Point of Interest (POI) for Psychrometric Chart

Definition

The POI is found at an (x,y) co-ordinate.

Where it occurs

It is defined by coordinate (t, omega) where t is the dry bulb temperature in Celcius and omega is the specific humidity - kg (moisture) per kg (dry air).

Special features

On our graphs, a small red circle indicates its position.

How to draw it

(1) Locate the mouse at a point on the graph and left-click. The table will then report the corresponding psychrometric variables. These are: dry bulb temperature; wet bulb temperature; dew point; partial pressure of steam; saturation pressure of steam; relative humidity; specific humidity (omega); specific enthalpy of steam, kJ/kg(steam); total specific humidity, kJ/ kg(steam + dry air); total specific volume, m^3(steam + dryair)/kg(dry air).

(2) Choose pair of inputs from the drop down box. Options are: dry bulb temperature and relative humidity (in per cent); dry bulb temperature and specific humidity; dry bulb temperature and wet bulb temperature; specific humidity and total specific enthalpy. Complete the text boxes and press the "SetPOI" button.

Restrictions, limitations and innaccuracy

The simulation is provided for pedagogical purposes only. It should not be employed in formal design calculations, or for summative college assessments. All types of temperature (dry bulb, wet bulb and dew point) are restricted to the range between 0 and 50°C. The specific humidity and steam pressure are not allowed to exceed their saturation values; if necessary they are reset to the saturation value and RH=100%. Steam enthalpy and saturation pressure are computed with IAWPS 97 equations. Air properties are calculated using the Ideal Gas Law, in particular the isobaric specific heat capacity is taken as 1.005 kJ/kg K. An iterative calculation is required and used to establish parameters from the dry and wet bulb temperatures. An iterative calculation is required and used to establish parameters from the specific humidity and total specific enthalpy.

The theory

The Ideal Gas Law is used to calculate most air and steam properties with the exception of the specific enthalpy of steam and the saturation pressure of steam. For these I use the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam and see here for the revised release and in particular their Figure 1 detailing the boundaries between regions that very broadly represent subcooled water (1), superheated steam (2), and saturated steam/ water (4).

Psychrometric variables are calculated as follows:

For specified dry bulb temperature (t) and relative humidity ( $ \phi $ )

Set a warning flag if $ \phi > 1 $ and reset $ \phi =1 $
Using IAWPS calculate saturation pressure from dry bulb temperature $$ p_g = f_{IAWPS} (t+273.15) $$
Calculate the partial pressure of "steam" (water vapour) $$ p_s = \phi p_g $$
Calculate the specific humidity $$ \omega = 0.622 \frac {p_s}{p_{baro}-p_s} $$
Using IAWPS calculate the specific enthalpy of steam. (Avoid algorithm input pressures below the triple-point pressure.) $$ h_s = f_{IAWPS} (max(0.006112 bar, p_s), t+273.15) $$
Using IAWPS calculate the dew point. This is the saturation temperature corresponding to pressure ps \begin{align} t_{dew} &= f_{IAPWS}(p_s) \qquad p_s > 0.006112 bar \\ t_{dew} &= NaN \qquad otherwise \end{align}
Calculate the total specific enthalpy $$ H^* = c_{pa} t + \omega h_s \qquad (c_{pa}=1.005 kJ/kgK) $$
Using Ideal Gas Law, calculate the total specific volume $$ v^* = \frac{t+273.15}{p_{baro}}(R_a + \omega R_s) $$
Calculate the wet bulb temperature using Parish and Putnam (Nasa Technical note TND8401) , employing their slightly different estimate of $p_g$. Start a Golden Search with a guess of the wet bulb temperature, $t_{wet1}$. \begin{align} p_{g1} (t_{wet1}) &= 6.112\times10^{-3} \times exp(17.67 \times t_{wet1}/(t_{wet1}+243.5)) \qquad sat. \; pressure \; at \; t_{wet1} \\ A_1 &= 6.6 \times 10^{-4}+7.57 \times 10^{-7} \times t_{wet1} \qquad psychrometric \; constant \\ p_{s1} &= p_{g1} - A_1 \times p_{baro} (t-t_{wet1}) \qquad estimated \; steam \; pressure \\ p_{s1} &\equiv p_s \implies \; correct \; choice \; of \; t_{wet1} \end{align}

For specified dry bulb temperature (t) and specific humidity ( $ \omega $ )

Calculate the partial pressure of steam $$ p_s = \omega \frac {p_{baro}}{0.622 + \omega} $$
Using IAWPS calculate the saturation pressure. $$ p_g = f_{IAWPS} (t+273.15) $$
Calculate the relative humidity $$ \phi = \frac{p_s}{p_g} $$

The remaining values are calculated with the previous procedure for specified values of dry bulb temperature (t) and relative humidity ( $ \phi $ ).

For specified specific humidity ($\omega$) and total specific enthalpy ( $ H^* $ )

Calculate the partal pressure of steam $$ p_s = \omega \frac {p_{baro}}{0.622 + \omega} $$
Predict the dry bulb temperature, taking the isobaric specific heat capacities of dry air and steam as respectively 1.005 and 1.882 kJ/kg K, $$t_1 = \frac{H^*-2501 \times \omega}{1.005+1.882 \times \omega } $$
Predict $H^*$ corresponding to temperature $t_1$
Correct to $ t_1 $ $$ t \approx t_1 + \frac {H^*-H^*_1}{1.005 + 1.882 \omega} $$

Refer to the previous procedure for specified values of dry bulb temperature (t) and specific humidity ( $ \omega $ ).

For dry bulb temperature ( $t$) and wet bulb temperature( $t_{wet} $ )

Calculate the saturation pressure at the wet bulb temperature. $$ p_{g} (t_{wet}) = 6.112\times10^{-3} \times exp(17.67 \times t_{wet}/(t_{wet}+243.5)) \qquad sat. \; pressure \; at \; t_{wet} \\ $$
Calculate the psychrometric constant and thus the partial pressure of steam. \begin{align} A &= 6.6 \times 10^{-4}+7.57 \times 10^{-7} \times t_{wet} \qquad psychrometric \; constant \\ p_{s} &= p_{g} - A \times p_{baro} (t-t_{wet}) \qquad estimated \; steam \; pressure \\ \end{align}
Calculate the specific humidity $$ \omega = 0.622 \frac {p_s}{p_{baro}-p_s} $$

Refer to the previous procedure for specified values of dry bulb temperature (t) and specific humidity ( $ \omega $ ).

Exercises

Move the POI to different parts of the graph. Note the changes to values in the table. In particular move the POI along horizonal lines and vertical lines. Attempt to place the POI at $t=20^oC$, specific humidity $\omega=0.02$. Note that the chart moves the POI downward and onto the saturation curve, whereupon $\omega= 0.01470$.

Links

IAWPS Revised release .

My notes on psychrometric properties