MOLLIER DIAGRAM A NO-NONSENSE GUIDE TO USING IT
(
e φ + . 0d = 17,6 (/ ) 0L
17,6
)
100-φ 4,065
100
P P = φ .100 d
dv
H +36 0wb = 27,81n 45,5
0 . c HX= 2500,8+c . 0 pl
L
pw
L
P P= M 1+ x. M d
b
w
L
H = cpl. 0L+2500,8+cpw.x. 0L
AN EASY-TOREAD TOOL STILL IN USE TODAY.
INTRO Ever wonder what applications looked like a century ago? Here is the story of Richard Mollier one of the first programmers in an era before smartphones and computers. Richard Mollier was a professor of Applied Physics and Mechanics and a pioneer of experimental research in thermodynamics in the late 19th century. He carried out meticulous calculations for every state and property of air. The result: the emblematic HX diagram. An easy-to-read tool still in use today. In this whitepaper we explain what the Mollier diagram is and how to read it.
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CHAPTERS Intro 2 Chapters 3 Part 1 – The age of efficiency
Back in the day
5
It started with a homicide
6
Get the friction out of the system
6
Part 2 – The purpose ot he diagram
Temperature lines
8
Absolute humidity
9
Relative humidity
9
Specific enthalpy
10
Air density
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Part 3 – Dew point and wet bulb temperature
Finding the dew point
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Finding the wet bulb temperature
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Part 4 - Getting started
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7
11
14
Energy efficiency 15
Step 1 - Calculating cooling coil
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Step 2 - Heater capacity
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Step 3 - Humidifying the air
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Wrapping things up 20 Sources
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PART 1
THE AGE OF EFFICIENCY
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Bless the century in which we are living. There are so many things that make our life so much easier – from the active park assist function on your car to the supermarket order app on your smartphone with same-day delivery of your groceries. All of this efficiency rests upon advanced hardware and software. Computers don’t get tired or make mistakes, so they have taken over many dull and repetitive tasks and been incorporated in all layers of our society.
BACK IN THE DAY Before the advent of computers, all those boring jobs had to be done in person. If you had to make a thousand calculations, you would have to work your way through them yourself. This was an issue that bothered Richard Mollier, a professor of applied science and mechanics in late-19th-century Germany. He worked on the big technology of his day – steam engines. This required finding out the properties of water in a given state, which in turn called for endless calculations.
Image 1: A picture of Richard Mollier
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IT STARTED WITH A HOMICIDE Hanging out in a café one day reading a newspaper, Mollier came upon the story of a homicide in a neighbouring village. Stressed as he was with the mathematical problems in his work, he found this story a welcome diversion. There were three suspects in the case: the wife, the mailman and a mistress who was ten years the victim’s junior. The journalist had written a list with all the facts known about the suspects, which looked something like this: Suspect: Wife Age: 35 Motive: Jealousy Alibi: Drinking tea with friends As Mollier was reading the story, with the mathematical problems from his work still fresh in the back of his mind, he had a revelation: What if he made a chart with all the thermodynamic suspects for every state? He got to work and made it happen.
GET THE FRICTION OUT OF THE SYSTEM To be honest, I don’t know if it happened exactly this way. I like to think it did. The fact is, Mollier found a way to simplify calculations involving thermodynamic processes. If you calculate all the properties of a thousand given states, you develop a chart with all the data you will need in the future. While connecting the dots, Mollier ended up with the famous H-S diagram which plots total heat against entropy. This shows the state and every property which belongs to it in a fairly simple chart.
Image 2: Mollier famous H-S diagram
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PART 2
THE PURPOSE OF THE DIAGRAM
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Now that he had a taste for it, Richard Mollier moved on to other diagrams that used enthalpy (h) as one of the axes like the HX diagram. The diagram provides a graphic representation of the relationship between physical conditions and the corresponding changes in the system: the two can be linked simply by drawing some lines and knowing what their intersections represent.
TEMPERATURE LINES
(DIAGR AM 1)
Constant temperature lines in the diagram are largely horizontal, but slightly tilted. Each line corresponds to a temperature, and they are simple and proportionate – in other words, if you need the line for 21.5°C and this is not indicated in the graph, you can simply imagine a line exactly in the middle between those for 21 and 22°C.
