Old Question Papers 2006-11-2

7/30/2019 Old Question Papers 2006-11-2

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INDIAN INSTITUTE OF TECHNOLOGY

Date : Time : 2 hours Full Marks : 30 No. of students : 73

Mid-Semester 2006 Mechanical Engineering Subject No. ME60085/ME60215

B.Tech(AgFe),DD(ME),M.Tech(ME,CR,AgFe) Subject: Refrigeration Systems

Answer all questions

Marks for each question is shown in the margin in parenthesis.Make suitable assumptions wherever necessary. State the assumptions clearly

1. A saturated, single stage vapour compression refrigeration system working with refrigerant R22has a refrigeration capacity of 100 TR. The system operates between an evaporator temperature

of 7 C (saturation pressure is 621.22 kPa) and a condensing temperature of 32 C (saturationpressure is 1255.2 kPa). The refrigeration effect under these conditions is 168.6 kJ/kg. Thevalues of specific volume of refrigerant at the inlet and exit of the compressor are 0.03798 m3/kgand 0.02011 m3/kg, respectively. The system uses a 4-cylinder, reciprocating compressor thatoperates at 3000 RPM. The compressor has a stroke-to-bore ratio of 0.8, a clearance factor of0.05 and an isentropic efficiency of 0.85. If the actual volumetric efficiency of the compressor is80% of the clearance volumetric efficiency, find a) actual COP of the system and b) stroke andbore of the compressor cylinders. (3+3 = 6)

2. A window air conditioner with a refrigeration capacity of 1.5 TR works for 8 hours a day. Thecompressor motor has an efficiency of 85%. The compressor is a 2-cylinder, reciprocatingcompressor with a bore of 5 cm, stroke-to-bore ratio of 0.8 and a rotational speed of 3000 RPM.The indicator diagram of the compressor has an area of 12 Joules, while the frictional meaneffective pressure is 0.5 bar. A separate motor, which drives the condenser and evaporator fans,

consumes 80 Watts. Find a) actual COP of the air conditioner considering power consumption ofboth compressor and fan motors, b) annual running cost of the air conditioner, if the cost ofelectricity is Rs. 5 per kWh.

(4+2 = 6)

3. A backward curved centrifugal compressor has an impeller radius of 0.5 m and runs at 9000

RPM. The blade angle at impeller exit is 60 and the flow coefficient (ratio of normal component ofvelocity to tip speed) is 0.3. The compressor compresses water vapour that enters the compressor

at 4.5 C (saturation pressure is 0.8424 kPa). The flow area at the periphery of the impeller is 0.04m2. Assuming ideal compression with an average isentropic index of compression of 1.322 andneglecting tangential component of velocity at the impeller inlet, find a) pressure at the exit of the

impeller, b) temperature at the exit of the impeller, c) mass flow rate of water vapour through thecompressor, and d) Power input to the compressor. Water vapour may be assumed to behave asan ideal gas with a molecular weight of 18 kg/kmol. (2+1+2+2 =7)

4. A single stage vapour compression refrigeration system working with refrigerant R22 has a

refrigeration capacity of 10 TR. The system operates between an evaporator temperature of 7 C

and a condensing temperature of 54 C. The system employs a liquid-to-suction heat exchangerthat has an effectiveness of 0.8. The isentropic efficiency of the compressor is 0.85. A counterflow,tube-in-tube type condenser is to be designed for this system. Coolant water at a temperature of

36 C and with a mass flow rate of 0.5 kg/s, enters the condenser. The coolant water flows throughthe inner tube of the condenser that has an inner diameter of 2.24 cm and an outer diameter of2.54 cm. A constant convective heat transfer coefficient of 5000 W/m2.K may be assumed on thewaterside. The average heat transfer coefficient on the refrigerant side may be taken as 150


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W/m2.K in the desuperheating zone and as 1700 W/m2.K in the condensing zone. The foulingfactor on waterside is 0.0002 m2.K/W, while it may be neglected on the refrigerant side. Theresistance offered by the tube wall may also be neglected. The state of refrigerant at the exit ofevaporator and condenser is saturated.

a) Using the refrigerant property data given below, find the required length of the condenser tube

Temperature, C Dryness fraction Pressure (bar) Enthalpy (kJ/kg)

7 1 6.215 407.554 1 21.27 417.654 0 21.27 268.9

The gas constant of R22 is 0.09615 kJ/kg.K, average specific heat (CP) of vapour at 6.215 bar is0.75665 kJ/kg.K and the average isentropic index of compression is 1.185. Specific heat of liquidwater is 4.18 kJ/kg.K. Assume the superheated vapour to behave as an ideal gas.

b) Everything else remaining same, what is the required tube length if integral fins that increasethe heat transfer area by a factor of 2 (Atotal with fins : Abare tube is 2:1) are added on refrigerant side?

The fin efficiency may be taken as 90%.

c) What problem do you encounter if you try to design the condenser assuming a constantcondensing temperature throughout the condenser?

(7+3+1 = 11)

End of the paper


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INDIAN INSTITUTE OF TECHNOLOGY KHARAGPUR

Date : Time : 2 hours Full Marks : 30 No. of students : 70Mid Semester, Autumn 2007 Mechanical Engineering Subject No. ME60085

DD/PG(ME2,AgFe,Cryo) Subject Name : Refrigeration SystemsAnswer all questions

Instructions: Make suitable assumptions wherever necessary, but state them clearly. Marks foreach question are shown in parenthesis

1. A designer wishes to improve the performance of a vapour compression refrigeration systembased window air conditioner by replacing the refrigerant R-22 with water (R-718). In both cases,the window air conditioner has a cooling capacity of 1.5 TR (1.0 TR = 3.517 kW) and operatesbetween an evaporator temperature of 7oC and a condensing temperature of 35oC. The refrigerantat the exit of the condenser is saturated, while the suction vapour has a useful superheat of 15 K.The following data are available for both the refrigerants.

