Mollier-hx diagram

The Mollier h, x diagram (formerly ix diagram), enthalpy-water load diagram, makes it possible to describe changes in the state of humid air through heating, humidification , dehumidification, cooling and mixing of different amounts of air. It applies to a certain air pressure (usually for atmospheric air pressure, e.g. 100 kPa), i.e. for isobaric changes of state . The parameters temperature , humidity , enthalpy and density can be read off immediately. Changes in status can be determined graphically. The diagram was proposed by Richard Mollier in 1923 (see also Psychrometry ). ${\ displaystyle p}$

Structure of the diagram

The Mollier h, x diagram is shown in an oblique coordinate system . The choice of the oblique coordinate system increases the reading accuracy for the unsaturated area of humid air, which is important for technical applications. To construct the oblique-angled diagram proposed by Mollier, the x-axis is rotated clockwise until the isotherm t = 0 ° C is horizontal in the unsaturated area of the moist air. The lines of constant specific enthalpy run from top left to bottom right. The lines of constant water content (also water load) run vertically. ${\ displaystyle h}$ ${\ displaystyle x}$

For practical reasons, the horizontal axis ( abscissa ) on which the water content is plotted does not run through the origin of the coordinates. The partial pressure of the water vapor can be specified as the second x-axis , as this only depends on the water content and the air pressure . The specific enthalpy is plotted on the vertical axis ( ordinate ) . In some diagrams, the temperature is incorrectly shown on the ordinate. ${\ displaystyle x}$ ${\ displaystyle p _ {\ text {w}}}$ ${\ displaystyle x}$ ${\ displaystyle p}$ ${\ displaystyle h}$

The diagram shows families of curves for the air temperature , the density of the moist air and the relative humidity . ${\ displaystyle t}$ ${\ displaystyle \ rho _ {\ text {f}}}$ ${\ displaystyle \ phi}$

In some diagrams, a so-called edge scale with the ratio of the change in the specific enthalpy to the change in the water load is shown all around . With the help of the edge scale, changes in state can be easily represented graphically, e.g. B. the change of state with steam humidification. ${\ displaystyle {\ frac {\ Delta h} {\ Delta x}}}$

The index indicates that the enthalpy of humid air is composed of the enthalpy of dry air and the enthalpy of water . The mass of dry air is chosen as the reference value . ${\ displaystyle 1 + x}$ ${\ displaystyle H _ {\ text {Wed}}}$ ${\ displaystyle H _ {\ text {l}}}$ ${\ displaystyle H _ {\ text {w}}}$ ${\ displaystyle m _ {\ text {l}}}$

${\ displaystyle h _ {\ text {1 + x}} = {\ frac {H _ {\ text {Mi}}} {m _ {\ text {l}}}} = {\ frac {H _ {\ text {l} } + H _ {\ text {w}}} {m _ {\ text {l}}}} = h _ {\ text {l}} + x \ cdot h _ {\ text {w}}}$

${\ displaystyle x = {\ frac {m _ {\ text {w}}} {m _ {\ text {l}}}}}$

Structure of the h, x diagram. The picture shows the enthalpy shares for two states with the same temperature on the isotherm drawn in red.
Point 1 is in the area of unsaturated air,
point 2 in the fog area.
The symbols mean: h = specific enthalpy in kJ / kg, s = state of saturation, t = temperature in ° C, c = specific heat capacity in kJ / kg · K and x = water content in g / kg. The index p stands for constant pressure (usually 1 bar), the index extensions are L for air, D for water vapor and W for liquid water. Finally, the enthalpy of vaporization at 0 ° C should be mentioned.

{\ displaystyle r_ {0}}

The lines of the same temperature (isotherms) rise slightly in the area of unsaturated air, namely by the tangible enthalpy portion of the water vapor. At the saturation point (relative humidity φ = 1) the lines bend downwards, because beyond the maximum vapor content, water can only be contained in the air in liquid form in the form of small water droplets (mist). In the foggy region, the isotherm only deviates by the low perceptible enthalpy of the additional water component from the isenthalpic running through the saturation point . The origin of the diagram is 0 ° C for dry air ( ). ${\ displaystyle x = 0}$

In the area of unsaturated air, there are now curves of equal relative humidity φ, which are created by an even division of the respective isothermal sections between φ = 0 and φ = 1. The relative humidity becomes lower and lower the warmer the air becomes if the amount of water x does not change.

