Exercise 5.3 - Spray Dryer I (2020)
Exercise 5.3 - Spray Dryer I (2020)
Exercise 5.3 - Spray Dryer I (2020)
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Spray dryer I
The graph on the right illustrates a spray drying
system which is used for the drying of a product. The
liquid feed is atomised in small droplets, which then
are allowed to fall through hot air. The moisture
evaporates, and when moisture has evaporated, the
dissolved components become solid, and form powder
particles. The conditions of all flows can be found by
clicking on the following link: Conditions spray dryer I
Question: Make a Grassmann diagram of this system. As the solids in the product do not
change, you can leave out the standard exergy of the solids. As you need to know the exergy of
all flows to make a Grassmann diagram, the following sub questions can be defined:
a) What is the total exergy (W) of the cold and hot air? Start with question a
b) What is the total exergy (W) of the natural gas? Start with question b
c) What is the total exergy (W) of the feed and product? Start with question c
d) What is the wma (wma=kg moisture/kg dry air of moist air)? Start with question d
e) What is the total exergy of the moist air? Start with question e
Laboratory of
f) Make the Grassmann diagram. Which
Food Process operator is the least efficient?
Engineering Start with question f
Conditions spray dryer I
In this exercise the given standard conditions are: P0=1 atm, T0=293K, w0=0.008 kg/kg. However, in our Mathcad-
calculations we worked with T0 of 293.15. We are not fully consistent and accurate as for the actual temperatures
of air and product we calculated with +273 instead of +273.15
Be aware that the standard pressure is 1 atm, whereas the actual pressures in this exercise are given in bar (and
calculations accordingly). However, the differences you might find will be minimal.
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Question a: What is the total exergy (W) of the cold air General data:
(ca) and hot air (ha)? All data required to calculate the cpp 1.83 kJ/(kgK)
exergy are provided on this slide. cpw 4.18 kJ/(kgK)
cpa 1.01 kJ/(kgK)
cps 1.84 kJ/(kgK)
Cold air Hot air
ϕ (kg dry air/h) 122212 122212 26.142 MJ/kg
Bca 0W
A)
Bha 4.73 W
Bca 7.91 W
B)
Bha 1.06 W
Bca 2.85 W
C)
Bha 3.82 W Cold air Hot air
ϕ (kg dry air/h) 122212 122212
Bca 5.80 W
D) T (°C) 58.2 175
Bha 3.87 W P (bar) 1 1
Laboratory of w (kg/kg) 0.008 0.008
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Question a: What is the total exergy (W) of the cold air General data:
(ca) and hot air (ha)? All data required to calculate the cpp 1.83 kJ/(kgK)
exergy are provided on this slide. cpw 4.18 kJ/(kgK)
cpa 1.01 kJ/(kgK)
cps 1.84 kJ/(kgK)
Cold air Hot air
ϕ (kg dry air/h) 122212 122212 26.142 MJ/kg
C) Bgas 6.43 W
D) Bgas 5.62 W
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Question b: What is the total exergy (W) of the natural General data:
gas? All data required to calculate the exergy are cpp 1.83 kJ/(kgK)
provided on this slide. cpw 4.18 kJ/(kgK)
cpa 1.01 kJ/(kgK)
cps 1.84 kJ/(kgK)
Nat. gas
ϕ (kg/h) 412.44 26.142 MJ/kg
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Question b: What is the total exergy (W) of the natural General data:
gas? All data required to calculate the exergy are cpp 1.83 kJ/(kgK)
provided on this slide. cpw 4.18 kJ/(kgK)
cpa 1.01 kJ/(kgK)
cps 1.84 kJ/(kgK)
Nat. gas
ϕ (kg/h) 412.44 26.142 MJ/kg
Bgas 6.43 W This is not the correct answer. You have forgotten
C)
to include the gas flow rate. The net calorific value
is the total amount of energy that is released by
combustion of a fuel or gas (at environmental T
D) Bgas 5.62 W and P). Thus, for natural gas, 54 MJ of energy is
produced per kg of natural gas. Now you can also
Laboratory of calculate the exergy of the natural gas flow.
Food Process Engineering
Question c: What is the total exergy (W) of the feed and General data:
product flows? All data required to calculate the exergy cpp 1.83 kJ/(kgK)
are provided on this slide. cpw 4.18 kJ/(kgK)
cpa 1.01 kJ/(kgK)
Bfeed 1.42 W
A)
Bproduct 1.86 W Feed Product
ϕ (kg/h) 8534 4501
Bfeed 9.59 W T (°C) 80 90
B)
Bproduct 1.11 W P (bar) 200 1
%solids 52 97.5
Bfeed 8.50 W
C)
Bproduct 1.70 W
Bfeed 1.15 W
D)
Bproduct 1.52 W
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Question c: What is the total exergy (W) of the feed and General data:
product flows? All data required to calculate the exergy cpp 1.83 kJ/(kgK)
are provided on this slide. cpw 4.18 kJ/(kgK)
cpa 1.01 kJ/(kgK)
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Question d: What is the moisture content wma of moist General data:
air (wma=kg moisture/kg dry air)? All data required to cpp 1.83 kJ/(kgK)
calculate the wma are provided on this slide. cpw 4.18 kJ/(kgK)
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Question d: What is the moisture content wma of moist General data:
air (wma=kg moisture/kg dry air)? All data required to cpp 1.83 kJ/(kgK)
calculate the wma are provided on this slide. cpw 4.18 kJ/(kgK)
C) Bma -1.9 W
D) Bma 3.4 W
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Question e: What is the total exergy of the moist air? All General data:
data required to calculate the exergy are provided on this cpw 4.18 kJ/(kgK)
slide. cpa 1.01 kJ/(kgK)
cps 1.84 kJ/(kgK)
26.142 MJ/kg
Moist air
49.94 kJ/kg
ϕ (kg dry air/h) 122212
527.2 kJ/kg
T (°C) 90
Mw 0.01802 kg/mol
P (bar) 1
w (kg/kg) 0.041 Ma 0.02897 kg/mol
1000 kg/m3
T0 293.15 K
molecular
Food Process Engineering weights of air and vapour are comparable.
Question e: What is the total exergy of the moist air? All General data:
data required to calculate the exergy are provided on this cpw 4.18 kJ/(kgK)
slide. cpa 1.01 kJ/(kgK)
cps 1.84 kJ/(kgK)
26.142 MJ/kg
Moist air
49.94 kJ/kg
ϕ (kg dry air/h) 122212
527.2 kJ/kg
T (°C) 90
Mw 0.01802 kg/mol
P (bar) 1
w (kg/kg) 0.041 Ma 0.02897 kg/mol
1000 kg/m3
T0 293.15 K
B) Bma 2.7 W
= J/kg dry air
C) Bma -1.9 W
D) Bma 3.4 W
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As you finished all questions, you know the exergy of all flows and are now able
to make the Grassmann diagram. You can open ESankey to make the Grassmann
diagram.
After you finished the Grassmann diagram, you can check it by clicking on the
link: I finished the Grassmann diagram. Determine which operator is least
efficient.
You can see that the burner is the least efficient part of the spray dryer, as a lot of
exergy is destroyed in the burner. This exergy is irreversibly lost to the environment!
If the moist air out of the spray dryer is not reused and is discarded into the
environment, it will also be lost.
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Check full answer question a
Check full answer question b
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Full answer question a:
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Full answer question e:
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