Adiabatic Saturation Process of Moist Air

[Soumalya]

I am facing some overwhelming doubts while trying to study 'Psychrometrics'.Currently I am bamboozled trying to understand the process of adiabatic saturation of moist air.

Some of the textbooks claim that a true adiabatic saturation process proceeds along the line of constant enthalpy of moist air in a psychrometric chart.But again from an energy analysis applied to an adiabatic saturator as a control volume the exit enthalpy of moist air is greater than the inlet enthalpy of moist air by an amount equal to the product of the difference in specific humidities at inlet and exit conditions and the enthalpy of liquid water supplied at the adiabatic saturation temperature.

Also I am confused when a textbook says " The adiabatic evaporative cooling process involves a decrease in sensible enthalpy, which is exactly offset by an increase in latent enthalpy" which again implies the total enthalpy remains same.

The same textbook says," In a perfectly insulated adiabatic saturator the moist air passing through the saturator will take on additional water vapor (the dew-point temperature and humidity ratio will increase) and the dry-bulb temperature of the air will decrease until the air is fully saturated with water vapor. The latent energy necessary to evaporate the water comes from the sensible energy of the moist air passing through the saturator."

The two quoted statements keeps me wondering if the 'sensible and latent enthalpies' and 'sensible and latent energies' of moist air are the same thing.But this seems contradictory as sensible energy and latent energy in thermodynamics are part of internal energy of a fluid and they cannot be the same as sensible enthalpy and latent enthalpy.

Considering that under steady operating conditions of an adiabatic saturator the 'sensible energy' released from moist air is exactly equal to the latent heat of vaporization of water at the water temperature(adiabatic saturation temperature)this 'sensible energy' would be equal to a change in 'sensible enthalpy' of air only if the partial pressures of dry air and water vapor in moist air were constant during the flow as energy released during a constant pressure process is equal to a change in enthalpy.But the partial pressures of both dry air and water vapor in an adiabatic saturation process varies from inlet to exit of the saturator and 'sensible energy' released from air cannot be equal to its 'sensible enthalpy' change!

Can somebody help me resolve my confusions?

 

[Chestermiller]

I am facing some overwhelming doubts while trying to study 'Psychrometrics'.Currently I am bamboozled trying to understand the process of adiabatic saturation of moist air.

I am confused when a textbook says " The adiabatic evaporative cooling process involves a decrease in sensible enthalpy, which is exactly offset by an increase in latent enthalpy" which again implies the total enthalpy remains same.

The total enthalpy change between the inlet streams and outlet stream of the device is equal to zero, as required by the open system version of the first law of thermodynamics. The decrease in sensible enthalpy that they are talking about is that of the original moist air passing through the device. The increase in latent enthalpy is the amount of heat required to convert the liquid water to water vapor at the adiabatic saturation temperature.

The same textbook says," In a perfectly insulated adiabatic saturator the moist air passing through the saturator will take on additional water vapor (the dew-point temperature and humidity ratio will increase) and the dry-bulb temperature of the air will decrease until the air is fully saturated with water vapor. The latent energy necessary to evaporate the water comes from the sensible energy of the moist air passing through the saturator."

They should have said "... from the sensible energy of the original moist air passing thorugh the saturator."

Some of the textbooks claim that a true adiabatic saturation process proceeds along the line of constant enthalpy of moist air in a psychrometric chart.But again from an energy analysis applied to an adiabatic saturator as a control volume the exit enthalpy of moist air is greater than the inlet enthalpy of moist air by an amount equal to the product of the difference in specific humidities at inlet and exit conditions and the enthalpy of liquid water supplied at the adiabatic saturation temperature.

I don't understand what you are saying here. Maybe you can write some equations.

Chet

 

[Soumalya]

The total enthalpy change between the inlet streams and outlet stream of the device is equal to zero, as required by the open system version of the first law of thermodynamics. The decrease in sensible enthalpy that they are talking about is that of the original moist air passing through the device. The increase in latent enthalpy is the amount of heat required to convert the liquid water to water vapor at the adiabatic saturation temperature."Chet

I don't understand what you are saying here. Maybe you can write some equations.

Please refer to the attachment as is highlighted in the red box the total enthalpy change of moist air is not exactly equal to zero but h₂-h₁=(ω₂-ω₁)h_f2

where, h₁ and h₂ represent the enthalpy of moist air per unit mass of dry air at inlet and exit conditions
h_f2 represents the enthalpy of liquid water at the adiabatic saturation temperature.

The above relation is obtained applying steady flow energy equation to the adiabatic saturator modelling it as a two inlet one exit control volume undergoing a steady operation.

They should have said "... from the sensible energy of the original moist air passing thorugh the saturator."

This is understandable.But what I would precisely like to clarify is whether this decrease in sensible energy of the moist air from inlet to exit of the saturator is equal to the decrease in its sensible enthalpy from inlet to exit?

