Pressure Enthalpy chart

Pressure Enthalpy Chart

It is a chart used to explain and analyze refrigeration and air conditioning systems. It consist of pressure on ordinate axis and enthalpy on abscissa. 

Before explaining the pressure enthalpy chart(shown in fig) lets discuss about some common terms that will be used.

Pressure lines: Pressure lines originated from vertical axis (y-axis) and are horizontal lines drawn parallel to abscissa (x-axis). (light blue line in fig)

Enthalpy lines: Enthalpy lines originated from horizontal axis and are vertical lines drawn parallel to vertical axis(Y-axis). (Red color in fig)

Critical point: Critical point separate the saturated liquid and saturated vapor curve.

Critical temperature: Critical temperature is the temperature above which the vapor can never be liquefied at any pressure. to liquefied vapor, temperature must be reduced.

Critical Pressure:  It is the pressure above which the vapor can never be liquefied at any temperature. To liquefied the vapor, Pressure must be reduced.

Saturated liquid curve: It is the left side curve of bubble, where refrigerant is in saturated liquid state at corresponding pressure.

Saturated Vapor curve: It is the right side of the bubble, where refrigerant can be found in complete vapor form at corresponding pressure. 

Sub-cool region(l): The left side of bubble till critical pressure is where refrigerant present at lower temperature than the  saturated temperature is sub-cool region of Pressure enthalpy chart.

Super-heat region (v): The right side of bubble, where refrigerant found in super-heat condition (temperature of refrigerant is more than the saturated vapor temperature) is super-heat region of pressure-Enthalpy chart.

Liquid-vapor mixture region: the space in between the bubble where refrigerant found in both vapor and liquid state.

Temperature lines: These lines are almost vertical lines in subcool and superheat region and horizontal in between bubble (liquid vapor mixture). (green lines in fig)

Specific volume lines: These lines originated from saturated vapor curve and are at an angle to horizontal. (dark blue in fig)

Entropy lines: These lines originated from saturated vapor lines and move upward with an angle from vertical lines. (orange lines in fig)

Fig.

In an ideal refrigeration cycle following processes follow.

Compression: The refrigerant enters the compressor in saturated state where it is compressed isentropically from evaporator pressure (low pressure) to condenser pressure using external work. Every refrigerant have a temperature with a pressure and refrigerant have a specified pressure at ambient temperature. So main work of compressor is to compress the refrigerant above that pressure.  In compressor, the pressure and temperature of refrigerant increase. The entropy of refrigerant at suction and discharge remains same.

W_compressor= m_ref*(h2-h1)            (1)

where: m_ref= mass flow rate of refrigerant
           h1=enthalpy at evaporator outlet
           h2=enthalpy at compressor outlet.

Condensation: The refrigerant enters in condenser in superheated condition. So first the refrigerant desuperheated till condenser temperature. This is done in initial length of condenser and in discharge pipe. Then refrigerant is condensed at constant temperature and pressure (in case of zeotropic blends, pressure and temperature change during phase change). the refrigerant is in saturated liquid state at the end of condenser.

HRR=m_ref(h2-h3)                               (2)

where: HRR= heat rejection rate
            h2= enthalpy at discharge
            h3=enthalpy at condenser outlet

Expansion: The saturated liquid from condenser enters into expansion tube either a capillary tube or expansion valve. The high pressure  liquid refrigerant flow through the expansion device and experience reduction in pressure which ultimately reduce the temperature. At the inlet of capillary, refrigerant is in pure liquid form but at outlet it has some vapor along with it while entering in to evaporator. The amount of vapor at capillary outlet depend upon the difference in pressure of evaporator and condenser. More the difference, more will be vapor. because the refrigerant has to evaporate more to reduce overall temperature by converting latent heat in to sensible heat. (as latent heat is approximate 1000 times the sensible heat). 

First law of thermodynamics holds good for expansion device as below:

m_ref*cp_l*(T3-T4)=m_ref*h_fg*x      (3)

 x=(h4-h1)/(h_fg)                                      (4)

where: m_ref=mass flow rate of refrigerant
            cp_l=specic heat for liquid refrigerant
            h4=enthalpy at evaporator inlet
            h1=enthalpy at compressor inlet
            h_fg=latent heat of vaporization of refrigerant at evaporator temperature.
            x=amount of vapor present at evaporator inlet (dryness fraction)

The left hand side of equation 3, is the sensible cooling which refrigerant undergo while right hand side the latent heat.
         
As principle of expansion devices is evaporative cooling. please refer below link for more:

 http://athermocreation.blogspot.in/2017/10/evaporative-cooling.html.

Vaporisation(cooling):  Vaporization of refrigerant occur in evaporator, where it take the heat from surrounding and produce the refrigeration effect by vaporizing itself in evaporator.

m_ref*(h1-h4)=m*(1-x)*h_fg=NRE        (5)

where: NRE=Net refrigerating effect
            m_ref=mass flow rate of refrigerant
            h1=enthalpy of refrigerant at evaporator outlet
            h4=enthalpy of refrigerant at evaporator inlet
            x=dryness fraction of refrigerant at evaporator inlet.

Coefficient of performance:  It is the ratio of net cooling effect to the compressor work done.

COP= (h1-h4)/(h2-h1)                                (6)

Heat Rejection factor: It is the ratio between the heat rejected in condenser to heat absorbed in evaporator.

HRF=(h2-h3)/(h1-h4)                                  (7)

where HRF= heat rejection factor
           h4=enthalpy at evaporator inlet

Difference between ideal PH chart and Real PH chart:  (!) In reality, refrigerant enter in the compressor in superheated state rather than in saturated vapor state. So that liquid refrigerant do not enter in to the compressor under any condition. It is done either by expansion valve or in case of capillary by capillary suction heat exchanger.

(2) Second difference is that after exiting from the condenser, refrigerant is cooled below its saturated temperature to increase the refrigeration effect by reducing the amount of vapor present at evaporator inlet.

(3) Third difference is that, the compression of refrigerant is n completely not an isentropic process practically. Because as per second law process occur only if there is an increase in universal entropy.

(4) The work done of compressor is more than the ideal work done because there is loss of heat in windings of compressor and also from compressor top by circulating oil to take heat from compressor and exit it to surrounding.

(5) Also the pressure of refrigerant at suction is not same as that of evaporator due to pressure loss in evaporator and suction tube.

(6) In condenser there is also loss of pressure due to fluid flow. Pressure loss should be minimized by proper selection of equipment and pipes of proper diameters and proper movement of refrigerant.