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Journal of Engineering Studies and Research – Volume 23 (2017) No. 3
36
THE MODELING OF GRAPHICAL AND ANALYTICAL DRYING
PROCESS PARAMETERS RELATIONS IN CO2 ENVIRONMENT
NATALIA TISLINSCAIA1, MIRCEA BERNIC1
*
, ANDREI LUPASCO1,
VLADIMIR ZAVIALOV2, MIHAIL MELENCIUC1, IANA TISLINSCAIA1
1Technical University of Moldova, Department of Processes Machines and Apparatus,
Stefan cel Mare Bd. 168, Chisinau, MD-2004, Republic of Moldova
2National University of Food Technologies, Volodymyrska str. 68, Kyiv, 01601, Ukraine
Abstract: The engineering calculation of such dryer could be approximately done using Id-
diagrams. There is such a diagram for air based dryers graphical and analytical calculation.
The use of this diagram for CO2 modified environment is impossible; because it shows the
thermo-physical characteristics for air which significantly differs from those of CO2.
We made a tentative of modeling and calculate all the necessary parameters based on which
there was created an Id-diagram for CO2 modified environment.
Obtained graphical relations for temperature, enthalpy, moisture content and partial
pressure will allow one to use them for CO2 modified environment based dryers.
Keywords: CO2, Dryer, drying, Id-diagram, modified environment, relative humidity
1. INTRODUCTION
Drying is one of the main conservation methods for foods. But dehydration process in hot air flow presumes a
tight contact with the oxygen, which for some products, like apples and pears is highly undesirable, as it leads to
product’s oxidation and as a result to quality parameters reduction. One of the methods reducing dehydration
process oxygen contact of vegetal row material is CO2 modified environment use.
2. MATERIALS AND METHODS
The diagram was constructed for barometric pressure of p = 745 mmHg = 100 kPa, which can be adopted as
average annual air pressure. Practically the diagram can be used for any CO2 modified environment dryer
calculation, as within usual deviations of air pressure the values of i and d changes slightly. Id-diagram presents
a graphical interpretation of moist air enthalpy equation. It shows the relation between main moist air
parameters. Each point (dot) on the diagram lights up any state (of the moist air) with quite certain parameters.
To find out any of the moist air characteristics is sufficient to know only two parameters of its state.
On the diagram there are also shown the lines for temperature constant, for relative humidity constant, for partial
water vapors pressure, for humid thermometer temperature constant. The moisture content that shows the
quantity of vapor in an absolute dry CO2 environment, which means characterizes the weight composition of wet
gas, was calculated by the formula:
*
Corresponding author, email: mirceabernic@gmail.com
© 2017 Alma Mater Publishing House
Journal of Engineering Studies and Research – Volume 23 (2017) No. 3
37
par
par
CO
vapor
CO
vapor
PP
P
M
M
G
G
d
22
(1)
where Gvapor – mass of water vapor in moist CO2; GCO2 – mass of dry CO2 in the same volume;, Ppar – partial
pressure; Mvapor – molecular weight of water vapor.
In the same time, the partial pressure will be calculated using the well-known formula:
satpar PP
(2)
Considering the molecular weight of vapor Mvapor = 18 and of CO2 M CO2 = 44 [1], equation (1) will become:
sat
sat
sat
sat
PP
P
PP
P
d
409.0
44
18
(3)
Since the saturated pressure can be approximated as a third degree polynomial, than:
27.5933.2857018.8159.0 23 tttPsat
(4)
Knowing, the foregoing, the final equation for moisture content calculation (1) will gain the form:
27.5933.2857018.8159.0
27.5933.2857018.8159.0
409.0 23
23
tttP
ttt
d
(3)
(Note: this formula is valuable for t > 10°C)
3. RESULTS AND DISCUSSION
In such way, taking in account equation (5), one could begin construct the lines for relative humidity constant ψ
= const. We calculated and presented graphically (Figure 1) the functional relations for ψ = 100, 90, 80, 70, 60,
50, 40, 30, 20, 10 and 5% relative humidity.
Moist CO2, as heat transfer agent, is characterized by the enthalpy I (heat content), equal to the sum of the
enthalpies of dry gas and water vapor.
vaporCO IdtcI 2
(6)
where cCO2 – specific heat capacity of dry CO2, [J/(kg·grd)], t – air temperature, [°C], Ivapor – enthalpy of
overheated steam, [J/kg].
