Psychrometry (from the Greek ψυχρομετρία, composed of ψυχρός, "cold", and μετρία, "measurement")[1] is a branch of science dedicated to the study of the thermodynamic properties of humid air and the effect of atmospheric humidity on materials and comfort human.[2][3].
Humid air is made up of a mixture of dry air and water vapor. The calculation of its parameters can be done analytically using the equations that relate them or graphically using diagrams constructed from those equations. In practice, this second method is used more, due to its speed without great loss of accuracy and because it offers a visual result of the transformation. With the appearance of digitalized measurement systems, all these operations are carried out automatically thanks to the calculation capacity of computer devices programmed for this purpose.
Uses
Psychrometric calculation and the study of air transformations are necessary for its conditioning in a multitude of fields: food preservation in chambers, air conditioning of premises, drying and manufacturing processes of medicines, metrology, explosive atmospheres, environments in computer rooms, textile industry, clean rooms, etc.
Psychrometric diagram
A psychrometric diagram or psychrometric chart is a graph made up of families of curves, drawn from the equations of state that relate the parameters that characterize the air-water vapor mixture.
In order to determine all the parameters of humid air, at least three of them need to be known in advance. With this premise, it is difficult to represent the resolution of a problem in a two-dimensional graph. To solve the problem, one of the variables is fixed: atmospheric pressure. This implies that a different diagram is required for each location, depending on its altitude above sea level, or, solving the problem on any diagram and subsequently correcting the results based on the pressure difference between the diagram used and the location in question. Most diagrams are constructed for sea level pressure (101,325 Pa).
Once this problem has been solved, it is a matter of marking a point on some coordinate axes[4] based on two known variables and reading the value of all the other lines that pass through that point, which represent a constant value of each parameter and have been drawn from the corresponding equations of state.
Psychrometry
Introduction
Psychrometry (from the Greek ψυχρομετρία, composed of ψυχρός, "cold", and μετρία, "measurement")[1] is a branch of science dedicated to the study of the thermodynamic properties of humid air and the effect of atmospheric humidity on materials and comfort human.[2][3].
Humid air is made up of a mixture of dry air and water vapor. The calculation of its parameters can be done analytically using the equations that relate them or graphically using diagrams constructed from those equations. In practice, this second method is used more, due to its speed without great loss of accuracy and because it offers a visual result of the transformation. With the appearance of digitalized measurement systems, all these operations are carried out automatically thanks to the calculation capacity of computer devices programmed for this purpose.
Uses
Psychrometric calculation and the study of air transformations are necessary for its conditioning in a multitude of fields: food preservation in chambers, air conditioning of premises, drying and manufacturing processes of medicines, metrology, explosive atmospheres, environments in computer rooms, textile industry, clean rooms, etc.
Psychrometric diagram
A psychrometric diagram or psychrometric chart is a graph made up of families of curves, drawn from the equations of state that relate the parameters that characterize the air-water vapor mixture.
In order to determine all the parameters of humid air, at least three of them need to be known in advance. With this premise, it is difficult to represent the resolution of a problem in a two-dimensional graph. To solve the problem, one of the variables is fixed: atmospheric pressure. This implies that a different diagram is required for each location, depending on its altitude above sea level, or, solving the problem on any diagram and subsequently correcting the results based on the pressure difference between the diagram used and the location in question. Most diagrams are constructed for sea level pressure (101,325 Pa).
There are three types of diagrams according to their construction:
The Mollier diagram: uses as independent variables; the specific humidity on the abscissa axis and the enthalpy on the ordinate, so that the vertical parallel lines are lines of constant specific humidity and the horizontal parallel lines are lines of constant enthalpy, the other variables are represented by families of curves with different inclinations. The axes in this diagram form an angle much less than 90°, usually 40°.
The origin of enthalpies is taken at t=0 °C and w= 0 g water vapor/kg dry air.
The ASHRAE diagram (American Society of Heating, Refrigerating and Air-Conditoning Engineers) is the one proposed by this American entity, a leader in air conditioning research and technology. The variables chosen for the axes are: dry temperature on the abscissa and specific humidity on the ordinate. The vertical axis is located to the right of the plane, unlike Mollier's which is located to the left. The axes form an angle slightly greater than 90°. The origin of enthalpies is the same as that of Mollier.
