MECH 390

Assignment #3 (Refrigeration)
Assignment date: Tuesday Jan 30, 2007
Due date: Tuesday Feb. 06, 2007

Problem 1:
Figure below shows a steam jet refrigeration system that produces chilled
water in a flash chamber. The chamber is maintained at a vacuum pressure by
the steam ejector, which removes the vapor generated by entraining it in the
low-pressure jet and discharging into the condenser. The vacuum pump
removes air and other non-condensable gases from the condenser shell. For
the conditions shown on the figure, determine the make-up water and cooling
water flow rates in kg/h.

Vacuum pump
Ejector nozzle
Sat. vapor at Steam jet
200 kPa
Sat. vapor

1 7
Cooling water in
Make-up water 6 @ 15 C
@ 15 C
5
Flash chamber 25 C
P = 4 kPa
water Condenser
4 5C 8
Cooling load
142 tons Condensate
2 return to drain
QL

25,000 kg/h
Pump
3

Note: 1 ton (of refrigeration) = 211 kJ/min.

M. Bahrami MECH 390 (W 07) Assignment #3 1

Problem 2:
The schematic diagram of a two evaporator refrigeration cycle is shown in the
figure below where refrigerant R-134a is used. The arrangement is used to
achieve refrigeration at two different temperatures with a single compressor
and a single condenser. The low-temperature evaporator operates at -18C with
saturated vapor at its exit and has a refrigerating capacity of 3 tons. The
higher-temperature evaporator produces saturated vapor at 3.2 bar at its exit
and has a refrigerating capacity of 2 tons. Compression is isentropic to the
condenser pressure of 10 bar. There are no significant pressure drops in the
flows through the condenser and the two evaporators, and the refrigerant
leaves the condenser as saturated liquid at 10 bar. Calculate:
1) the mass flow rate of refrigerant through each evaporator, in kg/min
2) the compressor power input, in kW
3) the rate of heat transfer from the refrigerant passing through the condenser,
in kW.
Qout
3 2
Condenser

Win
Expansion
valve Compressor

4 1
Evaporator 2 7 8

Expansion
valve
Qin, 2 = 2 tons

Expansion
valve
6
Evaporator 1

5 Qin, 1 = 3 tons

M. Bahrami MECH 390 (W 07) Assignment #3 2

Problem 1 Solution:
Assumptions:
1) each component is analyzed as a control volume at steady-state
2) the pump work is negligible
3) kinetic and potential energies effects are negligible
4) no heat transfer with the surroundings.
Analysis:
First we fix each state of the system.
State 1: sat. vapor, 200 kPa  h1 = 2706.7 kJ/kg
State 2: sat. liquid, 5°C  h2 = 20.98 kJ/kg
 

State 3: h3  h2  w
 pump
m  h2
 2
0


State 4: Q load  142 ton  1.798  10 6 kJ / h

Q load  1.798  10 6 
h4  h3  
 20.98     92.9kJ / kg
m  25,000 
State 5: T5 = 15°C; h5 ≈ hf (T5) = 62.99 kJ/kg
State 6: sat. vapor, 5°C  h6 = 2510.6 kJ/kg
State 7: sat. vapor, 4 kPa  h7 = 2554.4 kJ/kg
State 8: sat. liquid, 4 kPa  h8 = 121.46 kJ/kg
Now, consider a control volume enclosing the flash chamber:
   
m 4 h4  m 5 h5  m 2 h2  m 6 h6
   
m4  m2 m5  m6
thus
 
m 5  h5  h6   m 2  h2  h4 

m 5  734.6 kg / h

Next, consider a control volume enclosing the steam jet ejector.

  
m1 h1  m 6 h6  m 7 h7
  
m 7  m1  m 6 or,

M. Bahrami MECH 390 (W 07) Assignment #3 3

 
  
 m6  m6 m6
1   h1   h6  h7    0.7766
 m7  m7 m7

m 7  945.9 kg / h
Finally, for the condenser

m 7  h7  h8   m cw  hcw,out  hcw,in 
 

hcw,in = hf (15°C) = 62.99 kJ/kg and hcw,out = 104.89 kJ/kg

Thus,

m cw  54,920 kg / h

Problem 2 Solution:
Assumptions:
1) each component is analyzed as a control volume at steady-state
2) all processes are internally reversible, except for throttling through expansion valves
3) the compressor and exp. valves are adiabatic
4) potential and kinetic energies effects are negligible.
T 2

P = 10 bar

7
4 3.2 bar

8
-18 C 5
1
6 s

Analysis:
Fix each of the principal states:
State 3: P3 =10 bar, sat. liquid  h3 = 105.29 kJ/kg
State 4: Throttling process  h4 = h3 = 105.29 kJ/kg
State 5: Throttling process  h5 = h4 = 105.29 kJ/kg
State 6: T6 = -18 °C, sat. vapor  h6 = 236.53 kJ/kg
State 7: P7 = 3.2 bar, sat. vapor  h7 = 248.66 kJ/kg

M. Bahrami MECH 390 (W 07) Assignment #3 4

State 8: Throttling process  h8 = h7 = 248.66 kJ/kg
Fixing state 1 and 2 requires the mass flow rates through the evaporators. Thus:
 
Q in,1  m 6  h6  h5 

 Q in ,1 3tons 211kJ / min
m6    4.823kg / min
 h6  h5   236.53  105.29 kJ / kg 1ton
and

 Q in, 2 2tons 211kJ / min
m8    2.943kg / min
 h7  h4   248.66  105.29 kJ / kg 1ton
State 1: Now, for adiabatic mixing streams 6 and 8 to form stream 1:
 
 

m 6 h6  m 8 h8   m 6  m 8 h1  0
 
 
m 6 h6  m 8 h8
h1   
 241.13kJ / kg
m 6  m8
Having the enthalpy and pressure of state 1, the specific entropy is found s 1 = 0.9493
kJ/kg.K.
State 2: P2 = 10 bar, s2 = s1  h2 = 282.3 kJ/kg
b) the compressor power is:

  

w c   m 6  m 8  h2  h1   5.329 kW
 

For the condenser


  

Q out   m 6  m 8  h2  h3   22.91 kW
 

M. Bahrami MECH 390 (W 07) Assignment #3 5