In the present study of the evaporation heat transfer of R-134a in a narrow annular duct, the gap between the inner and outer circular pipes is fixed at 1.0, 2.0 and 5.0 mm with the refrigerant saturated temperature set at 5℃, 10℃ and 15℃. The refrigerant mass flux ranges from 100 kg/m2s to 700 kg/m2s, the imposed heat flux is chosen at 5, 10 and 15KW/
m2, and the mean refrigerant vapor quality is varied from 0.05 to 0.95. A data reduction analysis is needed to calculate the evaporation heat transfer coefficient from the raw data measured in the horizontal annular duct. The data reduction process is described in the following.
3.1 Single-Phase Heat Transfer
The imposed heat flux to the refrigerant flow in the annular duct is calculated on the basis of the total power input Qt and the total outside heat transfer area of the inner pipe of the annular duct As. The total power input is computed from the product of the measured voltage drop across the cartridge heater and the electric current passing through it. Hence the net power input to the test section Qn is equal to (Qt – Qloss). The imposed heat flux at the outside surface of the inner pipe is then evaluated from the relation
q = Q /A (3.1) n s
where V and I respectively represent the measured voltage drop and current. The total heat loss from the test section Qloss is evaluated from the correlation for natural convection
( )
To reduce the heat loss from the test section, we cover the test section with a 2.5-cm thick polyethylene insulation layer. We measured the mean temperature of the outside surface of the insulation layer Tins and ambient temperature Ta. Hence Qloss =hNi
(
T - T Ains a)
i os ,where Aos is the outside surface area of the insulation layer and N a a
os
h =Nu ik D . Note that
Dos is the outer diameter of the cylindrical insulation layer. The results from this heat loss test indicate that the heat loss from the test section is generally less than 1% of the total power input no matter when single-phase flow or two-phase evaporating flow is in the duct.
The average single-phase convection heat transfer coefficient for the refrigerant flow over the entire heated surface in the annular duct is defined as
n where Qn is the net power input to the liquid refrigerant in the annular duct and Tr,ave is the average of the measured inlet and outlet temperatures of the refrigerant flow through the test
section, which is taken as the average bulk liquid refrigerant temperature. Note that Tw denotes the average outside surface temperature of the inner pipe measured at the selected thermocouple locations. The outside surface temperature at each thermocouple location is deduced from the measured inside surface temperature of the inner pipe by subtracting the radial temperature drop due to the radial heat conduction in the pipe wall. Thus we have
o i
w w,i n
w
ln(D /D ) T =T -Q
2πk L (3.6)
3.2 Two-Phase Heat Transfer
In the two-phase test, we also estimate the heat loss from the test section by measuring the outside surface temperatures of the polyethylene insulation layer and the ambient temperature. The estimated heat loss from the test section by the procedures outlined above in section 3.1 is less than 0.5% for all cases and hence can be neglected.
The vapor quality of R-134a entering the test section inlet is evaluated from the energy balance for the preheater. Based on the temperature drop on the water side, the heat transfer in the preheater is calculated from the relation,
w,p w,p p,w w,p,i w,p,o
Q =W c (T -T ) (3.7)
While the heat transfer to the refrigerant in the preheater is the summation of the sensible heat transfer (for the temperature rise of the refrigerant to the saturated value) and latent heat transfer (for the evaporation of the refrigerant),
w,p sens lat
Q =Q +Q (3.8)
here
sens r p,r r,sat r,p,i lat r fg p,o
Q =W c (T -T )
Q =W i x (3.9)
The above equations can be combined to evaluate the refrigerant quality at the exit of the preheater that is considered to be the same as the vapor quality of the refrigerant entering the test section. Specifically,
( )
The total change of the refrigerant vapor quality in the test section is then deduced from the net heat transfer rate from the electric heater to the refrigerant in the test section, thus
n r fg
Q x W i
Δ = (3.11)
The mean vapor quality for the evaporation of R-134a in the test section at the middle axial location z=80 mm is
in 2
m
x =x +Δx (3.12)
Finally, the circumferential by average heat transfer coefficient for the evaporation of R-134a at the middle axial location in the test section is determined from the definition
(
n s)
Here Twall is the circumferential average outside surface temperature of the inner pipe at the middle axial location.
3.3 Uncertainty Analysis
Uncertainties of the heat transfer coefficients are estimated according to the procedures proposed by Kline and McClintock for the propagation of errors in physical measurement [29]. The results from this uncertainty analysis are summarized in Table 3.1.
Table 3.1 Summary of the uncertainty analysis
Parameter Uncertainty Annular duct geometry
Length, width and thickness (%) ±1.0%
Gap size (%) ±5.0%
Area (%) ±2.0%
Parameter measurement
Temperature, T (℃) ±0.2
Temperature difference, △T (℃) ±0.28
System pressure, P (MPa) ±0.002
Mass flux of refrigerant, G (%) ±2 Single-phase heat transfer
Imposed heat flux, q (%) ±4.5
Heat transfer coefficient, hr,l (%) ±12.5 Evaporation heat transfer
Imposed heat flux, q (%) ±4.5
Mean vapor quality, xm (%) ±9.5 Heat transfer coefficient, hr (%) ±14
CHAPTER 4