 

[Chestermiller]

Please refer to the attachment as is highlighted in the red box the total enthalpy change of moist air is not exactly equal to zero but h₂-h₁=(ω₂-ω₁)h_f2

where, h₁ and h₂ represent the enthalpy of moist air per unit mass of dry air at inlet and exit conditions
h_f2 represents the enthalpy of liquid water at the adiabatic saturation temperature.

The above relation is obtained applying steady flow energy equation to the adiabatic saturator modelling it as a two inlet one exit control volume undergoing a steady operation.

Yes, although you didn't provide the attachment, I agree with this equation. So?

This is understandable.But what I would precisely like to clarify is whether this decrease in sensible energy of the moist air from inlet to exit of the saturator is equal to the decrease in its sensible enthalpy from inlet to exit?

This statement says that something is equal to itself. Is that what you meant?

Chet

 

[Soumalya]

Yes, although you didn't provide the attachment, I agree with this equation. So?

Oops! I will try again!

So how is the total enthalpy change equal to zero?

h₂-h₁=(ω₂-ω₁)h_f2>0⇔h₂>h₁

This statement says that something is equal to itself. Is that what you meant?

I assume you mean to say 'sensible energy' change and 'sensible enthalpy' change are identical terms?

 

[Soumalya]

Yes, although you didn't provide the attachment, I agree with this equation. So?

I just figured out the complete meaning of your sentence "The total enthalpy change between the inlet streams and outlet stream of the device is equal to zero, as required by the open system version of the first law of thermodynamics"

I got confused in my thoughts as in some of the books an adiabatic saturation process(they use the term evaporative cooling) is shown to follow a constant wet bulb temperature line which is shown to be nearly coincident with constant enthalpy lines and hence they assume the process follows a constant enthalpy line.This can't be true as the total enthalpy of the moist air differs by an amount (ω₂-ω₁)h_f2 from inlet to exit.

But I am still confused while differentiating between 'sensible enthalpy' and 'sensible energy'.Isn't the latter supposed to be the part of the internal energy of a fluid that is a measure of the average kinetic energy of the molecules?

 

[Chestermiller]

I just figured out the complete meaning of your sentence "The total enthalpy change between the inlet streams and outlet stream of the device is equal to zero, as required by the open system version of the first law of thermodynamics"

I got confused in my thoughts as in some of the books an adiabatic saturation process(they use the term evaporative cooling) is shown to follow a constant wet bulb temperature line which is shown to be nearly coincident with constant enthalpy lines and hence they assume the process follows a constant enthalpy line.This can't be true as the total enthalpy of the moist air differs by an amount (ω₂-ω₁)h_f2 from inlet to exit.

But I am still confused while differentiating between 'sensible enthalpy' and 'sensible energy'.Isn't the latter supposed to be the part of the internal energy of a fluid that is a measure of the average kinetic energy of the molecules?

I feel that they meant enthalpy, but they just weren't precise enough with regard to their choice of terms.

Chet

 

[Soumalya]

I feel that they meant enthalpy, but they just weren't precise enough with regard to their choice of terms.

Statement I: " The adiabatic evaporative cooling process involves a decrease in sensible enthalpy, which is exactly offset by an increase in latent enthalpy".

Statement II: " In a perfectly insulated adiabatic saturator the moist air passing through the saturator will take on additional water vapor (the dew-point temperature and humidity ratio will increase) and the dry-bulb temperature of the air will decrease until the air is fully saturated with water vapor. The latent energy necessary to evaporate the water comes from the sensible energy of the moist air passing through the saturator."

Looking at statement I this seems correct as 'sensible enthalpy' of moist air which is the sum of the sensible enthalpies of dry air and water vapor in it decreases during an adiabatic saturation process.The sensible enthalpy of dry air decreases as dry-bulb temperature of air decreases and sensible enthalpy of water vapor decreases as both dry bulb temperature of air decreases and dew-point temperature of air increases.

If we assume the term (ω₂-ω₁)h_f2≅0 as the amount of water vapor added to dry air during the process is often very small then we may assume, h₂≅h₁.

Thus the total enthalpy of moist air may be assumed to remain constant with only the proportions of sensible and latent enthalpies changing during the process.

Looking at the second statement the amount of energy released from moist air as its dry bulb temperature decreases(which I assume is what the author means by the term 'sensible energy') is utilized to evaporate water from the "pool" at the adiabatic saturation temperature i.e, to supply the latent enthalpy of vaporization to the water molecules at the saturation temperature.

But according to one statement by the author(please refer to the attachment) the amount of energy released(sensible energy) would have been equal to the change in sensible enthalpy of air only if the partial pressures of dry air and water vapor were constant during the process.I say this because the author has written the statement which basically means ,'the amount of energy released or absorbed(heat transferred) during a 'constant pressure' steady flow process involving no shaft work is exactly equal to the difference in enthalpies of the fluid'.The partial pressures of dry air and water vapor keeps on changing during the process.

