Calculate performance of counter-flow and cross-flow cooling towers using the Merkel (NTU) method in real time. Instantly determine approach temperature, cooling range, make-up water, and evaporation rate across three charts.
Tower Type
Water-Side Conditions
Inlet Water Temperature Tw1
°C
Outlet Water Temperature Tw2
°C
Circulating Water Flow L [kg/s]
kg/s
Air-Side Conditions
Inlet Wet-Bulb Temperature Twb
°C
L/G Ratio (liquid/gas)
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Approach temperature is too small. Set outlet water temperature sufficiently above the wet-bulb temperature.
Results
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NTU
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Approach [°C]
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Cooling Range [°C]
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Effectiveness [%]
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Make-Up Water [kg/s]
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Evaporation Rate [%]
Temp
Water and dry-bulb air temperature profile along tower height z/H.
Psych
Air enthalpy vs saturated air enthalpy at the water surface.
$h_s'$: saturated air enthalpy at the water surface $h_a$: air enthalpy Numerical integration with four Chebyshev points
What is the Cooling Tower Simulator (Merkel Method)?
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Cooling towers are those big devices on factory or building rooftops that emit white steam, right? What exactly do they do?
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Yes, they are 'heat rejection devices to the atmosphere.' Water heated by machinery or chillers is finely sprayed inside and brought into direct contact with air. As a portion of the water evaporates, it absorbs latent heat of vaporization (about 2500 J per gram) from the surroundings, significantly lowering the temperature of the remaining water. Think of it as a giant version of an outdoor air conditioner unit.
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What is the 'Merkel method'? It sounds complicated...
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It's a calculation method proposed by Fritz Merkel of Germany in 1926. Simply put, it's based on the idea that 'the rate of heat transfer from water to air is proportional to the difference between the saturated air enthalpy at the water surface and the bulk air enthalpy.' Integrating this over the entire tower yields a number called 'NTU' (Number of Transfer Units), and the larger the NTU, the larger the cooling tower required.
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The 'approach temperature' is around 3°C. Is smaller better?
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Exactly! The approach temperature is 'outlet water temperature − inlet wet-bulb temperature,' and it physically cannot go below zero because water can never be cooled below the wet-bulb temperature. In practice, it's often designed to be 3–8°C. A smaller value means higher performance, but the required NTU (i.e., fill volume) increases rapidly, driving up equipment costs. Try moving the slider to bring the outlet water temperature closer to the wet-bulb temperature and observe the change in NTU.
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Looking at the 'L/G Sensitivity Analysis' tab, NTU jumps sharply as the L/G ratio increases. Why is that?
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The L/G ratio is 'mass flow rate of water ÷ mass flow rate of air.' A larger L/G means relatively less air, so each kilogram of air must handle more heat. This causes the air enthalpy to rise steeply, reducing the difference (heat transfer driving force) between the saturated enthalpy at the water surface and the air enthalpy. With a smaller driving force, more 'units' are needed to transfer the same amount of heat, hence NTU increases. In large power plant cooling towers, L/G ≈ 0.8–1.2 is used to balance fan power and tower volume.
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The makeup water amount is quite large. Does that much really evaporate?
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Yes, it's a significant amount. Evaporation loss is estimated at about 0.2%/°C of the cooling range. For a range of 13°C, about 2.6% of the circulating water evaporates. For a circulating water flow of 100 kg/s, that's 2.6 kg/s (about 9.4 m³/h). Adding drift loss and blowdown (planned discharge to prevent concentration), a large power plant cooling tower can use millions of tons of water annually. In water-scarce regions, switching to dry cooling towers or water-saving types is under discussion.
Physical Model & Key Equations
The core of cooling tower performance analysis is the Merkel equation. Integrating heat and mass transfer through the fill height gives the required number of transfer units (NTU).
$c_{pw}$: water specific heat, about 4.186 kJ/(kg·K); $h_s'(T_w)$: saturated air enthalpy at water temperature $T_w$; $h_a$: bulk air enthalpy. All enthalpies are in kJ/kg dry air.
This simulator uses four-point Chebyshev numerical integration.
