🌊 Cooling Tower Merkel Integral (KaV/L)

Calculate cooling tower mass transfer demand (Merkel number KaV/L) via Chebyshev 4-point quadrature, thermal effectiveness, range, approach, and evaporation loss.

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated

Mass Transfer

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⚡ Solves 28

💾 Downloads 497 📦 Fortran Code 6.4 KB

📅 Released Jun 2026

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🌊 Induced Draft Counter-Flow Cooling Tower & Film Packing Simulation

Real-time visual simulation of hot water spray, evaporative mass transfer & upward air drafting

📝 Configuration & Presets

🏭 Industrial (37°C → 29°C) ⚡ Power Plant (3500 m³/h) 🏢 HVAC Chiller Loop ☀️ Desert Arid Climate

🌡️ Water Temperatures & Flow

Hot Water Inlet Temp T_w,in [°C]:

Cold Basin Outlet Temp T_w,out [°C]:

Circulating Water Flow L [m³/h]:

Liquid-to-Gas Mass Ratio L/G: Standard range: 0.8 to 1.8

🌤️ Ambient Psychrometric Air State

Ambient Dry Bulb Temp T_db [°C]:

Design Wet Bulb Temp T_wb [°C]: Theoretical cooling limit

CTI Merkel Formulations:
• Merkel Integral: KaV / L = ∫ [ c_w dT_w / (h_sat − h_a) ]
• Range = T_w,in − T_w,out | Approach = T_w,out − T_wb
• Thermal Effectiveness: η = Range / (T_w,in − T_wb) × 100%
• Evaporation Loss: Q_evap ≈ 0.0018 · L · Range [m³/h]

📊 Merkel Analysis Results

📊 Output Summary
💾 Fortran Source

Tower Characteristic / Merkel Number

KaV / L = 1.399

Thermal Effectiveness: 61.5 % (Range = 8.0 °C, Approach = 5.0 °C)

L/G = 1.25

Evaporation Water Loss 7.20 m³/h 1.44 % of circulation

Fan Air Flow Demand 338,305 m³/h 199,120 CFM

Thermal Cooling Heat Rejected 4,642 kW 1,320 Tons

Approach to Wet Bulb 5.0 °C T_wb = 24.0 °C

📈 Merkel Number (KaV/L) vs Liquid-to-Gas Ratio (L/G)

📉 Thermal Effectiveness (%) vs Approach to Wet Bulb (°C)

=================================================================
 THERMOFLUIDCALC — COOLING TOWER MERKEL INTEGRAL REPORT
=================================================================
Case Title                 : Petrochemical / Industrial Process Counter-Flow Tower
Water Flow Rate (L)        : 500.0 m3/h (2201.5 GPM)
Water Temperatures In/Out  : 37.0 °C / 29.0 °C (Range = 8.0 °C)
Ambient Air Dry/Wet Bulb   : 32.0 °C / 24.0 °C (Approach = 5.0 °C)
Liquid-to-Gas Ratio (L/G)  : 1.250
-----------------------------------------------------------------
MERKEL NUMBER (KaV / L)    : 1.3989 (Chebyshev 4-pt Quadrature)
Thermal Effectiveness      : 61.54 %
Heat Rejected              : 4,641.8 kW (1,320 TR)
Evaporative Water Loss     : 7.20 m3/h (31.7 GPM)
Required Airflow           : 338,305 m3/h (199,120 CFM)
=================================================================

📘 Calculation Methodology & CTI Standards

Merkel Enthalpy Driving Force

The Merkel theory unifies sensible and latent heat transfer into a single potential: the enthalpy difference between saturated air at the water interface and bulk moist air:

                    KaV/L = ∫ [ cw dTw / (hsat − ha) ]
                

Chebyshev 4-Point Quadrature

CTI Bulletin P-130 specifies evaluation at 4 standard points across the cooling range ($10\%, 40\%, 60\%, 90\%$) for high numerical accuracy without manual graphical integration.

Key Engineering Assumptions

Lewis factor $Le_f = 1.0$ (equal mass and heat transfer boundary layers).
Negligible reduction in water flow rate along the tower fill.
Saturated air at water temperature interface.

ThermoFluidCalc Engineering Report