4.2. Theory
In the equations that follow, the following symbols with subscripts and superscripts are used, as follows.
Symbol | Name | Units |
SMER | Specific moisture extraction rate | kg/(kW∙h) |
MER | Moisture extraction rate | kg/h |
COP | Coefficient of performance | - |
cp | Specific heat at constant pressure | kJ/(kg∙K) |
T | Temperature | K |
RH | Relative humidity | - |
d | Absolute humidity | kg water vapor/kg dry air |
DR | Drying rate | g/(g∙h) |
rs | Evaporative latent heat of water | kJ/kg |
h | Enthalpy | kJ/kg |
m | Mass flow rate | kg/s |
QL | Cooling capacity of heat pump | kW |
QH | Heating capacity of heat pump | kW |
TM | Torque of the compressor | N∙m |
n | Rotation rate of the compressor | r/min |
W | Power consumption | kW |
x | Fresh air entering rate | - |
Subscript | Name | |
dr | drying chamber | |
evap | evaporator | |
cond | condenser | |
ref | refrigerant | |
air | circulated air | |
in | inlet | |
out | outlet | |
comp | compressor | |
HPD | heat pump dryer | |
eh | electric heater | |
A HPD without an electric heater consists of a heat pump system and drying chamber.
In the ideal model, the process of heating hot air in the drying chamber can be regarded as a hot air adiabatic cooling process, as follows.
However, in practice, the hot air enthalpy decreases when hot air flows through the drying chamber, as follows.
For materials, there is the following formula.
where
t1 and
t2 are the drying times (in h), and
Mt and
are the moisture contents (in db) at times
t and
, respectively.
In the drying chamber, the lost moisture of the material migrates to circulated air. The following formula can be obtained according to the law of conservation of mass.
where G is the mass of the absolute drying material.
There are two heat exchange processes with the heat pump system during the hot air cycle, as follows.
The enthalpy value of circulated air is calculated as follows.
For the heat pump system, there is the following formula.
By adjusting the motor frequency, the compressor speed and the compressor power can be controlled.
The heating coefficient of performance (COP) formula is as follows.
4.3. Discussion and Analysis of the Closed Type HPD
The enthalpy–humidity diagram of circulated air is used to analyze and discuss the closed type HPD. As shown in
Figure 8, the air flowed through 1-2(1’-2’) in the drying chamber. It was expected that point 2 was delegated the outlet parameter from the mainly drying chamber, as shown in Formula (4).
is enthalpy loss of circulated air when the hot air passes through the drying chamber. When the BAR was zero, the air flowed through 2-3-4 (2’-3’-4’) in the evaporator. The heat absorbed from condenser through 4-1(4’-1’).
According to the second law of thermodynamics, heat will not flow spontaneously from a cold object to a hot one, so
is indispensable for HPD. According to the first law of thermodynamics, for a closed type HPD, the formula is as follows.
where
is HPD’s heat change value per unit time, in kJ/s.
When HPD is in a steady-state, is greater than . Many researchers use the auxiliary condenser to remove excess heat from the system. As we all know, this will waste a lot of energy. For a closed type HPD, if the inlet of the drying chamber maintains a constant temperature, should be small to save energy. The compressor power can be controlled by adjusting the frequency converter, so it is achievable to decrease .
It is known that if
decrease,
will decrease. As shown in
Figure 5, 1-2-3-4 is the cycle of circulated air when compressor frequency is high and 1’-2’-3’-4’ is the cycle of circulated air when compressor frequency is low. In the experiment, we found that drying rate (DR) will decrease when the air humidity at the inlet of the drying chamber increases. This is consistent with Hao-Yu’s research conclusions [
21]. According to Formula (7),
. This increases the time for drying the material to the specified moisture content and the electric energy consumed by the fan. This, in turn, affects the MER and SMER values of HPD.
As we know from experimental data, when the hot air circulation mode of the HPD is the closed type, the performance of the HPD is greatly affected by the BAR. As shown in
Figure 5, if the system operated at different BARs, air flow from the main drying chamber divided into two paths. One was 2’-3’-5’ which flowed through the evaporator and extracts the moisture from the air. The other path flows through the air bypass duct. The two airs mixed at point 6’. The heat absorbed from the condenser from 6’ to 1’. Thus, the HPD with air bypass duct could decrease the heat absorption as follows.
After HPD enters steady-state conditions, the COP of the heat pump system tends to be stable. Compared with the HPD without an air bypass duct, the heating capacity of the HPD with an air bypass duct is reduced, and the compressor work is reduced as follows.
According to the fluid flow continuity equation, a closed HPD’s circulated air can be calculated using the equation as follows.
Point 6’ is the confluence of
and
, with the following equation.
Circulated air at the outlet of the drying chamber is at a high temperature and high humidity, it needs to flow through the evaporator to reduce its temperature and humidity. As BAR increases, the amount of air flowing through the evaporator decreases, and the heat exchange effect of evaporator will increase. However, the improvement of the heat transfer effect of the evaporator is not unlimited and, as the BAR increases, the flow of air through the evaporator drops to a certain amount, and d5’ can no longer be reduced.