Heat balance between air-side and water-side enthalpy exchange:
$p_{sat}$ [kPa] is calculated from the Tetens equation: $p_{sat} = 0.61121\exp\!\left(\frac{(18.678 - T/234.5)\,T}{257.14+T}\right)$
Frequently Asked Questions
The Merkel method includes a simplification that ignores water loss due to evaporation, but its practical accuracy is sufficient (error within a few percent) and it is the standard method for HVAC and plant design. The Popper method is a more rigorous extended version that corrects for this evaporation loss. This simulator is based on the Merkel method but covers most design calculations.
Effectiveness ε = (actual cooling range) / (theoretical maximum cooling range = Tw1 − Twb), a dimensionless index that divides the actual cooling capacity by the maximum possible value. NTU is a difficulty index indicating 'how difficult a task is being performed' and corresponds to equipment size (packing volume). ε is used for system evaluation, while NTU is used for equipment design.
In counterflow, air and water flow in opposite directions, so the outlet air contacts the hottest inlet water, maximizing thermal efficiency. Crossflow allows easier inspection and cleaning of the packing. For the same NTU, counterflow is about 8–10% more compact. You can switch between configurations in this simulator and observe the change in NTU (×0.92 correction).
Makeup water flow rate = sum of evaporation loss + drift loss + blowdown. Evaporation loss ≈ circulating water flow rate × 0.002 × cooling range [°C], drift loss ≈ circulating water flow rate × 0.02%, blowdown = evaporation loss ÷ (COC − 1). COC (cycles of concentration) is managed by electrical conductivity and is typically set to 3–5.
The approach temperature (outlet water temperature − wet-bulb temperature) represents a physical lower limit; as the wet-bulb temperature rises, the outlet water temperature must also rise. For example, if a design uses a wet-bulb temperature of 28°C and an outlet water temperature of 32°C (approach 4°C), when the actual wet-bulb temperature reaches 30°C, the outlet water temperature can only drop to a minimum of 34°C. This causes a chain reaction where the condenser temperature of the chiller increases and COP decreases. It is important to conservatively select the design wet-bulb temperature.
The Merkel method treats the entire cooling tower as a one-dimensional integral and is suitable for overall sizing and operating parameter studies. CFD (Computational Fluid Dynamics) can visualize three-dimensional flow, local heat transfer, and maldistribution inside the packing, and is used for shape optimization and diagnosing uneven inflow. In practice, the typical sequence is overall design using the Merkel method → detailed improvement using CFD.
What is Cooling Tower?
Cooling Tower (Cooling Tower Performance Calculator is a fundamental topic in engineering and applied physics. This interactive simulator lets you explore the key behaviors and relationships by directly manipulating parameters and observing real-time results.
By combining numerical computation with visual feedback, the simulator bridges the gap between abstract theory and physical intuition — making it an effective learning tool for students and a rapid-verification tool for practicing engineers.
Physical Model & Key Equations
The simulator is based on the governing equations behind Cooling Tower Performance CalculatorMerkel. Understanding these equations is key to interpreting the results correctly.
Each parameter in the equations corresponds to a slider in the control panel. Moving a slider changes the equation's solution in real time, helping you build a direct connection between mathematical expressions and physical behavior.
Real-World Applications
Engineering Design: The concepts behind Cooling Tower Performance CalculatorMerkel are applied across mechanical, structural, electrical, and fluid engineering disciplines. This tool provides a quick way to estimate design parameters and sensitivity before committing to full CAE analysis.
Education & Research: Widely used in engineering curricula to connect theory with numerical computation. Also serves as a first-pass validation tool in research settings.
CAE Workflow Integration: Before running finite element (FEM) or computational fluid dynamics (CFD) simulations, engineers use simplified models like this to establish physical scale, identify dominant parameters, and define realistic boundary conditions.
Common Misconceptions and Points of Caution
Model assumptions: The mathematical model used here relies on simplifying assumptions such as linearity, homogeneity, and isotropy. Always verify that your real system satisfies these assumptions before applying results directly to design decisions.
Units and scale: Many calculation errors arise from unit conversion mistakes or order-of-magnitude errors. Pay close attention to the units shown next to each parameter input.
Validating results: Always sanity-check simulator output against physical intuition or hand calculations. If a result seems unexpected, review your input parameters or verify with an independent method.