Chapter SM 7 : Evaporators and Condensers
SM 7. 1 Introduction
Evaporators and condensers are sensible heat exchangers in which one of the fluids, the refrigerant, changes phase. They are constructed similar to the sensible heat exchangers described in Chapter 13. An evaporator in a chilled water system would typically be a shell and tube exchanger with refrigerant contained in the shell and outside the tubes. Water would flow through the tubes and be cooled by the evaporation of the refrigerant. The liquid refrigerant from the condenser passes through the expansion valve and then enters the evaporator as a low temperature mixture of vapor and liquid. The vapor is usually slightly superheated before it leaves the evaporator and enters the compressor. Most of the heat transfer occurs during the change of phase.
Direct expansion coils (DX) are used in systems in which air is cooled and dehumidified. The refrigerant flows inside the tubes of the coil and evaporates while air flows over the surfaces. As this refrigerant stream passes through the coil, the liquid portion evaporates and the vapor fraction progressively increases so that the leaving stream is entirely vapor. In most DX coil applications the air is dehumidified. Direct expansion coils are common in appliances such as refrigerators, air-conditioners, and the air handlers found in typical HVAC distribution systems.
As with evaporators, there are two basic types of condensers. In water-cooled condensers, constructed as shell and tube exchangers, relatively cool water flows through the tubes. Refrigerant condenses on the outside of the tubes and then drains from the bottom of the exchanger. Air-cooled condensers are similar to cooling coils, with the refrigerant condensing inside tubes and transferring heat to the relatively cool air stream flowing over the outside of the tubes. In evaporative condensers liquid water is sprayed over the outside of the tubes and then evaporates into the air stream flowing over the tubes. The performance of these heat and mass exchangers is covered in Chapter SM 4.
The refrigerant typically enters a condenser from the compressor as superheated vapor. The vapor is cooled to saturation, condensed and then subcooled slightly. In the desuperheating section both the refrigerant and cooling fluid change in temperature, while during the phase change the temperature of the refrigerant is constant as it condenses. Although the majority of the heat transfer is from the refrigerant during the phase section, a significant portion does occur during de-superheating.
SM 7. 2 Thermal Performance of Shell-and-Tube Evaporators
Flooded evaporators are common in chilled water circuits where heat is transferred from water flowing through tubes to a refrigerant evaporating on the outside of the tubes. A flooded shell and tube evaporator is shown in Figure 7.1. The tubes are relatively small diameter (1 inch or 2 cm) and closely spaced, and only a few tubes are shown in Figure 7.1.
Figure 7.1 Shell and tube flooded evaporator
The tubes are submerged in a pool of liquid refrigerant with a pump used to circulate the liquid refrigerant so that it continually flows over the heat transfer surfaces. In some applications the two-phase mixture leaving the expansion valve is separated into liquid and vapor components with only the liquid is sent to the evaporator. This reduces the flow through the evaporator. As the liquid evaporates the vapor leaves, usually with a small amount of superheat, and is sent to the compressor. The chilled water is then circulated to coils where it cools and dehumidifies and air stream.
Direct expansion evaporators are also used to cool liquids. The exchanger is a shell and tube type similar to that shown in Figure 7.1. However, in a direct expansion liquid evaporator the refrigerant is inside the tubes and evaporates as it flows.
Although the detailed fluid flow and heat transfer characteristics of these two types of evaporators are different, the same basic ideas apply. In the section where the refrigerant evaporates the refrigerant temperature is constant and the capacity rate ratio is zero. In the superheating section the refrigerant temperature changes and the capacitance rate ratio is finite. Different effectiveness relations would apply to these two sections. However, since most of the heat is transferred during the evaporation process, the approximation that C* is zero for the entire evaporator is usually sufficiently for the design or evaluation of an evaporator.
Example 7.1 illustrates the calculation of the performance of an evaporator and shows the degree of error in assuming that the capacitance rate ratio is zero throughout. Although this example is for a cooling a liquid the same ideas would apply for sensible cooling of an air or another gas stream.
"Example 7.1 An evaporator is used to chill a liquid water flow rate of 150 gpm that enters at 45 F. The refrigerant is a flow of 7550 lbm/hr of R-22 that enters at a quality of 0.1 and a temperature of 30 F. The evaporator has an overall heat transfer conductance of 60,000 Btu/hr-F. Determine heat transfer rate, the refrigerant outlet state, and the water outlet temperature."
"The performance will first be calculated assuming that the evaporator is a single heat exchanger with a capacitance rate ratio of zero. Then, the evaporator will be evaluated as two exchangers: an exchanger in which the refrigerant evaporates and one in which the refrigerant vapor is superheated. The relations in Section 7.3 will be used to find the thermal performance."
