Engineering task and calculation objective
The module calculates state changes of humid air during humidification and dehumidification according to the VDI Wärmeatlas (VDI Heat Atlas, 12th edition 2019). Humid air is balanced as a mixture of dry air and water vapor; the central quantities are the moisture content (humidity ratio in kg of water per kg of dry air), the relative humidity, the specific enthalpy, and the dew point and wet-bulb temperatures. The state changes correspond to the familiar paths in the Mollier h-x diagram (psychrometric chart).
Humid air calculations are needed in HVAC and ventilation engineering, in drying processes, cooling towers and spray humidifiers, and in the design of coolers on which water vapor condenses. To humidify or dehumidify air, the water and energy balances must be kept consistent: during heating, the moisture content remains constant and the relative humidity drops; during cooling below the dew point, condensate forms; during evaporative humidification, the state change runs almost along a line of constant enthalpy.
The module provides the state variables before and after the state change as well as the transferred water and heat quantities, replacing graphical work in the h-x diagram with a reproducible calculation.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Determine the initial state of the humid air: From temperature, total pressure and relative humidity (or alternatively wet-bulb or dew point temperature), the water vapor partial pressure, moisture content and specific enthalpy of the inlet state are calculated. The basis is the saturation vapor pressure of water at the respective temperature.
- Specify the state change: The process is selected: heating or cooling at constant moisture content, cooling with dehumidification below the dew point, adiabatic evaporative humidification, steam humidification, or mixing of two air streams.
- Establish the water balance: All moisture contents are referred to the unchanging mass of dry air. The difference of the moisture contents before and after the state change gives the water quantity added or removed; for dehumidification, the amount of condensate produced.
- Establish the energy balance: Via the specific enthalpies of the humid air (contributions of dry air, water vapor and, if applicable, liquid water), the required heating or cooling duty is determined. In evaporative humidification, the enthalpy of vaporization of water provides the cooling of the air stream.
- Check the final state and limits: The final state is checked for physical consistency: relative humidity at most 100 %; falling below the dew point means fog or condensate formation. The dew point and wet-bulb temperatures of the final state serve as control quantities for the equipment design.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Total pressure | p | bar |
| Density in dry air inlet | ρLE | kg/m³ |
| Dry air flow | ML | kg/s |
| Vapour stream | MD | kg/s |
| Humidity loading at air inlet | YE | kg/kg |
| Humidity loading at air outlet | YA | kg/kg |
| Alteration of humidity loading | ΔY | kg/kg |
| Length of the humidification zone | LB | m |
| Length of the balance zone | LAus | m |
| Height of humidifier channel | H | m |
| Width of humidifier channel | B | m |
| Area of humidifier channel | A | m² |
| Temperature of air inlet | ϑLE | °C |
| Temperature at air outlet | ϑla | °C |
| Air velocity at inlet of humidifier | uLE | m/s |
| Inlet temperature of steam | ϑD | °C |
| Req. number of vapour distributions | nR | – |
| Actual number of vapour distributions | Dampfverteilrohre | – |
| Corrected number of vapour distributions | Dampfverteilrohre | – |
| Length of vapour distributions | LR | m |
| Allowable vapour mass flow / unit length | MDmax | kg/h m |
| Reduced vapour mass flow / unit length | MDmax,red | kg/h m |
| Wall distance a | a | mm |
| Wall distance b | b | mm |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Total heat transfer performance | Q | kW |
| Heat transfer performance (dry) | Qtr | kW |
| Heat transfer performance (wet) | Qfe | kW |
| Transfer area dry section | Atr | m² |
| Transfer area wet section | Afe | m² |
| Total transfer area | Atotal | m² |
| Number of tube rows | n | – |
Calculation options
Option
Humidification by adding vapour · Humidification by evaporation · Dehumidification - determination of cooling area · Dehumidification - determination of state at outlet
Worked example
Outdoor air at 30 °C and 50 % relative humidity at 1,013.25 mbar total pressure is to be evaluated for a drying plant. Required are the moisture content, specific enthalpy and dew point temperature of the state — a worked example of how to calculate humid air properties.
Given values
| Air temperature t | 30 °C |
| Relative humidity φ | 50 % |
| Total pressure p | 1,013.25 mbar = 101.325 kPa |
| Saturation vapor pressure ps(30 °C) | 4.247 kPa |
Solution
Water vapor partial pressure
pD = φ · ps = 0.5 · 4.247 = 2.124 kPa
Moisture content (humidity ratio)
x = 0.622 · pD / (p − pD) = 0.622 · 2.124 / (101.325 − 2.124)
x = 0.01331 kg/kg ≈ 13.3 g of water per kg of dry air
The factor 0.622 is the ratio of the molar masses of water (18.015 g/mol) and dry air (28.96 g/mol).
Specific enthalpy
h1+x = cp,L · t + x · (ΔhV + cp,D · t) = 1.005 · 30 + 0.01331 · (2,500 + 1.86 · 30)
h1+x = 30.15 + 34.03 = 64.2 kJ/kg of dry air
Dew point temperature
Required is the temperature at which ps = 2.124 kPa. From the vapor pressure table (ps(18 °C) = 2.064 kPa, ps(19 °C) = 2.197 kPa), interpolation gives:
tdew ≈ 18.4 °C
Cooling surfaces colder than 18.4 °C will dehumidify this air.
Result
| Moisture content x | 0.01331 kg/kg (13.3 g/kg) |
| Specific enthalpy h1+x | ≈ 64.2 kJ/kg dry air |
| Dew point temperature | ≈ 18.4 °C |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
Why is the moisture content referred to the dry air and not to the total humid mass?
Because the mass of dry air remains constant in all humidification and dehumidification processes, while the total mass changes with the water exchange. With the humidity ratio x in kg of water per kg of dry air, the water and energy balances become linear, and mixtures of two air streams can be represented as a simple division of a line segment in the h-x diagram.
What is the difference between dew point and wet-bulb temperature?
The dew point is the temperature at which the air just reaches saturation when cooled at constant moisture content — condensation begins there. The wet-bulb temperature (adiabatic saturation temperature) establishes itself during adiabatic evaporation of water into the air stream; it lies between the dew point and the dry-bulb temperature. Evaporative coolers can cool the air at most down to the wet-bulb limit; surface coolers dehumidify only below the dew point.
What influence does the total pressure have on the calculation?
The moisture content depends on the total pressure via the ratio of vapor partial pressure to total pressure: at the same conditions (temperature, relative humidity), air at 2,000 m altitude or in sub-atmospheric systems carries more water per kg of dry air than at standard pressure. h-x diagrams therefore always apply only to one reference pressure; the module calculates with the actual system pressure.
Why does the air temperature drop during evaporative humidification?
The enthalpy required to evaporate the water (around 2,500 kJ per kg of water) is extracted from the air stream. Since no heat is supplied to the system from outside, the state change in the h-x diagram runs almost along an isenthalpic line: the moisture content rises and the temperature falls, at most down to the wet-bulb temperature.