Diagram 1: Temperature lines
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ABSOLUTE HUMIDIT Y
(DIAGR AM 2)
The vertical lines in the diagram represent absolute humidity in grams per kilogram, with a range from 0 to 40 g/kg. They show how much water vapour the air can contain at different temperatures: the warmer the air, the more water vapour it can contain.
REL ATIVE HUMIDIT Y
(DIAGR AM 3)
The curved lines in the diagram represent the relative humidity of air. As we mentioned above, air can hold a fixed amount of water vapour. Relative humidity is the ratio of existing water vapour in the air to the maximum possible amount of vapour the air could potentially contain. The 100% humidity line is also called the saturation line. This is the maximum amount of vapour that air in a given condition can contain.
Diagram 2: Absolute humidity
Diagram 3: Relative humidity
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SPECIFIC ENTHALPY
(DIAGR AM 4)
The diagonal lines in the diagram represent specific enthalpy, which indicates the internal energy of the air. Again, as with humidity, this is higher when the air is hotter.
AIR DENSIT Y
(DIAGR AM 5)
The last set of lines in the diagram are the lines of air density, which range from 1.1 to 1.35 kg/ mÂł. Colder air is heavier than hotter air as colder molecules are packed more closely together and thus denser in low temperatures. As temperature rises, the atoms enter a more excited state, and space between them increases, reducing density.
Diagram 4: Specific enthalpy
Diagram 5: Air density
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(
e φ + . = 0d 17,6 (/ ) 0L
17,6
)
100-φ 4,065
P P = φ .100 dv
d
100 H +36 0wb = 27,81n
0 . c HX= 2500,8+c . 0 pl
L
pw
45,5
H = cpl. 0L+2500,8+cpw.x. 0L
L
PART 3
DEW POINT AND WET BULB TEMPERATURE
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The dew point and wet bulb temperature are two important variables that can be read indirectly from the Mollier diagram. The dew point is the temperature at which air starts to condense. The wet bulb temperature is the theoretical temperature read by a thermometer covered in watersoaked cloth over which air is passed.
FINDING THE DEW POINT
(IMAGE 3)
As an example, let us imagine an arbitrary state, like 25°C with 50% relative humidity. You can find the dew point by drawing a line from the point where the 50% relative humidity curve intersects with an imaginary line indicating a temperature of 25°C in the graph straight down to the saturation line (which, as you remember, represents 100% relative humidity). The temperature corresponding to this point is the dew point temperature – in this case 14°C.
Image 3: Finding the dew point
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FINDING THE WET BULB TEMPERATURE
(IMAGE 4)
For the wet bulb temperature, we again start from the point where relative humidity is 50% and temperature is 25°C, but instead of a vertical line, we follow the specific enthalpy line down to the saturation line. The temperature at this point is the wet bulb temperature, or around 18.3°C in our example.
Image 4: Finding wet bulb temperature
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PART 4
GETTING STARTED
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The diagram is used to engineer an air handling unit. In this example, we will show you how to calculate the following aspects of a unit using the Mollier diagram: • • •
Cooling coil Heater capacity Steam humidifie
We start by establishing the outside and inside conditions. This is our field of operation, which sets the boundaries within which we work. A common mistake is to set the conditions extremely high. To be ‘on the safe side’. We often get requests for outside conditions like 50°C – 80%RH. Not only are these impossible ambient conditions, it will make the installation unnecessary heavy and more difficult to operate. For this example, we will assume the following conditions: Outside: Inside:
35 °C – 70% RH 21 °C – 60% RH
Energy ef ficiency
Every system reduces energy loss by using the heat or cold that are already present and transferring part into the outside air. There are a range of ways to reduce energy, each of which has its pros and cons. In this example, we will use one of the most common methods: a recirculation rate of 50%.