"Problem specifications"
T_w_i = 45 "F" "Temperature"
V_dot_w = 150 "gpm" "Volume flow rate"
T_r = 30 "F" "Temperature"
x_i = 0.1 "Quality"
m_dot_r = 7750 "lbm/hr" "Mass flow rate"
UA = 60000 "Btu/hr-F" "Overall UA"
"Refrigerant properties"
h_r_i = enthalpy(R22,T=T_r,x=x_i) "Btu/lbm" "Enthalpy"
p_r = pressure(R22,T=T_r,x=1) "psia" "Pressure"
"Water properties"
rho_f = density(water,T=T_w_i, x = 0) "lbm/ft3" "Density"
cp_f = specheat(water, T =T_w_i, x = 0) "Btu/lbm-F" "Specific heat"
m_dot_w = rho_f*V_dot_w*convert(gpm,ft^3/hr) "lbm/hr" "Mass flow rate"
C_w = m_dot_w*cp_f "Btu/hr-F" "Capacitance rate"
"The evaporator is analyzed as a single exchanger with C_star = 0 for entire exchanger. The effectiveness is taken from Table 13.1."
Ntu_0 =UA/C_w "Ntu"
epsilon_0 = 1-exp(-Ntu_0) "Effectiveness"
epsilon_0 = Q_0/Q_max_0 "Effectiveness"
Q_max_0 = C_w*(T_w_i - T_r) "Btu/hr" "Maximum heat flow"
"Energy balances are used to determine the outlet state of the water T_w_0_o and refrigerant h_r_0_o "
Q_0= C_w*(T_w_i - T_w_0_o) "Btu/hr" "Heat flow"
Q_0 = m_dot_r*(h_r_0_o - h_r_i) "Btu/hr" "Heat flow"
h_r_0_o = enthalpy(R22,T=T_r_0_o,p=p_r) "Btu/lbm" "Enthalpy"
Results
Treating the evaporator as a single heat exchanger results in a heat transfer rate of 620,100 Btu/hr. The refrigerant outlet temperature is 35.1 F, corresponding to 5.1F of superheat. The outlet water temperature is 36.8 F. These results will serve as a reference for the performance calculated assuming that the evaporator has two sections.
"The second performance calculations will treat the exchanger as two evaporators. The first section will be where the refrigerant evaporates and the second section will be where it is superheated."
"For the evaporating section the value of C_star is zero and the effectiveness is from Table 13.1. The overall conductance for this section will be expressed as UA_e = F*UA where F is the fraction of the UA in the evaporation section. At the end of this section the refrigerant is saturated vapor at 30 F and the enthalpy h_r_x at the end of this section is known (174.0 Btu/lbm).
The temperature of the water at the end of the evaporation section, T_w_x, is not known because the water has been cooled in the superheating section. As a result the performance of this section cannot be obtained directly. The solution for this section is coupled to that for the superheating section and obtained through iteration.
For the evaporation section:"
h_r_x = enthalpy(R22,T=T_r,x=1) "Btu/lbm" "Enthalpy"
Ntu_e = F*UA/C_w "Ntu"
epsilon_e = 1-exp(-Ntu_e) "Effectiveness"
epsilon_e = Q_e/Q_max_e "Effectiveness"
Q_max_e = C_w*(T_w_x - T_r) "Btu/hr" "Maximum heat flow"
Q_e = m_dot_r*(h_r_x - h_r_i) "Btu/hr" "Heat flow"
Q_e = C_w*(T_w_x - T_w_o) "Btu/hr" "Heat flow"
"For the superheating section the value of C_star is finite. The geometry is assumed to be counterflow and the effectiveness is from Table 13.1. The overall conductance of this exchanger is the remaining fraction of the entire exchanger, or UA_s = (1-F)*UA.
The unknown water temperature T_w_x couples the solution for the superheater to that for the evaporation section.
The capacitance rate of the refrigerant vapor is determined using the specific heat of the vapor and the mass flow rate, and the minimum capacitance is smaller of the water and refrigerant capacitance rates.
For the superheating section”
C_r_s = m_dot_r*cp_r "Btu/hr-F" "Capacitance rate"
cp_r = specheat(R22,T=T_r,x=1) "Btu/lbm-F" "Specific heat"
C_min_s = min(C_w,C_r_s) "Btu/hr-F" "Capacitance rate"
C_max_s = max(C_w,C_r_s) "Btu/hr-F" "Capacitance rate"
C_star_s =C_min_s/C_max_s "Capacitance rate ratio"
Ntu_s = (1-F)*UA/C_min_s "Ntu"
epsilon_s= (1-exp(-Ntu_s*(1-C_star_s)))/(1-C_star_s*exp(-Ntu_s*(1-C_star_s))) "Effectiveness"
epsilon_s = Q_s/Q_max_s "Effectiveness"
Q_max_s = C_min_s*(T_w_i - T_r) "Btu/hr" "Maximum heat flow"
Q_s = m_dot_r*(h_r_o_s - h_r_x) "Btu/hr" "Heat flow"
h_r_o_s = enthalpy(R22,T=T_r_o_s,p=p_r) "Btu/lbm" "Enthalpy"
Q_s = C_w*(T_w_i - T_w_x) "Btu/hr" "Heat flow"
"The total heat transfer equals the sum of the evaporation and superheat sections."