Fluid NBP,o

C

Latent heat ofvaporization, hfg,

kJ/kg

Avg. liquidsp.heat, cp,f

kJ/kg.K

Avg. vapoursp.heat, cp,g

kJ/kg.K

Gas

constantkJ/kg.KAt Pe At Pc At Pe At Pc At Pe At PcR-22 -40.81 199.3 172.3 1.19 1.15 0.77 0.95 0.0962R-718

99.97 2484.3 2417.9 4.2 4.18 1.90 1.93 0.4615

Where Pe and Pc are evaporator and condenser pressures. Using the above data and assumingisentropic compression, (a) compare power consumption of the R-22 based air conditioner withthat of R-718 based air conditioner, (b) Why in practice R-22 is used as the working fluid inwindow air conditioners, but not water, even though water is environment friendly, safe,inexpensive and is easily available? (6+2 = 8)

2. (a) With suitable diagrams, explain briefly why the cooling capacity of a reciprocatingcompressor decreases as the condensing temperature increases and/or the evaporatortemperature decreases? (b) In domestic refrigerators, the formation of frost on evaporatorsurfaces decreases the evaporator temperature by reducing the external airflow rate andincreasing the resistance to heat transfer. Assuming a reciprocating compressor based domesticrefrigerator to operate at a constant condensing temperature of 54oC (ambient temperature is43oC), find the evaporator temperature at which the cooling capacity of the refrigerator becomeszero. The refrigerant used in the refrigerator (R-134a) has a coefficient of expansion/compressionof 1.20 and the compressor has a clearance ratio of 0.05. (c) Do you expect the condensingtemperature to remain constant at 54oC during frost formation? The saturation pressure of R-134a

is related to its absolute temperature by the following formula: (2+3+1 = 6)

KinisTandkPainispwhereexpp sat06.33T

209441.14

sat

3. In a refrigeration system that uses a centrifugal compressor, saturated R134a vapour iscompressed isentropically from a temperature of 4oC to a pressure corresponding to a condensingtemperature of 36oC in a single stage. Calculate the speed of the impeller blades at the tipassuming radial blades and radial entry of refrigerant at impeller inlet. Use the saturation pressurevs absolute temperature formula given above (problem 2) and assume the isentropic coefficient ofcompression to be 1.20 and the vapour to behave as a perfect gas. The molecular weight of

R134a is 102.03 kg/kmol. (4)


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4. Milk at a temperature of 7oC and a flow rate of 4 kg/s arrives at a dairy plant where it is firstpasteurized at 73oC. The pasteurized milk is then chilled to 4oC before it is sent for packing anddistribution to customers. Two options, systems (a) and (b) shown in the figure have to be

considered for the required processes of pasteurization and chilling.In system (a), the milk is pasteurized using an electrical heater and is chilled in the evaporator of asingle stage saturated (SSS) vapour compression refrigeration system. In system (b) thecondenser of the SSS refrigeration system is used for pasteurization, while the evaporator of thesystem is used for chilling the milk. In both the systems, a regenerative heat exchanger (RHX) isused for heat recovery from the pasteurized milk. Both the systems (a) and (b) use ammonia asthe refrigerant and operate at an evaporator temperature of 1oC. The condensing temperature ofsystem (a) is 35oC as it rejects heat to a heat sink that is at 32oC. Using the heat transfer in thedesuperheating region and a counterflow heat exchanger, the condensing temperature of system(b) is maintained at 70oC. The compressors used in both (a) and (b) have an isentropic efficiencyof 0.8. The effectiveness of regenerative heat exchanger (RHX) is 0.9. The average specific heatof milk may be taken as 3.75 kJ/kg.K. The average isentropic index of compression (k) ofammonia may be taken as 1.28. The following saturated property data for ammonia are available:

Temp, oC Pressure,kPa

Quality Sp. enthalpy,kJ/kg

Sp. entropy,kJ/kg.K

Sp. volume,m3/kg

1 445.68 1.0 1606.5 6.0796 0.279251 445.68 0.0 347.78 1.4884 0.0016035 1350.8 1.0 1631.5 5.6801 0.09563

35 1350.8 0.0 509.23 2.0382 0.0017070 3313.5 1.0 1627.1 5.3131 0.0378770 3313.5 0.0 688.2 2.5770 0.00190Using the data given above:

a) Compare the total electrical power consumptions of systems (a) and (b)b) Why an auxiliary condenser is required in system (b)?c) What are the total entropy generation rates and exergetic (2nd law) efficiencies of systems (a)and (b)? Assume isobaric conditions in all heat exchangers. (7+1+4 = 12)

End of the paper

SSSVCRS

Milk in, 7oC

Milk out, 4oC

73oC

condenser

evaporator

SSSVCRS

Electrical

Milk in, 7oC

Milk out, 4oC

73oC

Auxiliarycondenser

evaporator

Refrigeran

Wc

WE

Wc

RHX RHX

(a) (b)

to 32oC to 32

oC


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INDIAN INSTITUTE OF TECHNOLOGY KHARAGPURDate : Time : 2 hours Full Marks : 30 No. of students : 60

Mid Semester, Autumn 2008 Mechanical Engineering Subject No. ME60085UG/DD/PG(ME2,AgFe) Subject Name : Refrigeration Systems


Instructions: Make suitable assumptions wherever necessary, but state them clearlyMarks for each question are shown in parenthesisUniversal Gas Constant = 8.314 kJ/kmol.K

1a. From the fundamental laws of thermodynamics, show that the COP of a vapour compressionrefrigeration system (VCRS) is given by:

In the above expression COPc is the COP of a Carnot refrigeration system operating betweenexternal heat source and sink temperatures of Te and Tc, respectively, qe is the refrigeration effect

of VCRS and

totalgens

is the total entropy generated. (4 marks)

1b. A room air conditioner maintains a room at 25 C when the ambient temperature is 43 C. Atthese conditions the system has a cooling capacity of 3.5 kW and its compressor consumes 1.2kW of power. The measured refrigerant mass flow rate is 27 grams/second and the entropic

average temperatures of refrigerant in evaporator and condenser are 7 C and 55 C, respectively.The actual isentropic efficiency of the compressor is 0.65. Assume that system irreversibility is dueto heat transfer in evaporator and condenser, non-isentropic compression and throttling only.Contribution of all other processes (including superheat horn) to irreversibility is negligible. Usingthis data find the entropy generation rate (in W/K) and irreversibility (in W) due to evaporator,compressor, condenser and expansion valve. (6 marks)

2a. Find the stroke length and bore of a reciprocating compressor used in a domestic refrigeratorusing the data given below. Also find the heat transfer (if any) from the compressor to thesurroundings, if the power input to the hermetic compressor is 100 watts.

Refrigeration capacity = 150 W; refrigeration effect = 130 kJ/kg; compressor speed = 2900 RPM,piston speed = 1.5 m/s, actual volumetric efficiency = 0.6. The compressor inlet and dischargeconditions are:

At compressor inlet: t = 32 C, v = 0.20902 m3/kg, h = 430.26 kJ/kg, s = 1.9086 kJ/kg.K

At compressor exit: t = 119 C, h = 498.12 kJ/kg, s = 1.9086 kJ/kg.K (6 marks)

2b. In a screw compressor, R134a enters the compressor as dry saturated vapour at 7 C(saturation pressure = 374.63 kPa). The refrigerant after being compressed in the compressor

enters a water-cooled condenser and condenses at a temperature of 36 C (saturation pressure =911.85 kPa). The average index of compression n is 1.18. If the screw compressor has a built-in

tc

te

Tc

Te

+

=

total gence

c

c

sTq

COP

COPCOP

1

All the temperatures shown in theschematic are entropic averagetemperatures.


