Multy-stages vapor compression refrigeration cycle homework due date 5/11

1
1- The figure shows a two-stage vapor compression 11
refrigeration system with flash gas removal, liquid to Condenser
suction heat exchanger one flooded evaporator and
water-cooled condenser. The evaporator is a brine- 10 HP
cooler (brine specific heat 4.3 kJ/kg K, brine density compress
1050 kg/m3); which cools the brine from 15 C to -10 C. or
If the following data are applicable for the cycle 9
- Braine volume flow rate = 2500 L/h
- Condenser pressure = 1 M Pa 2 8
- Intermediate pressure = 0.4 M Pa
- Evaporator pressure = 0.16 M Pa 3
- State 1 is saturated 7 LP compressor
- Each of the two compressors are:
a) polytropic with index n = 1.2 HE
b) compressor mechanical efficiency of 90 %
c) compressor-electric motor efficiency of 90 % 5 Evaporator 6
4
d) clearance ratio c = 4 %
i- Sketch the P-h diagram
Expansion valve
ii- Complet the following tables for saturated refrigerant properties
iii- Calculate the refrigeration capacity for the P, MPA ,hf, kJ/kg ,hg, kJ/kg
evaporator in TR: 1 107 271
0.4 64 256
0.16 31 261

State P, ℎ, State P, ℎ, kJ/kg Device Mass flow

MPa kJ/kg MPa rate, kg/s
1 7 Condenser
2 8 286 Low pressure
compressor
3 9 High pressure
compressore
4 57 10
5 11 329
6

Evaporator refrigeration load= ________________kW

P, kPa
= _________________TR

, h, kJ/kg
2- The figure shows two stage vapor compression
refrigeration cycle. All evaporators are flooded, and liquid 1 Condenser, TC = 45 oC 11
leaves the condenser as saturated fluid. Assume all
compressors are polytropic with polytropic index n = 1.3
and each compressor has a clearance ratio c = 4 %.
A- Draw the pressure-enthalpy diagram for the cycle C2 C3
B- Calculate the cycle-coefficient of performance if all
compressors are identical in bore, stroke, number of 10
cylinders, and speed of revalidation. 2 Evaporator B, TB = 5 C o 9
C- If the condenser is water cooled with water flow rate
of 9 L/s and water temperature rise of 8 oC.
Calculate the refrigeration capacity for each 8
evaporator in the cycle, TR F.G.
For Saturated- Refrigerant properties 3 I.C. 7
Saturation Saturation Enthalpy Enthalpy Saturated Saturated
C1
4
temp. pressure, of of liquid vapor
,C kPa saturated saturated Specific Specific
liquid, vapor, volume, vf, volume, Evaporator A, TA = -20 oC
hf, kJ/kg hg , kJ/kg m3/kg vg, m3/kg
5 6
45 2100 119 227 0.00107 0.008
5 728 57.4 215 0.00088 0.0265 , h7 = h11 = 250 kJ/kg
-20 315 23.6 202 0.000813 0.0609 F.G.I.C flash gas inter cooler
C compressor

