Hydronic HVAC Systems, DOAS + Active Chilled Beams & Sensible Cooling Engineering
Active Chilled Beam Induction Ratio & Cooling Formula
Calculate Induced Room Secondary Airflow Q_sec (L/s), Primary DOAS Ventilation Sensible Cooling (W), Secondary Hydronic Coil Sensible Cooling (W), and Total Chilled-Beam Sensible Capacity (W).
A tiny 28 L/s primary DOAS jet entrains 4x–5x room air across the chilled-beam coil—decoupling ventilation from zone sensible load!
Conventional VAV all-air systems haul huge ducts of air just to move sensible watts; Dedicated Outdoor Air System (`DOAS`) + **Active Chilled Beams** supply only dehumidified Primary Ventilation Air `Q_pri` (`L/s`) through high-velocity Venturi nozzles inside the ceiling beam! By turbulent jet entrainment (**Induction Ratio `IR = Q_sec / Q_pri`**, typically `3.0` to `5.5` with zero room fan motor!), `Q_sec = IR * Q_pri` (`L/s`) of warm room air at `T_room` (°C) is drawn upward across a dry `15–17 °C` chilled-water finned coil (kept strictly above room dew point so condensate pans are eliminated!), cooling to `T_sec,out` (°C) before mixing with `T_pri` (°C) and discharging across the ceiling via Coanda effect: Total Sensible Zone Cooling is `Q_tot = 1.20 * 1.006 * Q_pri * (T_room - T_pri) + 1.20 * 1.006 * (IR * Q_pri) * (T_room - T_sec,out)` watts!
Verify on a 2.4 m Laboratory Active Chilled Beam—Primary_DOAS_Airflow `Q_pri` = 28.0 L/s (B2), Nozzle_Induction_Ratio `IR` = 4.20 (B3 -> Induced Room Air `Q_sec = 117.6` L/s in E2), Room_Design_Temp `T_room` = 24.5 °C (B4), Primary_Supply_Temp `T_pri` = 14.0 °C (B5 -> Primary Air Cooling = `354.9` W in E3), and Secondary_Leaving-Coil_Temp `T_sec,out` = 17.5 °C (B6 -> Hydronic Coil Cooling = `993.8` W in E4): Total Chilled-Beam Sensible Capacity hits `1,348.7` W (`73.7%` delivered hydronically with zero terminal fan power!, E5)!
| Active Chilled Beam KPI (Qpri=28 L/s @ 14°C, IR=4.2, Troom=24.5°C, Tcoil=17.5°C) | Formula | Verified Output |
|---|---|---|
| Induced Secondary Airflow (L/s) | Primary_Air_L_s * Induction_Ratio_IR | 117.6 L/s (154.0 L/s @ high-nozzle IR=5.5) |
| Primary DOAS Sensible Cooling (W) | 1.20 * 1.006 * Qpri_L_s * (Troom - Tpri) | 354.9 W |
| Hydronic Coil Sensible Cooling (W) | 1.20 * 1.006 * Qsec_L_s * (Troom - Tcoil) | 993.8 W (1,301.4 W @ IR = 5.5) |
| Total Beam Sensible Cooling (W) | Primary_Cooling_W + Hydronic_Coil_W | 1,348.7 W (1,656.3 W @ IR = 5.5) |
Nozzle Induction Entrainment & Dual-Stream Chilled-Beam Cooling Formula
Validate `Primary_Air > 0` L/s, `Induction_Ratio IR` in `[1.5, 8.0]`, `T_pri < T_room`, and `T_sec,out` in `[12, T_room)` °C (`>= 14 °C` chilled water prevents ceiling condensation Rain-Out unless DOAS holds space dew point below `12 °C`)!
=LET(qp_l, B2, ir_n, B3, tr_c, B4, tp_c, B5, ts_c, B6, qs_l, qp_l * ir_n, wp_w, 1.2 * 1.006 * qp_l * (tr_c - tp_c), ws_w, 1.2 * 1.006 * qs_l * (tr_c - ts_c), IF(OR(qp_l <= 0, ir_n < 1.5, ir_n > 8, tp_c >= tr_c, ts_c < 12, ts_c >= tr_c), "Invalid Chilled Beam Input", ROUND(wp_w + ws_w, 1)))High-Induction Nozzle Plate Swap Check (Set Induction Ratio IR B3 = 5.50)
Select a higher-pressure small-orifice nozzle plate raising Induction Ratio `B3` from `4.20` to `5.50` at the exact same `28.0` L/s DOAS ventilation rate: Induced Secondary Airflow E2 rises to `154.0` L/s, Hydronic Coil Output E4 climbs to `1,301.4` W, and Total Beam Cooling E5 reaches `1,656.3` W!
=IF(ISTEXT(E5), E5, ROUND(1.2 * 1.006 * (B2 * B3) * (B4 - B6), 1))Try the example
Use the original values or change them to test your understanding.