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volume ratio of 2.5, find the built-in efficiency of the compressor. Show the compression processon a P-V diagram. (4 marks)

2c. A single stage centrifugal compressor operates at a rotational speed of 9000 RPM and yields a

pressure ratio of 3.0 while compressing a refrigerant that has an isentropic index () of 1.22. Theactual power consumption of the compressor under these conditions is 440 kW, while the motorthat drives the compressor has an efficiency of 85 percent. The actual compressor indicator

diagram has an area of 2.2 kJ. If the refrigerant enters the compressor at 7 C, find the refrigeranttemperature at the exit of the compressor, assuming the refrigerant to behave as an ideal gas.

(4 marks)

3. Due to ozone layer depletion, refrigerant R12 (critical temperature = 112 C, critical pressure =4136.1 kPa) used in car air conditioners had to be replaced. One of the environment friendlyrefrigerants suggested as replacement for R12 in car air conditioners is R744 (critical temperature

= 31 C, critical pressure = 7377.3 kPa). Using suitable system schematics and cycle diagrams,explain how the proposed system based on R744 will be different from the one based on R12, ifthe car is designed for tropical conditions such as ours. Also on a plot show qualitatively how theCOP of both the systems vary with compressor discharge pressure, when the evaporator

temperature is kept constant. Explain the variations briefly and interpret the trends in terms ofpractical applications. (6 marks)

End of the paper


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Date : Time : 2 hours Full Marks : 60 No. of students : 55Mid-Semester 2009 Mechanical Engineering Subject No. ME60085

ME(DD)/ME2/ME(AgFe) Subject Name : Refrigeration SystemsAnswer all questions

1. A dairy plant uses a vapour compression refrigeration system for chilling milk from 14oC to 4oC.The cooling water used for heat extraction enters the condenser at 31oC and leaves at 36oC. If therefrigeration system used has a refrigeration capacity of 120 kW and the compressor consumes18 kW, find the 2nd law efficiency and total entropy generation rate of the system. What is thewater flow rate in the condenser? State the assumptions made clearly. (6)

2. Prove that under certain assumptions, the COP of an ideal reciprocating compressor remainssame with or without clearance. State the assumptions clearly. (8)

3. Show qualitatively how the power consumption of a room air conditioner which was in offcondition varies with time soon after it is switched on. Assume that the air conditioner uses a

reciprocating compressor. Justify your answer with suitable equations. (6)

4. A domestic refrigerator operates at an evaporator temperature of -25oC and a condensingtemperature of 54oC. The isentropic efficiency of the compressor under these conditions is 0.6.The refrigerator has a cooling capacity of 100 watts, and the power input required is 120 watts.The refrigerated space is maintained at -21oC, while the ambient air is at 43oC. Assuming asaturated refrigeration cycle, and the internal losses to be due to non-ideal compression andthrottling only, find how much of the input power is wasted due to non-ideal compression and howmuch power is wasted due to throttling. (8)

5. In a certain refrigeration system, the displacement rate of the compressor is 5 litres per

second. The power input to the shaft is 1200 watts. Find the ideal indicated mean effectivepressure (mepideal) if the mean effective pressure due to valve pressure drops is 0.2 bar and thatdue to friction is 0.5 bar. Also find the ideal indicated power input and efficiency. (6)

6. A saturated, single stage vapour compression refrigeration system working with refrigerant R22has a refrigeration capacity of 300 TR. The system operates between an evaporator temperature

of 7 C (saturation pressure is 621.22 kPa) and a condensing temperature of 32 C (saturationpressure is 1255.2 kPa). The refrigeration effect under these conditions is 168.6 kJ/kg. Thevalues of specific volume of refrigerant at the inlet and exit of the compressor are 0.03798 m3/kgand 0.02011 m3/kg, respectively. The system uses a 8-cylinder, reciprocating compressor thatoperates at 3000 RPM. The compressor has a stroke-to-bore ratio of 1.0, a clearance factor of

0.05 and an isentropic efficiency of 0.8. If the actual volumetric efficiency of the compressor is80% of the clearance volumetric efficiency, find a) actual COP of the system and b) stroke andbore of the compressor cylinders. (10)

7. Explain with suitable justifications why there is an upper limit for the refrigeration capacity of areciprocating compressor. (8)

8. A screw compressor has a built-in-volume ratio of 6. Find the built-in-volume efficiency of thecompressor if the condenser-to-evaporator pressure ratio is 5 and the index of compression (n) is1.1. Show the compression process on P-V diagram. (8)

End of the paper


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INDIAN INSTITUTE OF TECHNOLOGY

Date : Time : 3 hours Full Marks : 50 No. of students : 72End Semester, Autumn 2006 Mechanical Engineering Subject No. ME60085

DD/PG(ME,CR & AgFe) Subject Name : Refrigeration SystemsAnswer all questions

Instructions: Make suitable assumptions wherever necessary and state them clearly---------------------------------------------------------------------------------------------------------------------

1a) Using cycle diagrams, discuss the limitations of single stage vapour compression refrigerationsystems. Explain with suitable diagrams how these limitations are overcome in large, commercialrefrigeration systems. (6)

1b) Shown below is a 100 TR, ammonia based multi-stage compression refrigeration system witha flash chamber for intercooling. (2+5+3 = 10)

The system operates at an evaporator temperature of 40o

C and a condensing temperature of36oC. The flash chamber is maintained at 3.6 bar.

a) Draw the p-h diagram of the systemb) Find the required volumetric displacement rates of compressor-I and IIc) Find the required power input to compressor-I and II assuming isentropic compression andsystem COP.

Assume that the refrigerant is saturated at the exit of evaporator, flash chamber and condenser.The actual volumetric efficiency of the compressors may be estimated using the equation:

pact,v r0285.0948.0 where rp is the pressure ratio.Use the property data given below for ammonia:T(oC)

Drynessfraction

Pressure(bar)

Sp. volume(m3/kg)

Enthalpy(kJ/kg)

Entropy(KJ/kg.K)

-40 1.0 0.717 1.553 1408.0 6.243-4.6 1.0 3.6 0.342 1457.0 5.683-4.6 0.0 3.6 178.766.2 Superheated 3.6 1626.0 6.24336 0.0 13.9 371.092.6 Superheated 13.9 1651.0

2. Find the total length of the tube required for the plate fin & tube type condenser used in thewindow air conditioner of 1.5 TR cooling capacity, which has a COP of 2.7. (6)

7

1

6

5

2

3

4

Compressor - I

Compressor - II

Flashchamber

Evaporator

Condenser

Use the data given below:


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Inner and outer diameters of the tube = 14 mm and 16 mm, respectivelyHeat transfer coefficient on air side = 50 W/m2.KHeat transfer coefficient on refrigerant side = 1000 W/m2.KBare tube area on air side (Ab) per m of tube = 0.045 m

2/m of tube lengthRatio of fin area to bare tube area (Af/Ab) = 20Fin efficiency = 0.8Thermal conductivity of tube material = 385 W/m.KCondensing temperature = 54oCTemperature of air at condenser inlet = 32oCTemperature of air at condenser outlet = 38oC

Assume the fouling resistance to be negligible both on the refrigerant as well as on the externalfluid sides.

