturated liquid at enthalpy h3_sat (kJ/kg) throttled isenthalpically across the thermostatic expansion valve (TXV) loses ~25–35% of its mass to flash vapor before ever entering the evaporator! Subcooling the liquid by ΔT_sub (K) at liquid specific heat Cp_liq (kJ/kg·K) lowers valve-inlet enthalpy to h3_sub = h3_sat - Cp_liq * ΔT_sub, raising Net Refrigerating Effect NRE = h1 - h3_sub (where h1 is superheated evaporator-exit enthalpy) WITHOUT adding a single kJ/kg of specific compressor work (h2 - h1)! That reduces required refrigerant mass flow m_dot = Q_cool / NRE and directly lifts Cycle Cooling COP = NRE / (h2 - h1)!
Verify on an 86 kW R-134a / R-513A Industrial Chiller—Cooling_Load_Q = 86.0 kW (B2), Superheated_Evap_Exit_h1 = 410.0 kJ/kg (B3), Saturated_Cond_Liquid_h3 = 250.0 kJ/kg (unsubcooled NRE = 160.0 kJ/kg, B4), Condenser_Subcooling_ΔT = 8.0 K (B5), Liquid_Cp = 1.50 kJ/(kg·K) (B6 -> Subcooled NRE = 410 - (250 - 12) = 172.00 kJ/kg in E2, a +7.50% NRE gain in E3!), and Compressor_Discharge_h2 = 453.0 kJ/kg (specific work = 43.0 kJ/kg, B7): Refrigerant Mass Flow drops to 86 / 172 = 0.5000 kg/s (E4) while Cycle Cooling COP rises to 172 / 43 = 4.0000 (E5)!
| Vapor-Compression Metric (86 kW, h1=410, h3_sat=250, ΔT_sub=8 K, Cp=1.5, h2=453) | Formula | Verified Output |
|---|---|---|
| Subcooled NRE (kJ/kg) | h1 - (h3_sat - Cp_liq * ΔT_sub) | 172.00 kJ/kg (160.00 @ 0 K Sub) |
| Subcooling NRE Gain Ratio | (Cp_liq * ΔT_sub) / (h1 - h3_sat) | 0.0750 (+7.50% Free Capacity) |
| Refrigerant Mass Flow (kg/s) | Cooling_Load_kW / Subcooled_NRE | 0.5000 kg/s (0.5375 @ 0 K Sub) |
| Cycle Cooling COP | Subcooled_NRE / (h2 - h1) | 4.0000 (3.7209 @ 0 K Sub) |
Subcooled Vapor-Compression Mass Flow & Cycle COP Formula
Validate Q_cool > 0, h2 > h1 > h3_sat > 0, ΔT_sub >= 0, and Cp_liq > 0!
=LET(qc_k, B2, h_1, B3, h_3s, B4, dt_s, B5, cp_l, B6, h_2, B7, IF(OR(qc_k <= 0, h_3s <= 0, h_1 <= h_3s, h_2 <= h_1, dt_s < 0, cp_l <= 0), "Invalid Vapor-Compression State", LET(nr_e, h_1 - (h_3s - cp_l * dt_s), ROUND(nr_e / (h_2 - h_1), 4))))Zero-Subcooling Saturated Receiver Check (Set Subcooling ΔT = 0 K)
Set Liquid_Subcooling B5 = 0 K: NRE E2 drops to 160.00 kJ/kg, forcing Compressor Mass Flow E4 up 7.5% to 0.5375 kg/s and cutting Cycle Cooling COP E5 from 4.0000 down to 3.7209!
=IF(ISTEXT(E2), E2, ROUND(B2 / (B3 - (B4 - B6 * B5)), 4))Try the example
Use the original values or change them to test your understanding.