The Carrier diagram. It is the most used currently. Everything said below refers to this diagram.
It represents the dry temperature in "abscissa" and the specific humidity in "ordinate". The axes form an angle of 92.5°, so the lines of constant humid air enthalpy and constant wet bulb temperature are practically straight lines. These two lines, actually hyperbola arcs, are almost coincident, in the area most commonly used, due to the adiabatic saturation process considered. Due to this circumstance, some diagrams only represent the wet bulb line and some also add a family of enthalpy deviation curves with respect to the value read on the wet temperature line.
Another consideration is the origin of enthalpies. In the Carrier diagram, the enthalpy value 0 is located at the point of dry temperature 0 °C and relative humidity 100%, different from those taken in the Mollier and ASHRAE diagrams, so the absolute enthalpy values for a given point are different in each diagram, but not the relative differences between two points, which are identical in all of them.
The different lines that make up the psychrometric diagram are defined below:
The dry temperature is one of the independent variables and is represented on the X axis. They are lines parallel to the Y axis. Its unit is °C.
Humidity is the other independent variable and is represented on the Y axis. They are lines parallel to the X axis. This axis is on the right of the diagram. Its unit is g or kg of water vapor/kg of dry air.
There is a direct relationship between specific humidity and partial vapor pressure, so sometimes a double scale is added on the Y axis representing partial vapor pressure. The constant vapor partial pressure lines are parallel to the X axis. Their unit is the pascal.
They are curved lines expressed as a percentage. The one corresponding to 100% is the so-called saturation curve, which limits the diagram on its left side.
They are hyperbola arcs, although in their graphic representation they are practically straight lines with a negative slope with respect to the axes. Its unit is °C.
They are hyperbola arcs, although in their graphic representation they are practically straight lines with a negative slope with respect to the axes and practically coinciding with those of constant humid temperature. The units of specific enthalpy are. kJ/kg of dry air. In the Technical system (still widely used) kcal/kg dry air.
As the dew temperature depends only on the partial pressure of the vapor, a third scale can be added to the diagram on the Y axis with the dew temperature, with the constant dew temperature line parallel to the X axis. Said temperature is usually represented on the saturation line, corresponding to a relative humidity of 100%.
They are apparently parallel lines with a certain slope on the axes. Its units are m³/kg dry air.
Psychrometric processes
Sensible and latent heat
An AHU is assumed that introduces kg/s of air into a room. The characteristics of that air are those corresponding to point t on the diagram, that is, temperature, enthalpy, and specific humidity. The air, after passing through the premises, is sucked in again by the AHU under the conditions of point t, that is, its temperature has gone from , absorbing a sensible charge, , its specific humidity has gone from , absorbing a latent charge, , and its enthalpy has gone from absorbing the total charge.
The total heat added to the air as it passes through the room will be:.
To break down the total heat into its sensible and latent components, the expressions[5] for the enthalpy of air and water as a function of temperatures and specific humidities can be taken into account:
Taking into account that the specific heat of dry air is and that the second addend is very small, in practice we take:
V being the volumetric flow rate in m³/s and taking the specific volume of air =0.833 m³/kg.
With these relationships, the air flow necessary to compensate for the local loads can be calculated.
Thermal factor and sensible heating factor
Any straight line on the psychrometric diagram represents a process in which the evolution of the properties of humid air takes place such that the increase in enthalpy is proportional to the change in specific humidity. Each linear process, therefore, has a thermal factor defined by:.
The line that meets this condition is known as maneuver line[6] and turns out to be a parameter that relates the conditions of the air flow before and after the transformation is carried out. The maneuver line is used to characterize a premises, an AHU or any equipment in which a single air stream has defined entry and exit conditions. To determine a complete conditioning process, it is essential to preset some property of the supply air, such as its dry temperature. There are infinite possibilities of eliminating loads from a room, combining the driven flow with the delivery conditions in various ways.
All these possible points representative of the supply air are found on a line that, passing through the point representative of the state of the premises, has the direction that corresponds to the given thermal factor. This line is called maneuver line of the premises:.