Calculation algorithms to create a psychrometric diagram for moist air, which is also for the creation of computer programs or macros for the state and physical characteristics of the dry and humid air (specific heat capacity , thermal conductivity , viscosity , thermal conductivity , Prandtl number found suitable), in "Bernd Glück: Condition and material values (water, steam, air) and combustion calculation" .

For practical use, the enthalpy zero points for dry air and water are determined as follows: at a temperature of 0 ° C applies to dry air and boiling water . ${\ displaystyle h _ {\ text {l}} = 0}$ ${\ displaystyle h '_ {\ text {w}} = 0}$

Conversion to other total pressure

An h, x diagram is only valid for a certain total pressure . The isotherms do not change with pressure changes - with ideal gases. The relative humidity changes proportionally with the total pressure. The conversion to other total pressures is done with the following equation: ${\ displaystyle p}$ ${\ displaystyle \ phi}$

{\ displaystyle {\ frac {p _ {\ text {prev}}} {p _ {\ text {Diagr}}}} = {\ frac {\ phi _ {\ text {prev}}} {\ phi _ {\ text {Diagr}}}}}

Examples of application

Represent processes in the diagram

h, x diagram showing relevant air treatment processes

To use the diagram, at least two variables must be known, the others can be derived from it: dry bulb temperature , dew point temperature , wet bulb temperature , relative humidity φ, absolute humidity , specific enthalpy and density.

From a point on the diagram, for example 30 ° C; 10 g / kg (point 1), the following information can be derived:

Dry bulb temperature: is read horizontally directly on the ordinate (30 ° C).
Dew point temperature: follow straight down to the dew line. Then read off the temperature on the ordinate (13.9 ° C; 10 g / kg [point 4]).
Wet bulb temperature: along the isenthalps to saturation. Then read off the temperature on the ordinate (19.5 ° C; 14.2 g / kg [point 6]).
Relative humidity: hyperbolic lines bounded by the dew line (37% RH).
Absolute humidity: can be read directly from the abscissa (10 g / kg).
Specific enthalpy: The isenthalps are lines of the same specific enthalpy (purple in the picture [56 kJ / kg]).
Density: The lines of the same density run with a slight gradient from left to right (green in the picture [1.143 kg / m³]).

Show changes of state in the Mollier h, x diagram:

Heating: When the air is heated, the state point shifts vertically upwards, for example from 30 ° C to 50 ° C (point 1 to point 3).
Cooling (without condensation): When the air is cooled, the state point shifts vertically downwards, opposite to the heating.
Humidification (1): When the air is humidified, the state point shifts to the right, for example from point 1 to point 5. This is a very theoretical process that is only approximately achieved by humidifying with relatively cold steam.
Humidification (2): With adiabatic humidification, for example with a spray humidifier, the state point shifts along the isenthalpic (from point 1 to point 6) in the direction of the dew line.
Dehumidification: When the air is dehumidified, the status point shifts to the left (point 2). However, this process is usually associated with a change in temperature. In the case of dehumidification through condensation, the point shifts to the bottom left, in the case of sorptive dehumidification to the top left.
Mixing of air streams: The representation of a mixing process of different air streams takes place by means of the "law of the averted lever".

The most illustrative of this approach is an example:

If an air flow A with 2,000 kg / h and 30 ° C; 10 g / kg (point 1) with air flow B at 1,000 kg / h and 15 ° C; 4 g / kg (point 7) mixed, the mixing point is on the straight line between points 1 and 7. The distance between the mixing point is exactly the proportion of the cold air flow in the mixed flow away from the warm point (1,000 kg / h = 1 / 3 of 1,000 kg / h + 2,000 kg / h = 3,000 kg / h). Since the influence of the cold air flow is carried away by the warm air, one speaks of the “lever turned away”. The mixing point is thus 25 ° C; 8 g / kg (point 8).

Air humidification

h, x diagram

The air drawn in from the environment is heated. The air has a certain temperature and contains a certain amount of water, as room air is never completely dry. This air is now heated by a heater in the dryer, which reduces the relative humidity (red arrow).