Steam enthalpy can be calculated using the empirical formula:
3
01097.12493 ttcrI vaporvapor
(7)
where r0 = 2493 · 103 – constant coefficient approximately equal to steam’s enthalpy at 0°C, cvapor – specific heat
capacity of steam, [J/(kg·grd)].
Journal of Engineering Studies and Research – Volume 23 (2017) No. 3
38
20
30
40
50
60
70
80
90
100
0,0000 0,2000 0,4000 0,6000 0,8000 1,0000
t, CO2
d, kg/kg
t, CO2
ѱ=1
ѱ=0.9
ѱ=0.8
ѱ=0.7
ѱ=0.6
ѱ=0.5
ѱ=0.4
ѱ=0.3
ѱ=0.2
ѱ=0.1
ѱ=0.05
Fig. 1. The dependency diagram of temperature vs moisture content in CO2 environment, for ψ = 100, 90, 80, 70,
60, 50, 40, 30, 20, 10 and 5% relative humidity.
For gasiform CO2 within ideal conditions one proposed a simplified expression for specific heat capacity
calculation [J/(kg·grd)] [2]:
tcCO 988.0818
2
(8)
This way CO2’s enthalpy can be calculated inserting formulas (5), (7) and (8) in equation (6):
27.5933.2857018.8159.0
27.5933.2857018.8159.0
409.0988.0818 23
23
tttP
ttt
ttI
3
1097.12493 t
(9)
Graphically for different intervals of d (for a more precise picture), the dependency of the enthalpy on the
moisture content, when ψ = const can be presented in the Figure 2.
Fig. 2. Graphical dependency of the enthalpy on the moisture content, at ψ = const, within d = 0 0.01 kg/kg
interval.
Journal of Engineering Studies and Research – Volume 23 (2017) No. 3
39
For a clearer visualization and a more precise enthalpy definition we divided the charts in different moisture
content intervals.
In the same time we calculated and represented the dependency of the enthalpy on the temperature at ψ = const,
in the following graphics (Figure 3), here, likewise the previous example, we used enthalpy intervals chart
division method.
Thereby for the interval I = 0
500 kJ/kg, this dependence will result in Figure 3.
0
100
200
300
400
500
20 30 40 50 60 70 80 90 100
I, kJ/kg
t, Co
I = f(t)
ѱ=1 ѱ=0.9 ѱ=0.8 ѱ=0.7
ѱ=0.6 ѱ=0.5 ѱ=0.4 ѱ=0.3
Fig. 3. Graphical dependency of the enthalpy on the temperature, at ψ = const.
Temperature constants lines t = const, or isotherms, were created using equation (9), calculating I at different
values of d, which at t = const are graphically represented as a straight line (Figure 4). Isotherms angle augments
since vapor’s enthalpy is increasing.
3
1097.12493988.0818 tdttI
(10)
Fig. 4. Isotherms constants lines for different enthalpies.
We modeled as well the approximating functions for some enthalpies.
Journal of Engineering Studies and Research – Volume 23 (2017) No. 3
40
Of particular interest is the moisture content determination mathematical model that includes the two factors of
temperature [°C] and enthalpy [kJ/kg]:
Itd 000245.000025.0002853.0
(11)
CO2 partial pressure line presented in the Id-diagram was constructed based on formula (3) for different moisture
content values thus Ppar measurement scale is presented in mm Hg (Figure 5).
par
par
par
pa
PP
P
PP
P
d
409.0
44
18
409.0
d
Pd
Ppa
(12)
4.71425 dPpa
(13)
Fig. 5. CO2 gas water vapor partial pressure.
4. CONCLUSION
Using the resulting modeling of analytical and graphical functional relations for enthalpy, moisture content and
temperature for different values of relative humidity, one can analyze drying processes as well as using those for
CO2 modified environment dryers calculation.
REFERENCES
[1] Planocskij, A.N., Ramm, V.M., Kagan, S.Z., Precessy i apparaty himicheskoj tehnologii. M. Izdatel’stvo
himija, 1968, p. 315.
[2] Acherkan, N.S., Spravochnik mashinostroitelja. Tom 2. M. Gosudarstvennoe nauchno tehnicheskoe
izdatel’stvo mashinostroitel’noj literatury, 1956, p. 562.