3a) Explain with suitable diagrams the working principle of a thermostatic expansion valve (TEV)with a cross-charged power element. What is the need for cross-charging? (4)

3b) A TEV is used in an R-134a based car air conditioner that operates at an evaporatortemperature of 7.2oC and a condensing temperature of 54oC. If the spring exerts a pressure of 80kPa, find the degree of superheat. Assuming the refrigerant vapour to behave as an ideal gas with

a gas constant of 81.49 J/kg.K and a (=cp/cv) value of 1.1, find the COP of the system if thecompressor has an isentropic efficiency of 0.7. The refrigeration effect at the operating conditionsis 130 kJ/kg. (6)

Use the following equation for estimating the vapour pressure data of R-134a.

KinisTandkPainispwhereexpp sat06.33T

209441.14

sat

4) It is proposed to use a simple, closed air cycle refrigeration system for air conditioning apassenger car. The system is to be designed such that minimum temperature at which heatrejection can take place is 50oC and the maximum temperature at which heat extraction from theconditioned space can take place is 0oC. The isentropic efficiencies of the compressor and turbineare 0.7 and 0.9, respectively. Neglecting pressure losses in the heat exchangers, find

a) The minimum pressure ratio required to obtain the operating temperatures mentioned above

b) Minimum pressure required to obtain the operating temperatures if the system operates

reversibly (isentropic efficiencies of turbine and compressor are equal to 1.0) and the value ofCOP at this condition (4+2+2 = 8)

5a) It is proposed to install a 1000 TR refrigeration system for air conditioning a large factory. Twooptions are to be considered: a conventional vapour compression refrigeration system and anatural gas driven vapour absorption refrigeration system. Out of these two systems, choose asystem based on the minimum life cycle cost using the data given below:

Evaporator temperature (Te) = 7oC, Condenser temperature (Tc) = 43

oC, Generator temperature =110oC. The actual COP of vapour compression system is given by:

265TT1COP70.0COP ecCarnotact


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The actual COP of vapour absorption system is 80 percent of the ideal COP. The cost ofelectricity = Rs. 5.5 per kWh, cost of natural gas = Rs. 12 per kg, calorific value of natural gas =50 MJ per kg.

Initial cost of compression system is Rs. 35000 per TR and that of absorption system is Rs. 42000per TR. The expected life of both the systems is 20 years. Neglect any change in the cost ofelectricity and cost of natural gas with time. (6)

5b) Write the chemical formula of the following refrigerants and state whether they come underozone depleting substances or not (4 X 1 = 4)

a) R123 b) R152a c) R290 d) R141b

a) Draw the system schematic and show the cycle on P-h and T-s diagrams

Common data:

1 TR = 3.517 kW, Universal gas constant = 8.314 kJ/kmol.K

--- end of the paper ---


Date : Time : 3 hours Full Marks : 50 No. of students : 70End Semester, Autumn 2007 Mechanical Engineering Subject No. ME60085

DD/PG(ME,CR & AgFe) Subject Name : Refrigeration SystemsAnswer all questions

Make suitable assumptions wherever necessary and state them clearly----------------------------------------------------------------------------------------------------------------

1) In a 50 TR capacity refrigeration plant, the refrigerated space is maintained at 27 C. The plantuses an R 22 based two-stage vapour compression system that uses a flash chamber, only for

flash gas removal. The refrigerant evaporates at 30 C in the evaporator and condenses at 36 C

in a water-cooled condenser. The flash chamber is maintained at a saturation temperature of2.4 C. The refrigerant at the exits of evaporator, flash chamber and condenser and at the inlet tothe 1st stage compressor is saturated. The compression in 1st and 2nd stage compressors isadiabatic but irreversible with an isentropic efficiency of 0.7 and 0.75, respectively. The isentropicindices of compression (k) for the 1st and 2nd stage compression are 1.1574 and 1.1170,respectively, and the specific volume of refrigerant at the inlet to the 2nd stage compressor is0.050485 m3/s. Using the property data given below.

b) Find the total power input to the system and system COPc) Find required cooling water flow rate in the condenser when the cooling water enters the

condenser at 28 C and leaves the condenser at 32 C.

d) Find entropy generation rate in evaporator, condenser and expansion valves and the rate ofexergy destruction (lost work) in the compressors.

T(oC)

Drynessfraction

Pressure(bar)

Sp. volume(m3/kg)

Enthalpy(kJ/kg)

Entropy(KJ/kg.K)

-30 0.0 1.639 - 165.88 0.86873-30 1.0 1.639 0.13553 392.69 1.80152.4 0.0 5.380 - 202.82 1.01022.4 1.0 5.380 0.043698 405.92 1.747236 0.0 13.89 - 244.38 1.1499

36 1.0 13.89 0.01679 415.54 1.7036(3+5+1+6 = 15)


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CO2 eva orator

NH3 condenser

Cascade condenser

CO2

NH3

2) A cascade refrigeration system shown below, uses CO2 as refrigerant for the low-stage andNH3 as refrigerant for the high-stage. The system has a refrigeration capacity of 100 TR. The

refrigerant CO2 evaporates at -36 C in the evaporator and condenses at 3 C in the cascade

condenser, while NH3 condenses at 39 C in the condenser and evaporates at 0 C in the cascadecondenser. Refrigerant at the exit of evaporator and condenser is saturated and there is nosuction line superheat. The isentropic indices of compression (k) for CO2 and NH3 are 1.27 and

1.28, respectively. The actual volumetric ( act,vol) and isentropic efficiencies ( act,is) of both CO2

and NH3 are given by the equation:65.0

pis,actvol,act r1.095.0 , where rp is the pressure ratioacross the compressor. Using the refrigerant data given below find a) the displacement rates ofthe compressor in m3/s and b) total power input and system COP.