The heated air is fed into the drum. She strokes the laundry, the water in the laundry evaporates (the air is humidified adiabatically). The heat of evaporation required for this is extracted from the warm air. As a result, the temperature in the air drops and the water load increases at the same time. The enthalpy of the air remains almost constant and can be read from the enthalpy lines in the Mollier diagram (blue arrow).

The humidified air is cooled down to the so-called wet bulb temperature. Once this temperature has been reached, no more water can be absorbed by the air.

International application

In the Anglo-Saxon region the " psychrometric chart" or " carrier diagram " (after Willis Carrier ) is used. Here the water load is plotted against the air temperature . The directions in the representation of the changes in the state of the air change accordingly. ${\ displaystyle x}$ ${\ displaystyle t}$

psychrometric chart, sea level (101.325 kPa), SI units

Individual evidence

^ ^A ^b Hans Dieter Baehr, Stephan Kabelac: Thermodynamics. Basics and technical applications. 14th edition. Springer, Berlin / Heidelberg 2009, ISBN 978-3-642-00556-5 , p. 296.

↑ ^a ^b ^c Günter Cerbe, Hans-Joachim Hoffmann: Introduction to Thermodynamics: from the basics to technical application. 11th edition. Hanser, Munich / Vienna 1996, ISBN 3-446-18849-5 , p. 287.

^ Hermann Recknagel, Eberhard Sprenger, Ernst-Rudolf Schramek (eds.): Pocket book for heating and air conditioning. 71st edition. Oldenbourg Industrieverlag, Munich 2003, ISBN 3-486-26534-2 , p. 136.

↑ ^a ^b Bernd Glück: State and material values (water, steam, air) and combustion calculation. 2nd Edition. Verlag für Bauwesen, Berlin 1991, ISBN 3-345-00487-9 .

^ Siegfried Baumgarth, Berndt Hörner, Josef Reeker: Handbook of air conditioning . Volume 1: Basics. 5th edition. CF Müller, Heidelberg 2008, ISBN 978-3-7880-7820-1 , p. 215.

↑ In this context, the dry bulb temperature is the temperature of the surrounding air, which is measured with a thermometer with a dry mercury bulb or a dry probe, i.e. the very common type of air temperature measurement. The cumbersome designation is only used to make the difference to the wet bulb temperature recognizable, at which the thermometer bulb is wrapped in a moist tissue during the measurement in order to record the amount of energy withdrawn through evaporation. Source: HJ Ullrich: Kältetechnik. Volume 1, self-published.

^ Klaus Jens: Lectures on building technology , at the Vienna University of Technology

literature

Humid air-h, x diagram. 1st edition. VDE Verlag, Dresden 2012, ISBN 978-3-8007-3386-6 .

Web links

Mollier diagram , see "Printable charts" (PDF) as HD vector graphics
An empty hx diagram for entering the states (PDF file) (7 kB) (ATTENTION! Pressure = 0.95 bar!)
Empty h, x diagrams for entering the states for different pressures / site heights
Excel sheet for the representation and calculation of processes in the Mollier h, x diagram
Mollier h, x diagram with automatic air pressure adjustment and values display. Open the ventilation calculator, click the link in the lower right corner of the spreadsheet

[baehr-1] A ^b Hans Dieter Baehr, Stephan Kabelac: Thermodynamics. Basics and technical applications. 14th edition. Springer, Berlin / Heidelberg 2009, ISBN 978-3-642-00556-5 , p. 296.

[cerbe-2] Günter Cerbe, Hans-Joachim Hoffmann: Introduction to Thermodynamics: from the basics to technical application. 11th edition. Hanser, Munich / Vienna 1996, ISBN 3-446-18849-5 , p. 287.

[3] Hermann Recknagel, Eberhard Sprenger, Ernst-Rudolf Schramek (eds.): Pocket book for heating and air conditioning. 71st edition. Oldenbourg Industrieverlag, Munich 2003, ISBN 3-486-26534-2 , p. 136.

[glueck-4] Bernd Glück: State and material values (water, steam, air) and combustion calculation. 2nd Edition. Verlag für Bauwesen, Berlin 1991, ISBN 3-345-00487-9 .

[5] Siegfried Baumgarth, Berndt Hörner, Josef Reeker: Handbook of air conditioning . Volume 1: Basics. 5th edition. CF Müller, Heidelberg 2008, ISBN 978-3-7880-7820-1 , p. 215.