The following formula can be derived based on Formula (10).
According to the above analysis, under the premise of keeping
unchanged or slightly increasing, increasing the value of
can improve the HPD performance index. According to the experimental results, under the conditions of this paper, the best SMER value is obtained when the BAR is equal to 0.4. However, with the rise of BAR,
d6’ will also rise, which will affect the HPD’s DR and MER, as shown in
Figure 9.
4.4. Discussion and Analysis of Open Type and Semi-Open Type HPD
The enthalpy–humidity diagram of circulated air is used to analyze and discuss the open type HPD. As shown in
Figure 10, point a (a’) indicates parameters of the outside ambient air. The heat was absorbed from the condenser through a–b (a’–b’), and the circulated air that flowed through b-c (b’-c’) in the drying chamber, as shown in Formula (7).
is the enthalpy loss of circulated air when the hot air passes through the drying chamber. The air flowed through c-d-e (c’-d’-e’) in the evaporator and was discharged to the outside environment.
As we know from experimental data, when the hot air circulation mode of the HPD is open type, the performance of the HPD is greatly affected by ambient conditions. As shown in
Figure 10, a-b-c-d-e is the cycle of circulated air when the ambient temperature and ambient humidity are low, and a’-b’-c’-d’-e’ is the cycle of circulated air when the ambient temperature and ambient humidity are high. According to the first law of thermodynamics, for the open type HPD, the formula is as follows.
Point a shows the inlet air state parameters of the HPD when the HPD works in a high ambient temperature and high ambient humidity, and point a’ shows the inlet air state parameters of HPD when the HPD works in a low ambient temperature and low ambient humidity. Ta is greater than Ta’, so if the lower temperature air is heated to the same temperature, the HPD needs to consume more power for the compressor and electric heater, and this would affect the HPD’s SMER. According to the experimental results,
, so a high ambient temperature and high ambient humidity reduce the open type HPD’s MER and material’s DR.
The enthalpy–humidity diagram of circulated air is used to analyze and discuss the semi-open type HPD. As shown in
Figure 11, point F(F’) indicates parameters of outside ambient air, circulated air, and outside ambient air mixed at point A (A’). The heat was absorbed from the condenser through A–B (A’–B’), and circulated air flowed through B-C (B’-C’) in the drying chamber, as shown in Formula (7).
is the enthalpy loss of circulated air when the hot air passes through the drying chamber. The air flowed through C-D-E (C’-D’-E’) in the evaporator and then divided two paths. One path mixed with the outside ambient air at point F (F’), and the other path discharged to the outside environment. Point A’s state parameters can be calculated as follows.
As we know from experimental data, when the hot air circulation mode of the HPD is open type, the performance of the HPD is greatly affected by ambient conditions. As shown in
Figure 11, E, F-A-B-C-D-E is the cycle of circulated air when the ambient enthalpy and ambient humidity are lower than circulated air’s enthalpy and humidity at the outlet of the evaporator respectively, and E’, F’-A’-B’-C’-D’-E’ is the cycle of circulated air when the ambient enthalpy and ambient humidity are higher than circulated air’s enthalpy and humidity at the outlet of the evaporator, respectively. According to the first law of thermodynamics, for the semi-open type HPD, the formula is as follows.
Point A shows the inlet air state parameters of the condenser when the HPD works in a high ambient temperature and high ambient humidity, and point A’ shows the inlet air state parameters of the condenser when the HPD works in a low ambient temperature and low ambient humidity. TA is greater than TA’, so if the lower temperature air is heated to the same temperature, the HPD needs to consume more power for the compressor and electric heater, and this would affect the HPD’s SMER. According to the experimental results, , so a high ambient temperature and high ambient humidity reduce the open type HPD’s MER and the material’s DR.
4.5. Discussion on Energy Consumption and Economic Considerations
As shown in
Figure 12, the analysis of the HPD’s electricity consumption through the heat pump, fan, electric heater, and control system accounted for 50, 39, 10, and 1% of total consumption, respectively. The fan consumes much power. This is mainly because the HPD uses a lot of duct valves and a complex duct layout to achieve the experimental requirements, and this affects SMER as shown in Formula (2). Thus, this machine needs more fluid mechanics analysis and optimization.
Global garlic production is approximately 25 million tons annually, and China’s garlic production is about 10 million tons. In order to improve product quality, dehydrated garlic slices have a larger market. At present, drying dehydrated garlic slices in China generally using hot air circulation drying. The energy consumption per unit product of the hot air circulation dryer is 2.8 (kw·h)/kg. In practical production, after reducing the energy consumption of the fan, energy consumption per unit product of HPD can be reduced to 1 (kw∙h)/kg. This is because traditional hot air circulation drying mainly uses electric heaters as heat sources. A large amount of heat energy in the air flowing out of the drying chamber is wasted. This heat can be recovered using the evaporator in the HPD.
The traditional hot air circulation drying model is as follows.
The formula for open type HPD model is Formula (24), that for the semi-open type HPD is Formula (28), and that for the closed type is Formula (14).