Type a line (ambient 35 °C 70 % RH charge air 3 bar after cooler 45 °C air flow 50 000 kg/h) or fill in the fields: the line and the fields stay in step.
Enter the intake air, as a temperature with the relative humidity or as a humidity ratio, the charge air pressure and the air temperature after the charge air cooler, and the calculator gives the water that condenses out of the charge air: in grams per kilogram of dry air, and with the air flow in kg/h and tonnes per day. It also gives the dew point at the charge air pressure and how far the air after the cooler is above or below it. It shows the working with your numbers, draws the saturation curve at your pressure, and gives a line you can copy or add to a request.
The condensed water is removed by the water mist catcher and the drain after the cooler. The calculator gives no recommended charge air or cooler outlet temperatures, which the engine maker sets, and does not size the cooler or its cooling water. The saturation pressure is worked out over liquid water from 0 to 100 °C; below 0 °C the saturation is over ice, which the calculator does not cover, and it says so instead of giving a figure.
The humidity ratio x1 = 0.622 pv / (pa - pv), with pv = RH x ps(t1) the vapour pressure and pa the ambient pressure. At 35 °C and 70 % RH: ps = 0.05629 bar, pv = 0.03940 bar, x1 = 0.622 x 0.03940 / (1.013 - 0.03940) = 0.02517 kg/kg, or 25.17 g/kg. The compressor does not change the humidity ratio.
After the cooler the air holds at most x2 = 0.622 ps(t2) / (p2 - ps(t2)) at the absolute charge air pressure p2. At 3 bar(g) (4.013 bar(a)) and 45 °C: ps = 0.09594 bar, x2 = 15.24 g/kg. The condensate is x1 - x2 = 9.94 g per kg of dry air; at 50 000 kg/h of air that is 485 kg/h, or 11.6 t per 24 h.
The vapour pressure of the charge air is pv2 = x1 p2 / (0.622 + x1) = 0.1561 bar; the dew point td is the temperature at which ps(td) = pv2, found by bisection: 54.8 °C. The same air at the ambient pressure has its dew point at about 28.7 °C: the pressure raises it, which is why water condenses although the air after the cooler is warmer than the intake air.
| Quantity | Relation | Note |
|---|---|---|
| Humidity ratio x | x = 0.622 pv / (p - pv) | kg water per kg dry air; 0.622 = 18.015 / 28.966, the ratio of the molar masses of water and dry air |
| Vapour pressure | pv = RH x ps(t) | ps by the IAPWS-IF97 saturation-pressure equation |
| Saturation after the cooler | x2 = 0.622 ps(t2) / (p2 - ps(t2)) | at the absolute charge air pressure |
| Condensate | x1 - x2, when above zero | kg water per kg dry air |
| Dew point at p2 | ps(td) = x1 p2 / (0.622 + x1) | solved by bisection on 0 to 100 °C |
| Absolute pressure | p2 = p(g) + pa | pa 1.013 bar(a) unless entered |
| Water from the air | m dry x (x1 - x2); m dry = m / (1 + x1) | kg/h; x 24 / 1000 for t per 24 h |
| Units | 1 kg/s = 3600 kg/h; 1 t/h = 1000 kg/h | 1 psi = 0.06894757293168 bar; 1 kgf/cm2 = 0.980665 bar |
The saturation pressure ps(t) comes from the IAPWS-IF97 equation over liquid water, from 0 to 100 °C. The humidity ratio is per kilogram of dry air; an air flow is taken as moist air and divided by (1 + x1) for the dry air; a flow marked dry air is used as it is.
The humidity ratio x = 0.622 pv / (p - pv) and its inverse pv = x p / (0.622 + x) are the standard psychrometric relations for moist air as a mixture of ideal gases: they are given in the ASHRAE Handbook — Fundamentals (chapter 1, with the factor 0.621945) and in independent engineering references and moist air libraries (with 0.62198); 0.622 is the ratio of the molar masses of water and dry air, 18.015 / 28.966, and the difference in the result is under 0.01 %. The saturation pressure is Eq. (30) of IAPWS-IF97 (IAPWS release R7-97) with the coefficients of Table 34, checked against the verification values of the release. That water condenses in the cooler when the charge air passes its dew point, and is removed by the water mist catcher and the drain after the cooler, is described in the marine engineering literature.
In four steps. The water in the intake air: pv = RH x ps(t1) and x1 = 0.622 pv / (pa - pv). The charge air pressure made absolute: p2 = gauge + pa. The most water the air can hold after the cooler: x2 = 0.622 ps(t2) / (p2 - ps(t2)). The condensate is x1 - x2 when that is above zero. Intake air at 35 °C and 70 % RH: ps = 0.05629 bar, pv = 0.03940 bar, x1 = 25.17 g/kg at 1.013 bar(a). Charge air 3 bar(g), 4.013 bar(a), 45 °C after the cooler: ps = 0.09594 bar, x2 = 15.24 g/kg. About 9.94 g of water condenses per kg of dry air; at 50 000 kg/h of air, 48 772 kg/h of it dry, that is 485 kg/h, or 11.6 t per 24 h.
Because the air is compressed. The humidity ratio x1 does not change in the compressor, but the partial pressure of the water vapour rises with the total pressure: pv2 = x1 p2 / (0.622 + x1). The dew point rises with it. Intake air at 35 °C and 70 % RH has its dew point at about 28.7 °C at 1.013 bar(a), but at 4.013 bar(a) the same air has its dew point at about 54.8 °C, so a cooler outlet at 45 °C is about 9.8 K below the dew point and water condenses.
From the vapour pressure of the charge air, pv2 = x1 p2 / (0.622 + x1), the inverse of the humidity ratio relation. The dew point td is the temperature at which the saturation pressure ps(td) equals pv2. The calculator finds it by bisection between 0 and 100 °C on the IAPWS-IF97 saturation-pressure equation, and shows the margin of the air after the cooler over it: above the dew point nothing condenses, below it the condensate is x1 - x2.
It is removed by the water mist catcher and the drain after the cooler: the separator takes the droplets out of the air, and the drain takes the water away. The calculator gives how much water there is to remove, in g per kg of dry air and, with the air flow, in kg/h and t per 24 h. The amount depends on the humidity and the temperature of the intake air, on the charge air pressure and on the air temperature after the cooler.
The calculator gives no recommended temperature: follow the engine maker’s guidance for the air cooler outlet temperature. What it gives is the water that condenses at the temperature entered, the dew point at the charge air pressure and how far the air after the cooler is above or below it, so the figures can be compared with the maker data.
The intake air temperature in °C (K and °F are read too) with the relative humidity in %, or a humidity ratio in g/kg or kg/kg; the charge air pressure in bar, mbar, kPa, MPa, psi or kgf/cm2, gauge or absolute, read as gauge when it has no mark; the ambient pressure, 1.013 bar(a) unless entered; the air temperature after the cooler; and the air flow in kg/h, kg/s or t/h if wanted. Temperatures from 0 to 100 °C: below 0 °C the saturation is over ice, which the calculator does not cover.
The calculator gives the water that condenses out of the charge air. When parts for the charge air cooler, the water mist catcher or its drain are needed, send the line from the calculator with the engine details and a photograph of the nameplate, and Vessel Core checks the details before an offer goes back.