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STEP 1 - CALCUL ATING COIL The cooling coil we are using is chilled water-fed, with a temperature of 12 °C in and 6 °C out. 1: Marking points in the diagram We start with the easy part, that is putting the fixed points into the diagram. We begin by locating the outside and inside condition and drawing a line between them. (Image 6) 2: Determining the mixing temperature Remember, we are recirculating 50% of the air for energy efficiency purposes. This means the temperature in front of the cooler will be a mix between outside and inside conditions. To calculate the mixing temperature, we use a simple equation: temp. mix =
(temp. outside * air amount outside) + (temp. inside * air amount inside) total air amount
Let us assume a total air amount of 20,000 m³/h. With a recirculation rate of 50%, this gives us 10,000 m³/h for both outside and inside air streams. Now we can calculate the mixing temperature: (35 * 10,000) + (21 * 10,000) temp. mix = 20,000 This gives us a mixing temperature of 28 °C. (Image 7)
Image 6: Outside and inside coditions
Image 7: Mixing temperature
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STEP 1 - CALCUL ATING COIL 3: Cooling the air The cooler dew point (CDP) is 9 °C and set on the saturation line. You’ll get the CDP by taking the average temperature of the cooling coil, which is 12 °C in and 6 °C out. To determine the cooler capacity, we follow the lines of constant enthalpy between the mixing temperature and CDP. This gives us 72 kJ/kg – 27 kJ/kg = 45 kJ/kg. (Image 8)
Image 8: Cooler capacity
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STEP 2 - HEATER CAPACIT Y The temperature behind the cooler will be around 9 °C. We can round up a degree because of the residual heat of the ventilator, resulting in a temperature of 10°C. Room temperature is 21 °C, giving a temperature differential of 11 °C. (Image 9) Now we have enough information to calculate the heater capacity using the Q=m*c*ΔT equation. For this example, resulting in a heater capacity of 76kW.
Image 9: Heating the air
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STEP 3 - HUMIDIF YING THE AIR In this example, we use a steam humidifier to bring the air up to a relative humidity of 60%. Cooling the air extracts a lot of moisture from it. (Image 10) Now, heating the air brought it to a temperature of 21 °C without changing the absolute humidity. Looking at this line, we see a gap of 2.2 g/kg between our current point and the desired value. (Image 11) Now we just need to convert the air amount of 20,000 m³/h to kg/s to find out how large the steam humidifier needs to be. For this example, resulting in a humidifier capacity of 15.2 kg.
Image 10: Extracting moisture by cooling
Image 11: Humidifying the air
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WRAPPING THINGS UP So, does this cover every detail? Of course not. For one thing, we didn’t integrate the bypass factor, which accounts for the fact that not every air particle running through the cooling coil is affected by the decrease in temperature. And what about all the different methods of energy recovery, like the heat recovery wheel, twin coils or cross heat exchangers? Or adiabatic humidifying? Like I mentioned above, this is a quick and dirty description of how the Mollier diagram can be used to give a fairly accurate estimation of an air handling unit’s capacities. To get familiar with the diagram, you can try using different conditions. This example only included summer conditions: see what happens with the capacity of the heater and steam humidifier when you set the outside conditions to -5 °C and 20% RH.
People who followed him would be free of this tedious job forever. In that sense, you can see Mollier as one of the first programmers, making complex tasks easier and more efficient. And we are still using the solution he found more than a hundred years ago!
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SOURCES Writing this white paper we have used the knowledge of our technical engineers who have based their findings on education and over 50 years experience. Furthermore we have consulted the following sources: Handboek installatietechniek ([2e dr] editie). (2002). ISSO. Lede, F., & Berge, R. V. D. (2018). Klimaatbeheersing 2 luchtbehandeling, ventilatie en koeling (1ste editie). Vakmedianet. Wikipedia contributors. (2020, 27 februari). Richard Mollier. Wikipedia. `https://en.wikipedia.org/wiki/Richard_Mollier
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(Pressure 1,013 bar / Sea level)
THE MOLLIER H - X DIAGRAM
Why make thousands of calculations every time you need to predict the state of a medium? Richard Mollier saved us a tremendous amount of time by giving us this powerful tool.
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you want to know more “Do about the Mollier diagram? I am keen to help you further!
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