(4+5 = 9)

Fluid T( C) P(bar) quality v(m3/kg) h(kJ/kg)

CO2

-36 11.67 0 - 121.01-36 11.67 1 0.03318 436.073 37.7 0 - 207.433 37.7 1 - 428.97

NH30 4.29 0 - 343.150 4.29 1 0.28930 1605.439 15.13 0 - 528.939 15.13 1 0.08545 1632.8

Cascade refrigeration system (Problem 2)

3) A H2O-LiBr based vapour absorption refrigeration system has a cooling capacity of 100 TR. The

system operates at an evaporator temperature of 5 C, a condensing temperature of 36 C and a

generator temperature of 110 C. The system employs a solution heat exchanger between

absorber and generator for internal heat recovery. The strong solution leaves the solution heatexchanger at a concentration of 0.6 and temperature of 42 C, at which the solution enthalpy is 155 kJ/kg. The weak solution leaves the absorber at a concentration of 0.5 and a temperature of

36 C, at which the solution enthalpy is 158 kJ/kg. The specific heat of both strong and weaksolution is equal to 2.57 kJ/kg.K, while the specific enthalpies of water vapour (hv) and liquid

water (hf) can be obtained using the equations:t18.4h;t88.12501h fv , where t is temperature in

C and hv and hf are in kJ/kg. Neglect solution pump work. Using the data given, find:

a) Mass flow rates of refrigerant, weak and strong solutionsb) Heat transfer rate and effectiveness of solution heat exchanger

c) System COP and second law efficiency (3+3+4 = 10)

4a) A refrigeration system that employs a multi-row, plate-and-fin type, air cooled condenser has arefrigeration capacity of 45 kW and a COP of 3.0. The refrigerant condenses at a temperature of

48 C, when the ambient air at a temperature of 35 C and a flow rate of 15 kg/s flows through thecondenser. The overall heat transfer coefficient based on airside is 30 W/m2.K. The bare andfinned tube areas on the airside are 0.8 m2/face area/row and 20 m2/face area/row, respectively.Find the number of rows required in the airflow direction, if the maximum face velocity of air is tobe limited to 5 m/s. Assume the density of air to be 1.2 kg/m3and the specific heat of air is 1.02kJ/kg.K. (5)

4b) A thermostatic expansion valve (TEV) without an external equalizer is to be used in arefrigeration system in which the refrigerant (R134a) enters the evaporator at a temperature of -

25 C. The spring of the TEV is set such that it exerts a constant force on the bellows that is


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equivalent to a pressure of 25 kPa. a) What is the degree of superheat, if pressure drop acrossevaporator is neglected? b) What is the actual degree of superheat at the exit of evaporator, if apressure drop of 10 kPa takes place in the evaporator. The saturation pressure (psat) of R134a can

be obtained using the equation: )06.33T(

209441.14)p(ln sat

, where psat is in kPa and T is in K.(2+2 = 4)

5) A 3.0 TR cold storage has to be installed in a remote area where there is no electricity. Twooptions that use solar radiation as shown in the figure given below are to be considered. In the 1stoption, a solar collector system (SCS) is used to generate power in an organic Rankine Cycle(ORC), and the power generated is used to drive the compressor of a vapour compressionrefrigeration system (VCRS). In the 2nd option, the solar collector system supplies the requiredheat input to the generator of a vapour absorption refrigeration system (VARS). For both thesesystems, the solar collector provides heat input (in the heat exchanger, HX) at an average

temperature of 120 C, while heat rejection to the surroundings takes place at a temperature of

30 C. The evaporator operates at -18 C. The solar collector system has an efficiency of 0.6 (i.e.,only 60% of the incident solar radiation is transferred in the heat exchanger). The heat enginecycle (ORC) has an efficiency that is 70% of Carnot efficiency, while the VCRS has a COP that is

40% of Carnot COP. The power transmission efficiency from turbine (T) to compressor (C) is 95%.The absorption system (VARS) has an efficiency that is 45% of the ideal COP. Evaluate boththese options on the basis of total solar collector area required assuming an average incident solarradiation of 800 W/m2 of collector area. (7)

Common data: 1 TR = 3.517 kW, specific heat of liquid water = 4.18 kJ/kg.K


HX

SCS

Qsolar

30 C

30C

-18 C

30 C

VARS

VCRS

C

18 C

30 C

H

ORC

Qsolar

T

30 C

Option 1: Solar (SCS) + Heat Engine (ORC) + Vapour Compression System (VCRS)

Option 2: Solar (SCS) + Vapour Absorption System (VARS)

SCS


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End Semester, Autumn 2008 Mechanical Engineering Subject No. ME60085DD/PG(ME,AgFe) Subject Name : Refrigeration Systems

Answer all questionsMake suitable assumptions wherever necessary and state them clearly

----------------------------------------------------------------------------------------------------------------1a. A H2O-LiBr based vapor absorption refrigeration system has a refrigeration capacity of 1000

kW. The system operates at an evaporator temperature of 5 C (evaporator pressure= 0.872 kPa)

and a condensing temperature of 50 C (condenser pressure=12.33 kPa). The temperature of

weak solution leaving the absorber is 40 C, while the temperature of strong solution leaving the

generator is 110 C. The strong and weak solution mass fractions are 0.66 and 0.578, respectively.From solution property data the following enthalpy values are available: enthalpy of refrigerant atevaporator exit = 2510 kJ/kg, enthalpy of refrigerant at condenser inlet = 2708 kJ/kg, enthalpy of

refrigerant at condenser exit= 209 kJ/kg, enthalpy of weak solution at absorber exit= 154 kJ/kg,

enthalpy of weak solution at generator inlet= 37.5 kJ/kg and enthalpy of strong solution at

generator exit= 13 kJ/kg. The average density of the H2O-LiBr solution is 1800 kg/m3. From the

above data, find: a) COP; b) Power input to solution pump and c) Heat transfer rate in solution

heat exchanger (6)

1b. Find the total entropy generation rate and second law efficiency for the above system if thesystem is used to cool external water, which enters the evaporator at a flow rate of 40 kg/s and

13 C. A separate stream of external water enters the absorber at a flow rate of 60 kg/s and 32 C,extracts heat from absorber and then flows through the condenser to extract heat from thecondensing refrigerant. The required heat input to the generator is supplied by condensing a low-

pressure steam in the generator. The steam enters the generator as saturated vapour at 125 Cand leaves as saturated liquid. Neglect all frictional pressure drops on both refrigerant as well asexternal fluid sides. (6)

2. A plate fin-and-tube air-cooled condenser with a face area of 0.3 m2has tubes arranged in 2rows. The tubes made of copper have an inner diameter of 10 mm and an outer diameter of 12mm. The aluminum fins used have thickness of 0.2 mm and are placed at fin pitch of 2 mm andthe fin efficiency is 0.8. The center-to-center distance between tubes (tube pitch) in a given row

and between adjacent rows is equal to 25 mm. Air at an inlet temperature of 35 C and a flow rateof 0.8 m3/s flows through the condenser, while the temperature of refrigerant on the condensing

side may be assumed to be equal to 54 C. The average heat transfer coefficients on air andrefrigerant side are 63 W/m2.K and 2100 W/m2.K, respectively. The heat transfer resistanceoffered by the tube wall and due to fouling may be neglected. Using the data given above find theheat transfer capacity of the condenser and temperature of air at the outlet of the condenser. The

average density and specific heat (cp) of air may be taken as 1.2 kg/m3

and 1.022 kJ/kg.K,respectively. To simplify calculations, the log mean temperature difference (LMTD) of condensermay be assumed to be equal to the arithmetic mean temperature difference.