Is the statement by the author correct?

 

[Chestermiller]

In the statement that you have circled in red, he is saying that, in the steady state version of first law of thermodynamics, the change in enthalpy for the streams entering and exiting the system is equal to the heat transferred from the outside minus the shaft work done. This is a more general statement that just for this specific problem. By the heat transfer, he is not referring to the exchange of sensible heat and latent heat in your device. He is talking about the external heat added to the system. In your device, that is zero, since the system is adiabatic.

Chet

 

[Soumalya]

In the statement that you have circled in red, he is saying that, in the steady state version of first law of thermodynamics, the change in enthalpy for the streams entering and exiting the system is equal to the heat transferred from the outside minus the shaft work done. This is a more general statement that just for this specific problem. By the heat transfer, he is not referring to the exchange of sensible heat and latent heat in your device. He is talking about the external heat added to the system. In your device, that is zero, since the system is adiabatic.

Chet

But why does he mention "a constant pressure steady flow process"?

This should be true regardless the pressure being constant or not, isn't it?

Again I would like to clarified more about this 'sensible energy' the author is talking about.He seems to mean by the term 'sensible energy' as the amount of energy that is released from moist air entering the device as its dry-bulb temperature drops.Suppose the dry-bulb temperature of moist air changes from t_DB1 to t_DB2 how do we write the expression for this 'sensible energy' liberated?

 

[Chestermiller]

But why does he mention "a constant pressure steady flow process"?

This should be true regardless the pressure being constant or not, isn't it?

This isn't clear. Maybe they are allowing for the possibility of non-ideal gas behavior, where the enthalpy is a function of both temperature and pressure. If the pressure changed and the enthalpy changed partially as a result of the pressure change, then the change in enthalpy could not be considered soley sensible heat, because sensible heat refers only to the effect of temperature on enthalpy. Just an educated guess.

Again I would like to clarified more about this 'sensible energy' the author is talking about.He seems to mean by the term 'sensible energy' as the amount of energy that is released from moist air entering the device as its dry-bulb temperature drops.Suppose the dry-bulb temperature of moist air changes from t_DB1 to t_DB2 how do we write the expression for this 'sensible energy' liberated?

$\dot{m}_{in}C_p(T_1-T_2)$

 

[Soumalya]

$\dot{m}_{in}C_p(T_1-T_2)$

This equation should account for the rate of 'sensible enthalpy change' of moist air as its dry-bulb temperature changes from T₁ to T₂ provided the humidity ratio of moist air(consequently the vapor pressure in air) is constant.Physically,this equation should represent the amount of energy released or absorbed by moist air as its dry-bulb temperature changes only if the partial pressures of dry air and water vapor components in moist air remains constant.

Am I correct?

 

[Chestermiller]

This equation should account for the rate of 'sensible enthalpy change' of moist air as its dry-bulb temperature changes from T₁ to T₂ provided the humidity ratio of moist air(consequently the vapor pressure in air) is constant.Physically,this equation should represent the amount of energy released or absorbed by moist air as its dry-bulb temperature changes only if the partial pressures of dry air and water vapor components in moist air remains constant.

Am I correct?

This would represent the change in enthalpy of the original gas stream which entered at the inlet to the evaporator (if we could separate it out from the actual exit stream). Of course, there is additional water vapor in the actual exit stream as a result of the water that evaporated. That's not included in this. This just conceptually represents the sensible enthalpy change of the part of the exit gas stream that constituted the inlet gas stream to the evaporator.

Chet

 

[Soumalya]

This would represent the change in enthalpy of the original gas stream which entered at the inlet to the evaporator (if we could separate it out from the actual exit stream). Of course, there is additional water vapor in the actual exit stream as a result of the water that evaporated. That's not included in this. This just conceptually represents the sensible enthalpy change of the part of the exit gas stream that constituted the inlet gas stream to the evaporator.

Chet

Strongly agreed!

So we could imagine that the original gas stream(moist air) entering the evaporator is undergoing only a change in its dry bulb temperature only from inlet to exit releasing an amount of thermal energy equal to a change in its enthalpy(sensible enthalpy).This would also be the 'sensible energy' released from the moist air.Again this energy is utilized to evaporate water from the "pool" supplying its latent heat of vaporization at the water temperature and is added back to air as a change in its latent enthalpy.This also brings additional enthalpy to moist air in the amount of (ω₂-ω₁)h_fTDB2 such that its total enthalpy increases slightly from inlet to exit.

This could be imagined as a sensible cooling process followed by a pure humidification process (only theoretically possible though) in a psychrometric skeleton chart.

I got it cleared!

Thank You