Normally, what is known are the conditions existing in the premises, with which its loads are calculated in the form of sensible and latent heat, making it easier to define a relationship with these values. The sensible heat factor[7] (FCS) is the ratio of the sensible heat to the total heat transferred to the air:.
The sensible heat factor is a dimensionless factor. As you can see:
The slope "Slope (mathematics)") of the sensible heat factor line is obtained from the scale on the right side of the diagram, together with the pole P, normally (26.7 °C, 50%), and a parallel must subsequently be drawn through the point that represents the conditions of the premises, which in turn are those at the entrance to the equipment, defining this line as the geometric location of the points where the exit conditions can be found.
There are several possible processes:
References
[1] ↑ Divry's New English-Greek and Greek-English Dictionary. D. C. Divry Inc. New York, 1983.
[2] ↑ Givoni B, A. 1976. Man, Climate and Architecture. Architectural Science Serves. Publishers. Ltd. London.
[3] ↑ Czajkowski, Jorge y Gómez, Analía. 1994. Diseño bioclimático y economía energética edilicia. Fundamentos y métodos. Ed. UNLP, Colección Cátedra. La Plata, Arg. ISBN 978-987-05-4908-6.
[4] ↑ En el caso de los diagramas psicrométricos, no se puede hablar de ejes cartesianos, ya que en ninguno de los casos son ejes ortoganales. Todos ellos forman un ángulo distinto de 90º con el fin de mejorar la representación visual. Las referencias en el texto a abcisas u ordenadas se hacen por comodidad y sobreentendiendo que no dan lugar a confusión.
Once this problem has been solved, it is a matter of marking a point on some coordinate axes[4] based on two known variables and reading the value of all the other lines that pass through that point, which represent a constant value of each parameter and have been drawn from the corresponding equations of state.
There are three types of diagrams according to their construction:
The Mollier diagram: uses as independent variables; the specific humidity on the abscissa axis and the enthalpy on the ordinate, so that the vertical parallel lines are lines of constant specific humidity and the horizontal parallel lines are lines of constant enthalpy, the other variables are represented by families of curves with different inclinations. The axes in this diagram form an angle much less than 90°, usually 40°.
The origin of enthalpies is taken at t=0 °C and w= 0 g water vapor/kg dry air.
The ASHRAE diagram (American Society of Heating, Refrigerating and Air-Conditoning Engineers) is the one proposed by this American entity, a leader in air conditioning research and technology. The variables chosen for the axes are: dry temperature on the abscissa and specific humidity on the ordinate. The vertical axis is located to the right of the plane, unlike Mollier's which is located to the left. The axes form an angle slightly greater than 90°. The origin of enthalpies is the same as that of Mollier.
The Carrier diagram. It is the most used currently. Everything said below refers to this diagram.
It represents the dry temperature in "abscissa" and the specific humidity in "ordinate". The axes form an angle of 92.5°, so the lines of constant humid air enthalpy and constant wet bulb temperature are practically straight lines. These two lines, actually hyperbola arcs, are almost coincident, in the area most commonly used, due to the adiabatic saturation process considered. Due to this circumstance, some diagrams only represent the wet bulb line and some also add a family of enthalpy deviation curves with respect to the value read on the wet temperature line.
Another consideration is the origin of enthalpies. In the Carrier diagram, the enthalpy value 0 is located at the point of dry temperature 0 °C and relative humidity 100%, different from those taken in the Mollier and ASHRAE diagrams, so the absolute enthalpy values for a given point are different in each diagram, but not the relative differences between two points, which are identical in all of them.
The different lines that make up the psychrometric diagram are defined below:
The dry temperature is one of the independent variables and is represented on the X axis. They are lines parallel to the Y axis. Its unit is °C.
Humidity is the other independent variable and is represented on the Y axis. They are lines parallel to the X axis. This axis is on the right of the diagram. Its unit is g or kg of water vapor/kg of dry air.
There is a direct relationship between specific humidity and partial vapor pressure, so sometimes a double scale is added on the Y axis representing partial vapor pressure. The constant vapor partial pressure lines are parallel to the X axis. Their unit is the pascal.