(8)3. In a 30 TR refrigeration capacity, flooded type shell-and-tube evaporator, refrigerant ammonia(NH3) flows in the shell side and brine flows through the tubes. The evaporator operates at a

temperature of 30 C, while the brine enters the evaporator at 18 C and leaves at 26 C. Thedryness fraction of NH3 after the expansion valve (float valve) is 0.2, while the dryness fraction of

NH3 at the exit of evaporator is 0.4. Saturated vapour at 30 C enters the compressor from the

surge tank. The latent heat of vaporization of NH3 at 30 C is 1360 kJ/kg. a) Find the mass flowrates of NH3 through the evaporator and compressor. b) Find the total number of tubes required if

the evaporator uses plain steel tubes with an outer diameter of 12 mm and an inner diameter of 10mm. Each tube is 1.5 m long. The average heat transfer coefficients on brine and NH3 side are3000 W/m2.K and 7000 W/m2.K, respectively. The fouling resistance on brine and NH3 sides are


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14

0.0001 m2.K/W and 0.00018 m2.K/W, respectively. Neglect tube wall resistance.(4+4 = 8)

4. A R134a based domestic refrigerator requires a refrigeration capacity of 120 W at 26 C for

freezer and 80 W at 2 C for fresh food compartment. Two options are to be evaluated. Option 1

uses a single stage vapour compression system with a single evaporator operating at 26 C andprovides refrigeration to both freezer and fresh food compartment. Option 2 uses two evaporators

and two independent compressors. In this option the low temperature evaporator operates at26 C and provides 120 W capacity for freezer, while the high temperature evaporator operates at

2 C and provides 80 W capacity to fresh food compartment. The compressed refrigerant from boththe compressors are mixed before the condenser. Both the options use a single condenser, which

operates at a condensing temperature of 54 C. The refrigeration effect at 26 C is 120 kJ/kg,

while it is 138 kJ/kg at 2 C. Assume that saturated vapour at evaporator temperature enters thecompressor for both the options, and the vapour behaves as an ideal gas with a gas constant of

0.0815 kJ/kg.K and an average (=cp/cv) value of 1.168. The isentropic efficiency and cost ofcompressor can be expressed as functions of compressor pressure ratio (rp) and/or refrigerationcapacity (Qe in watts). The cost of other components may be assumed to be same for both theoptions. The refrigerator has a life of 15 years and runs on an average 10 hours per day. The

average cost of electricity is Rs. 3 per kilowatt-hour (kWh). From suitable calculations find whichoption is better from total life cycle cost (initial + running) and other practical reasons.

)..) (..(

..)(.50

10950500030

60057

pe

e

rQefficiencyIsentropic

QRsincompressorofCost

+=

+=

The saturation pressure (psat) of R134a can be obtained using the equation:

)06.33T(

209441.14)p(ln sat

, where psat is in kPa and T is in K. (6)

5. Write brief but precise notes on any 4 of the following: (4 X 4 = 16)

a) Cascade refrigeration systemsb) Methods of producing refrigeration using solar energyc) Estimation of refrigerant pressure drop in condensers & evaporatorsd) Wilsons plote) Vapour jet refrigeration systemsf) Aircraft air conditioning systemsg) Vapour absorption refrigeration systems based on NH3-H2O

Common data: a) 1 TR = 3.517 kW; b) Specific heat of water = 4.18 kJ/kg.K



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End Semester, Autumn 2009 Mechanical Engineering Subject No. ME60085DD/PG(ME,AgFe) Subject Name : Refrigeration Systems

---------------------------------------------------------------------------------------------------------------------Answer any 5 questions

1a) With the help of suitable equations, plot the variation of power input to a centrifugalcompressor with flow rate for backward, radial and forward curved blades. Neglect the tangentialcomponent of velocity at the inlet to the impeller. (5)

1b) A cascade refrigeration system uses CO2 as refrigerant for low-stage and NH3 as refrigerantfor the high-stage. The system has to provide a refrigeration capacity of 30 kW and maintain therefrigerated space at36oC, when the ambient temperature (heat sink) is at 38oC. A temperaturedifference of 5 K is required for heat transfer in the evaporator, condenser and the cascadecondenser. Assume the temperature lift (Tcond-Tevap) to be same for both CO2 and NH3 cycles andfind a) Total power input to the system and b) Overall COP. Use the following equation forcalculating COP of a single stage system. (5)

0.85 1265c e

Carnot

T TCOP COP

=

, where Tc and Te are condensing and evaporating temperatures.

2a) The evaporator used in a domestic refrigerator has a UA value of 10 W/K. The average insidetemperature of the refrigerator is -15oC. The refrigerator is housed in a room which has atemperature of 30oC. The refrigeration load on the refrigerator under these conditions is 100 W. Ifthe average condenser temperature (Tc) is 54

oC, and the superheat at the evaporator exit is zero,find the required UA value for the condenser and the required power input to the compressor. The

isentropic efficiency of the compressor (is) is 50 %. The COP of the refrigerator can be estimatedusing the formula given below: (5)

. 1265c e

is Carnot

T TCOP COP

=

Where COPCarnot is the COP of the Carnot cycle operating at same Te and Tc.

2b) Find the total length of the tube required for the plate fin & tube type condenser used in thewindow air conditioner of 2.0 TR cooling capacity, which has a COP of 3.0. Use the data givenbelow. (5)

Inner and outer diameters of the tube = 14 mm and 16 mm, respectivelyHeat transfer coefficient on air side = 50 W/m2.KHeat transfer coefficient on refrigerant side = 1200 W/m2.KBare tube area on air side (Ab) per m of tube = 0.045 m

2/m of tube lengthRatio of fin area to bare tube area (Af/Ab) = 25Fin efficiency = 0.9Thermal conductivity of tube material = 385 W/m.KCondensing temperature = 54oCTemperature of air at condenser inlet = 35oCTemperature of air at condenser outlet = 43oC

3a) Explain briefly the working principle of capillary tube and explain why capillary tubes are not

used on large refrigeration capacity systems. (4)

3b) A thermostatic expansion valve (TEV) is used in an R-134a based car air conditioner thatoperates at an evaporator temperature of 7.2oC and a condensing temperature of 54oC. If the TEV


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16

spring exerts a pressure of 60 kPa, find the degree of superheat at evaporator exit. Assuming the

refrigerant vapour to behave as an ideal gas with a gas constant of 81.49 J/kg.K and a (=cp/cv)value of 1.1, find the COP of the system if the compressor has an isentropic efficiency of 0.7. Therefrigeration effect at the operating conditions is 130 kJ/kg. Use the following equation forestimating the vapour pressure data of R-134a. (6)

209414.41

33.06exp Tsatp

=

where psat is in kPa and T is in K.