1
3- The figure shows a refrigeration system with two 14
evaporators A and B. Evaporator B is a brine- cooler Condenser
(brine specific heat 4.3 kJ/kg K, brine density 1050
kg/m3) cooler which cool the brine from 15 C to -5 C. 11 12 13
Evaporator- A HP
The heat gain from surroundings to brine cooler wall is compressor
estimated to be 20 % of brine cooling load. If the
following data are applicable for the cycle 10
- Condenser pressure = 1.5 M Pa
- Intermediate pressure = 0.4 M Pa 2 9 8
Water intercooler
- Evaporator pressure = 0.1 M Pa
- State 1 is saturated 3
- Flooded evaporators 7 LP compressor
- Each of the two compressors are:
a) polytropic with index n = 1.4 HE
b) compressor mechanical efficiency of 90 %
c) compressor-electric motor efficiency of 90 % 5 Evaporator- B 6
4
d) clearance ratio c = 4 %
Expansion valve
i- Sketch the P-h diagram, transfer to your answer sheet and complet the following tables
State P, MPa ℎ, kJ/kg 𝜌, kg/ State P, MPa ℎ, kJ/kg 𝜌, kg/
m3 m3
1 1.5 600 8 1880
2 9 1800
3 0.4 500 10 1500 3.3
4 425 11
5 12
6 0.1 1455 13
7 0.75 14 1820
 Law pressure compressor High pressure compressor
Electric power input, kW 125 250
Brack power, kW
Indecated power, kW
Volumetric efficiency, %
Piston displacement, m3/s
Mass flow rate, kg/s
Heat rejection rate, kW
ii- Calculate the refrigeration capacity for each evaporator in TR
iii- Calculate the rate of brine volume flow rate, m3/hr
iv- Calculate the cycle, machine and system "plant" coefficient of performance
4- A two stage refrigeration system is shown in figure. 1 Condenser , h11,s = 245 kJ/kg
The operating pressures are 0.1, 0.5 and 2.5 MPa. The 11
refrigerant is saturated at exit from condenser and both 1
evaporators. Temperature of liquid refrigerant leaving 8 Evaporator A 9 10 HP
the flash inercooler is 7 oC. The low-pressure compressor,
compressor has the following specifications: number of  isc = 90 %

cylinders = 4, speed = 1500 rpm, cylinder diameter = 7

13 cm, stroke- to- diameter ratio = 1 and volumetric , h6,s = 223 kJ/kg
efficiency = 90 %. The high-pressure compressor has 2 6 6
an indicated power of 90 kW. Draw the P-h diagram
and calculate: 3
- The refrigeration capacities of the two LP compressor,
evaporators., TR  isc = 90 %
, h3 = 60.8 kJ/kg
- The cycle coefficient of performance.
Given that:
h3 = 60.8 kJ/kg h6,s = 223 kJ/kg h11,s = 245 kJ/kg 4 Evaporator- B 5

Expansion valve
and the saturation condition for the cycle refrigerant are
Sat. Sat. Sat. specific volume, m3/kg Sat specific enthalpy, kJ/kg
pressure, temperature,
MPa. C , vf , vg , hf , hg
2.5 53 0.00115 0.00641 135 231
0.5 -6 0.000853 0.0394 42.5 214
0.1 -45 0.000765 0.185 -10.1 191
5- The figure shows a two stage vapor
compression refrigeration system with
two flooded evaporators ( A & B) and an
open type flash gas removal and a flash
gas subcooler -intercooler. The two
compressors may be assumed adiabatic.
Given that:
- Condensing temperature = 35 C
- Evaporating temperature in
evaporator A= 0 C
- Evaporating temperature in
evaporator B= -30 C
- h,8= 62.8 kJ/kg
- h,11= 230 kJ/kg
- h,14= 270 kJ/kg
- Evaporator A refrigeration
capacity is 20 TR
- Evaporator B refrigeration
capacity is 10 TR N. B. Neglect the circulation pump power.
Draw the cycle on p-h diagram, then
Calculate:
- The cycle coefficient of performance
- The cycle heat rejection ratio
Refrigerant saturation properties
Saturation Saturation Enthalpy, kJ/kg Specific volume,m3/kg
Temperature, C Pressure, kPa Sat. liquid Sat. vapor Sat. liquid Sat. vapor
35 1870 110 227 0.00104 0.00931
0 624 50.4 213 0.000865 0.031
-30 208 99.2 196 0.00079 0.0906
 Air refrigeration cycle homework due date 12 / 11 /2023
1-The figure shows reduce-ambient air refrigeration 1
system used to maintain the aircraft-cabin pressure
and temperature at 100 kPa and 22 oC. If the
2 7 T1
equipment's specification as follows:
- Compressor pressure ratio = 3 and its adiabatic 3 4
" isentropic" efficiency is 75 % C1
- Heat exchanger effectiveness = 65 % HE T2
- Ram air turbine " T1" adiabatic efficiency = 75 9
% 8 5
- Main turbine " T2"adiabatic efficiency = 90 %
Cabin 6
- Ram air turbine power is negligible
- Main turbine power is used to drive the heat
exchanger's fan Cp,a= 1 kJ/kg K a = 1.4
- At full load conditions, the cabin cooling load
is 10 TR
The aircraft travel with speed of 800 km/h in ambient pressure of 34 kPa and temperature of -20 oC.
And air is supplied to the cabin at a temperature of 17 oC
- Draw the T-s diagram.
- Calculate the pressure and temperature for each stat in the cycle.
- Calculate the air mass flow rate through the cabin, kg/s
- Calculate the cycle COP
- At part load conditions, the cabin cooling load is 6 TR. Calculate the air mass flow rate bypassed around
the turbine T2