They are curved lines expressed as a percentage. The one corresponding to 100% is the so-called saturation curve, which limits the diagram on its left side.
They are hyperbola arcs, although in their graphic representation they are practically straight lines with a negative slope with respect to the axes. Its unit is °C.
They are hyperbola arcs, although in their graphic representation they are practically straight lines with a negative slope with respect to the axes and practically coinciding with those of constant humid temperature. The units of specific enthalpy are. kJ/kg of dry air. In the Technical system (still widely used) kcal/kg dry air.
As the dew temperature depends only on the partial pressure of the vapor, a third scale can be added to the diagram on the Y axis with the dew temperature, with the constant dew temperature line parallel to the X axis. Said temperature is usually represented on the saturation line, corresponding to a relative humidity of 100%.
They are apparently parallel lines with a certain slope on the axes. Its units are m³/kg dry air.
Psychrometric processes
Sensible and latent heat
An AHU is assumed that introduces kg/s of air into a room. The characteristics of that air are those corresponding to point t on the diagram, that is, temperature, enthalpy, and specific humidity. The air, after passing through the premises, is sucked in again by the AHU under the conditions of point t, that is, its temperature has gone from , absorbing a sensible charge, , its specific humidity has gone from , absorbing a latent charge, , and its enthalpy has gone from absorbing the total charge.
The total heat added to the air as it passes through the room will be:.
To break down the total heat into its sensible and latent components, the expressions[5] for the enthalpy of air and water as a function of temperatures and specific humidities can be taken into account:
Taking into account that the specific heat of dry air is and that the second addend is very small, in practice we take:
V being the volumetric flow rate in m³/s and taking the specific volume of air =0.833 m³/kg.
With these relationships, the air flow necessary to compensate for the local loads can be calculated.
Thermal factor and sensible heating factor
Any straight line on the psychrometric diagram represents a process in which the evolution of the properties of humid air takes place such that the increase in enthalpy is proportional to the change in specific humidity. Each linear process, therefore, has a thermal factor defined by:.
The line that meets this condition is known as maneuver line[6] and turns out to be a parameter that relates the conditions of the air flow before and after the transformation is carried out. The maneuver line is used to characterize a premises, an AHU or any equipment in which a single air stream has defined entry and exit conditions. To determine a complete conditioning process, it is essential to preset some property of the supply air, such as its dry temperature. There are infinite possibilities of eliminating loads from a room, combining the driven flow with the delivery conditions in various ways.
All these possible points representative of the supply air are found on a line that, passing through the point representative of the state of the premises, has the direction that corresponds to the given thermal factor. This line is called maneuver line of the premises:.
Normally, what is known are the conditions existing in the premises, with which its loads are calculated in the form of sensible and latent heat, making it easier to define a relationship with these values. The sensible heat factor[7] (FCS) is the ratio of the sensible heat to the total heat transferred to the air:.
The sensible heat factor is a dimensionless factor. As you can see:
The slope "Slope (mathematics)") of the sensible heat factor line is obtained from the scale on the right side of the diagram, together with the pole P, normally (26.7 °C, 50%), and a parallel must subsequently be drawn through the point that represents the conditions of the premises, which in turn are those at the entrance to the equipment, defining this line as the geometric location of the points where the exit conditions can be found.
There are several possible processes:
References
[1] ↑ Divry's New English-Greek and Greek-English Dictionary. D. C. Divry Inc. New York, 1983.
[2] ↑ Givoni B, A. 1976. Man, Climate and Architecture. Architectural Science Serves. Publishers. Ltd. London.
[3] ↑ Czajkowski, Jorge y Gómez, Analía. 1994. Diseño bioclimático y economía energética edilicia. Fundamentos y métodos. Ed. UNLP, Colección Cátedra. La Plata, Arg. ISBN 978-987-05-4908-6.
[4] ↑ En el caso de los diagramas psicrométricos, no se puede hablar de ejes cartesianos, ya que en ninguno de los casos son ejes ortoganales. Todos ellos forman un ángulo distinto de 90º con el fin de mejorar la representación visual. Las referencias en el texto a abcisas u ordenadas se hacen por comodidad y sobreentendiendo que no dan lugar a confusión.