4a) In a 300 TR capacity vapour absorption refrigeration system, chilled water enters theevaporator at 13oC and leaves at 7oC. The absorber rejects heat to external cooling water thatenters the absorber at 32oC and leaves at 36oC. The cooling water at 36oC then enters thecondenser to extract the condenser heat. The required heat input to the generator is supplied bycondensing saturated steam at 120oC. The cycle may be assumed to be symmetric (i.e., Qe = Qcand Qa = Qg). If the system has a COP of 0.7, find a) Total entropy generation rate in kW/K, and b)Second law efficiency. (Assume cp of water = 4.18 kJ/kg.K and 1 TR = 3.517 kW) (6)

4b) In a H2O-LiBr system, 1 kg/s of water vapour (hv=2504 kJ/kg) enters the absorber. The water

vapour is absorbed in the absorber by the strong solution (hss= 154 kJ/kg) coming from thegenerator. If the concentration of the strong solution entering the absorber is 0.66 and the

concentration of the weak solution (hws= 146 kJ/kg) leaving the absorber is 0.58, find the heatrejection rate in absorber. (4)

5) It is proposed to use a simple, open air cycle refrigeration system for air conditioning a railwaycompartment. In this system air from the exit of turbine enters the compartment directly and afterproviding the required cooling is compressed in the compressor, cooled in the high temperatureheat exchanger by rejecting heat to the surroundings and then flows into the turbine to completethe cycle. The refrigeration load on the compartment is 40 kW. The system is to be designed suchthat the compartment can be maintained at 101 kPa and 25oC, the design ambient temperature is45oC and a temperature difference of 7 K is required for heat transfer in the high temperature heatexchanger. To avoid cold discomfort to the passengers, the temperature of air at the inlet to thecompartment should be 10oC. The isentropic efficiencies of the compressor and turbine are 0.8and 0.9, respectively. There is a pressure drop of 0.5 bar in the high temperature heat exchanger.From the given information, find a) the required air flow rate, b) System COP and c) Entropygeneration rate in each component and total entropy generation rate. Comment on the efficiencyof each component. Take: cp = 1.005 kJ/kg.K and cv = 0.718 kJ/kg.K. (10)6) A vacuum cooling system based on steam jet refrigeration shown below is used to cool 100 kgof spinach (a leafy vegetable) from 22oC to 2oC in 30 minutes by evaporating water from spinach

in the vacuum chamber maintained at 2

o

C. Saturated motive steam at a pressure of 800 kPa fromthe boiler flows through the nozzle, entrains saturated water vapour from the vacuum chamberand leaves the diffuser as superheated vapour at an enthalpy of 2640 kJ/kg. Saturated liquid fromthe condenser is pumped to the boiler to complete the cycle. The nozzle has an efficiency of 0.8,while the entrainment efficiency is 0.9. The specific heat of spinach is 3.94 kJ/kg.K. Assuming aconstant evaporation rate of spinach and steady state operation, find a) Motive steam requiredfrom the boiler in kg/h, b) Heat rejection rate in the condenser in kW, c) Required diffuserefficiency, and d) System COP. Make suitable assumptions and state them clearly. The saturatedproperties of water are shown below. (10)

Psat

(kPa)

Tsat (oC) hf (kJ/kg) hv (kJ/kg) sf (kJ/kg

K)

sv (kJ/kg K)

0.706 2 8.401 2504 0.03064 9.1015.627 35 146.6 2564 0.505 8.351800 170.4 721.1 2769 2.046 6.663


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Schematic diagram of a vacuum cooling system for spinach (Problem 6)


Boiler, 800 kPa

Vacuum chamber2

oC

Condenser35

oC

Jet ejector

X=1

X=1

X=0

Pump

Spinach

To drainh=2640 kJ/kg


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Date : Time : 2 hours Full Marks : 60 No. of students : 16Mid-Semester 2010 Mechanical Engineering Subject No. ME60085ME(DD)/ME2 Subject Name : Refrigeration Systems

Temperature


1. A 300TR water chiller based on R134a operates at an evaporator temperature of 4oC and acondensing temperature of 40oC. Water which is to be chilled enters the evaporator at 15oC andleaves at 7oC, whereas the cooling water from a cooling tower enters the condenser at 32oC andleaves at 36oC. The system uses a compressor that has an isentropic efficiency of 0.75. Thecondition of refrigerant at the exits of condenser and evaporator is saturated. a) Using the statepoint property data given in the table, calculate the COP of the water chiller b) Also calculate theCOP using the expression given below, which is obtained by applying first and second laws fromthe beginning. Assume that the entropy generation ( ) is due to i) Non-isentropic compression,

ii) Heat transfer with finite temperature difference across condenser, iii) Heat transfer with finitetemperature difference across evaporator, iv) De-superheating, and iv) Throttling. c) Evaluate

various exergy losses in kW ( ) and comment on the suitable means for improvingthe performance of the system. (3+10+5 = 18)

Where is the Carnot COP of a refrigeration cycle operating between entropic average

temperatures of the heat source ( ) and heat sink ( ), Qe is the refrigeration capacity (in kW) and

is the entropy generation rate (in kW/K) due to ith irreversibility.

Quality Pressure Enthalpy Entropy4oC 0 337.9 kPa 57.25 kJ/kg 0.2239 kJ/kg.K4oC 1 337.9 kPa 252.8 kJ/kg 0.9293 kJ/kg.K40oC 0 1017 kPa 108.3 kJ/kg 0.3949 kJ/kg.K40oC 1 1017 kPa 271.3 kJ/kg 0.9154 kJ/kg.K- - 1017 kPa 275.7 kJ/kg 0.9293 kJ/kg.K

Table 1: Properties of R134a

2a. Using suitable equations and diagrams, explain under what conditions clearance in an ideal

reciprocating compressor affects only the capacity, but not the COP. (6)

2b. From laboratory measurements at a design condensing temperature of 54oC, the refrigerantmass flow rate (mr) and specific work input to the reciprocating compressor (wc) of a domesticrefrigerator are obtained as functions of evaporator temperature (te) as shown below:

and

where te is inoC, mr is in grams per second and wc is in kJ/kg.

For a design evaporator temperature of 23

o

C, a designer chooses an electrical motor of 160 Wcapacity with an efficiency of 0.95. a) Is the chosen motor capacity adequate at design conditions?b) If the evaporator temperature after each off-cycle is 43oC, find whether the motor will beoverloaded or not as the evaporator temperature reduces from 43oC to the design temperature of


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20

Evaporator-I

Evaporator-II

Condenser

FlashTank


Date : Time : 3 hours Full Marks : 100 No. of students : 16End-Semester 2010 Mechanical Engineering Subject No. ME60085

ME(DD)/ME2 /AgFe(UG) Subject Name : Refrigeration Systems

Answer all questionsMake suitable assumptions and state them clearly

1. The air conditioned compartment of a passenger train requires a design refrigeration capacity of30 TR. The design temperatures for inside compartment and outside ambient (heat sink) are 25oCand 43oC, respectively. Two options are considered: Option 1: A R22 based, saturated, singlestage vapour compression refrigeration system and Option 2:

A simple, open type air cyclerefrigeration system based on Bell-Coleman cycle. The following information is provided:

R22 system:T for heat transfer: evaporator = 18 K; condenser = 11 K, isentropic efficiency ofcompressor = 0.65, isentropic index of compression (k) = 1.082, saturated enthalpy and density ofrefrigerant at evaporator outlet = 407.4 kJ/kg and 26.24 kg/m3 and saturated enthalpy of

refrigerant at condenser outlet = 268.8 kJ/kg. The relation between saturation pressure andtemperature for R22 is given by the equation:

Air cycle: Tminimum for heat transfer at heat exchanger(s) = 5 K, isentropic efficiencies ofcompressor and turbine = 0.95, pressure ratio = 1.3 times the minimum pressure ratio required fora finite output. For air assume, cp = 1.005 kJ/kg.K and cv = 0.718 kJ/kg.K.