Ram air
2- The figure shows an air refrigeration system for a jet plane. The 1
cabinet pressure is 0.098 MPa and is maintained at 25 oC. The 2
compressor indicated power is 100 kW. The ambient conditions are
0.083 MPa and 5 oC. The ram air pressure is increased from 0.083 to 3 4 5
0.118 MPa, due to isentropic stagnation against the plane body. The
primary heat exchanger has an effectiveness of 0.6 The air is further
cooled in the regenerative heat exchanger down to 50 oC while on the Compressor
other side the cooling air is heated to 60 oC before being discharged. 8 c
a
If the isentropic efficiency of compressor and turbine is 0.9 and 0.8 b
i
respectively. Draw a neat T-s diagram of the cycle and calculate: n
fan
- The percentage of the total air flow used for regenerative Turbine
e
t
cooling.
- The cabin –cooling load in TR. 9 6
- The C.O.P. of the cycle and
- Fan power, kW
- Regenerative heat exchange effectiveness
 3- The reduce-ambient air refrigeration system is
used in an aircraft flying at a cruising speed of 1000
km/h. The ambient conditions are 0.04 MPa and -28
o
C. The ram-compression process is assumed to be
isentropic. The air leaving the compressor is cooled
to 60 oC in the heat exchanger. The pressure ratio of
the main gas- compressor is 3. The cabin is
maintained at 0.098 MPa and 22 oC. The isentropic
efficiencies for all compressors and turbines are 88
%. During a certain part load condition, the cabin
cooling load is 20 TR and supply air temperature is
12 C.
Draw a schematic flow and T-s diagrams of the cycle and determine:

i. Heat exchanger effectiveness.

ii. C.O.P. of the cycle
iii. Cycle relative efficiency.
iv. The air fraction bypass around the heat exchanger and expansion turbine.
v. The full load cooling capacity at full load conditions, TR " assume that the turbine inlet
conditions are constant"

4- The figure shows an air refrigeration

cycle used to maintain the cabin of air
craft with 20 TR cooling load at a pressure
of 100 kPa and -2 oC , The air craft speed
is 900 km/hr and the ambient conditions
are 80 kPa
and -28 oC.
If the cycle equipments has the following
specifications:
- Each compressor "C" has a
pressure ratio equal to 1.8 and
isentropic efficiency equal to 70 %
- Each turbine " T1 & T2" has
isentropic efficiency equal to 60 %
- Each heat exchanger effectiveness
equal to 60 %
- The power of turbine T1 is used to
20 TR
drive the fan
- The power of turbine T2 is
negligible
- The air mass flow rate through the cabin represents 80 % from that through each compressor
Draw the refrigeration cycle on T-s chart
Clculate the pressure and temperature for each state on the cycle " represent ure answer in a table form"
Clculate the cycle coefficient of performance
Schedule for week 4-5 & 6
from to Sheet Sec 1 Sec2 Sec 3 Sec4
Week
#4 22/10/2023 26/10/2023 V. C. R. C. 2,6 3,7 4,8 5,9
Week V. C. R. C.
#5 29/10/2023 02/11/2023 + Add 10,14 11, 4A 12,5A 13, 6A
Week
#6 05/11/2023 09/11/2023 Air ref 3,10 4,9 5,8 6,7