Q_ss = Q_e + Q_s "Btu/hr" "Heat flow"
Results and Discussion
For the superheating section the refrigerant has a capacitance rate of 1370 Btu/hr-F and it is the minimum capacitance rate. The capacitance rate ratio is 0.0182. Solving the set of equations simultaneously yields a fraction of the evaporating section of 0.9925. This shows that superheater section comprises only 0.75 percent of the surface area. The refrigerant and water outlet temperatures are 34.7 F and 36.8 F respectively. The refrigerant is superheated 4.7 F, which is only slightly less than the 5.1 F computed using the capacitance rate ratio of zero throughout.
Treating the evaporator as having the two sections yields a heat transfer rate of 619,700 Btu/hr, which is 0.4 % lower than that obtained by treating the evaporator as a single exchanger. For situations in which the amount of superheat is low (less than about 20 F or 10 C), the treatment of an evaporator as an exchanger in which one side has a phase change only is valid.
SM 7. 3 Thermal Performance of Direct Expansion Cooling Coils
In a direct expansion cooling coil, the refrigerant enters from the expansion valve as a low quality mixture of vapor and liquid. The liquid fraction evaporates during its passage through the coil and leaves at a slightly superheated condition. The temperature of the refrigerant is constant during the phase change process and, as discussed in Section 13.2, the capacitance of the refrigerant is infinite. Because the amount of superheat is small (5 – 10 F or 2- 5 C), a DX coil can be analyzed as an exchanger with a capacity rate ratio of zero.
On the air side of a DX coil there is usually both cooling and dehumidification. The design or analysis of a DX coil then brings in performance relations both for sensible heat exchanger and for heat and mass transfer. As discussed in Section 15.3, the performance of a cooling coil can be determined assuming two different conditions. The first is that the coil is completely wet and the second is that the coil is completely dry. The maximum of the heat transfer rates from these to determinations is quite close to the actual heat transfer rate for a coil that is partially wet. The analysis for the heat transfer only section can be treated using the sensible heat exchanger relations of Section 13.3 and illustrated for a shell and tube evaporator in Section 13.2. The analogy method for a chilled water coil was discussed in Section 15.4 and can be extended to a DX coil.
In a DX coil the refrigerant has an infinite sensible capacity rate, and by extension an infinite mass capacity rate. The parameter m* corresponds to the sensible capacity rate ratio C*, and is then zero for a DX coil. The Number of Transfer Units for mass transfer, Ntu*, is determined as presented in Section 13.6:
(7.1)
where U* is the overall mass transfer conductance based on the air-side area, Aa is the area on the air side, and is the air mass flow rate. The overall mass transfer conductance is given as
(7.2)
where cp is the specific heat of air, is the overall air-side surface efficiency for mass transfer, hc is the air-side convection coefficient, cs is the effective specific heat, Ur is the conductance on the refrigerant side, and Ar is the refrigerant-side area. The resistance of the surface separating the air and refrigerant is assumed negligible. The effective specific heat is estimated using a finite difference approximation around the temperature of refrigerant:
(7.3)
The effectiveness for the DX coil is then computed using the analogous relation for a sensible heat exchanger with a capacity rate ratio of zero
(7.4)
With the effectiveness, the heat transfer can be determined using the relation
(7.5)
where ha,in is the enthalpy of saturated air at the inlet conditions and hr, sat is the enthalpy of saturated air at the refrigerant temperature. The air outlet humidity ratio is then determined from an energy balance on the air flow
(7.6)
As with the chilled water coil, the analogy method yields only the outlet air enthalpy. The outlet temperature and humidity are determined using the relations presented in Section SM 2.2. Example 7.2 shows the determination of performance for DX coil.
"Example 7.2 Determine the performance of a DX coil. The air enters the coil at a dry bulb temperature of 75 F and a wet bulb temperature of 60 F with a volume flow rate of 5000 cfm. The refrigerant is R-22 at a temperature of 40 F that enters with a quality of 0.1 and leaves with 5 F superheat. On the airside the heat transfer conductance Ua is 50 Btu/hr-ft2 and the surface area is 360 ft2. On the waterside the heat transfer conductance Uw is 1000 Btu/hr-ft2 and the area is 18 ft2"
"Problem specifications
Air side”
p_atm = 14.7 "psia" "Atmospheric pressure"
T_a_i = 75 "F" "Dry-bulb temperature"
Twb_a_i = 60 "F" "Wet-bulb temperature"
V_dot_a = 5000 "cfm" "Volume flow rate"
“Refrigerant side”
T_r = 40 "F" "Refrigerant temperature"
DT_sh = 5 "F" "Temp. difference"
"Heat Exchanger Parameters"
U_a = 50 "Btu/hr-ft2-F" "Conductance"
A_a = 360 "ft2" "Area"
U_r = 1000"Btu/hr-ft2-F" "Conductance"
A_r = 18 "ft2" "Area"
"Air properties
Determine the properties of air, the mass flow rate, and the sensible capacitance rate for the air flow through the coil."
w_a_i = HumRat(AirH2O,T=T_a_i, p=p_atm,B=Twb_a_i ) "lbmw/lbma" "Humidity ratio"