Evaluate the above two options in terms of a) Operating pressures; b) Mass flow rates of workingfluids; c) Power consumption, and d) Exergy destruction rates (=Tamb.Sgen). (2+4+6+8 = 20 marks)

2. Shown here is an ammonia-based multi-stage, multi-evaporator system with a flash tank. The evaporator-I,which has refrigeration capacity of 20TR operates at an

evaporator temperature of 36oC, while evaporatorII witha refrigeration capacity of 40TR operates at an evaporatortemperature of 2oC. The refrigerant condenses at 38oC.The low and high- stage compressors have isentropicefficiencies of 0.65 and 0.8, respectively. The isentropicindices of compression for the low and high stagecompression processes are: 1.301 and 1.283,

respectively. Assume saturated condition for refrigerant atthe exit of the evaporators, flash tank and condenser.Using the saturated property data given below, find totalpower input to the system and cycle efficiency (=COP/COPIdeal).

T(oC) P (kPa) x h (kJ/kg) s(kJ/kg.K)

d (kg/m3)

-36 88.42 0 36.88 685.3-36 88.42 1 1414 6.169 0.7843

2 462.6 0 209.3 635.82 462.6 1 1464 5.595 3.71138 1471 0 380.8 582.638 1471 1 1489 5.176 11.38


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(10+5 = 15 marks)3a. Show that neglecting effects of shock and refrigerant vapour velocity at the exit of evaporatorand diffuser, the ratio of mass flow rate of motive steam to the mass flow rate of refrigerantthrough the evaporator (mb/mr) is given by the equation:

Where N, e and d are the isentropic efficiencies of nozzle, entrainment and diffuser,

respectively, h1 and h3 are the enthalpies at the inlet to the nozzle and diffuser, and h2s and h4s arethe enthalpies at the exits of the nozzle and diffuser when expansion in the nozzle andcompression in the diffuser are reversible and adiabatic.

(8 marks)3b. A Vapour Jet Refrigeration System based on the refrigerant R134a has a refrigeration capacityof 75 TR. The system operates at a boiler pressure of 2500 kPa, a condensing temperature of32oC and an evaporator temperature of 7oC. Saturated refrigerant vapour from the boiler entersthe nozzle and saturated refrigerant vapour at evaporator pressure enters the diffuser. Theisentropic efficiencies of nozzle, entrainment and diffuser are 0.8, 0.9 and 0.95, respectively.Saturated liquid leaves the condenser, a part of which is pumped to the boiler pressure and theremaining is throttled to the evaporator pressure. Based on this information find, a) COP and b)

cycle (or 2nd

law) efficiency based on internal temperatures. Use the following saturated propertydata for calculations. Assume at condenser pressure a constant vapour specific heat (Cp) of 1.08kJ/kg.K and neglect pumping work.

T oC P kPa X h kJ/k s kJ/k .K77.54 2500 1 280.8 0.892377.54 2500 0 169.6 0.575332 815.9 1 267.6 0.918132 815.9 0 96.48 0.35737 374.9 1 254.5 0.92787 374.9 0 61.33 0.2384

(8+4 = 12 marks)

4. A single stage vapour compression refrigeration system working with refrigerant R134a has arefrigeration capacity of 3 TR. The system operates between an evaporator temperature of 25 C

and a condensing temperature of 38 C. The isentropic efficiency of the compressor is 0.7. Acounterflow, tube-in-tube type condenser is to be designed for this system. Coolant water at atemperature of 27oC and with a mass flow rate of 0.6 kg/s enters the condenser. The coolantwater flows through the inner tube of the condenser that has an inner diameter of 3.5 cm and anouter diameter of 3.8 cm. A constant convective heat transfer coefficient of 3000 W/m2.K may beassumed on the waterside. The average heat transfer coefficient on the refrigerant side may betaken as 350 W/m2.K in the de-superheating zone and as 1700 W/m2.K in the condensing zone.

Integral fins (finned surface efficiency 0.95) are provided on the refrigerant side so that theheat transfer area increases by 2.5 times compared to a bare tube of same diameter. The fouling

factor on waterside is 0.0002 m2.K/W, while it may be neglected on the refrigerant side. The tubewall has a thermal conductivity of 385 W/m.K. The state of refrigerant at the exit of evaporator andcondenser is saturated. The average isentropic index of compression is 1.056. Assume therefrigerant vapour to behave as an ideal gas with a gas constant of 0.08148 kJ/kg.K and a vapourspecific heat of 1.218 kJ/kg.K at condenser pressure. Based on the information provided, findthe required length of the condenser, a) considering de-superheating and condensing zonesseparately, and b) assuming condensation throughout the condenser tube length. Use theproperties given below for calculations:

T(oC) P (kPa) x h (kJ/kg) s-25 106.5 0 19.04 0.0789

-25 106.5 1 235.3 0.950438 963.7 0 105.3 0.385538 963.7 1 270.4 0.9161

(10+5 = 15 marks)


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Cascade condenser

5. With suitable figures, assumptions and all relevant equations, explain clearly the step-wisecalculation procedure that can be used to estimate the required length of an adiabatic capillarytube for a given inlet and outlet conditions and mass flow rate. (10 marks)

6. A frozen food cold storage has to be maintained at 18oC by using a refrigeration system. Thecold storage has a cooling load of 10TR. It is proposed to employ a hybrid cascade system thatcombines a vapour compression refrigeration syetm (VCRS) with a vapour absorption refrigerationsystem (VARS) as shown in the figure. The vapour absorption system is driven by condensingsaturated steam available at 125oC in the generator. The latent heat of vapourization of steam at125oC is 2188 kJ/kg. Heat rejection from the system takes place to ambient that is at 38oC. All the

heat exchangers are designed with a T of 5K for heat transfer. The COPs of VCRS and VARSare given by the equations:

Where Tc and Te are the evaporating and condensing temperatures of the vapour compression

cycle, COPIdeal,VCRS is the ideal COP of VCRS operating between Tc and Te and is the isentropicefficiency of the compressor. COPIdeal,VARS is the ideal COP of VARS operating between agenerator temperature of Tg, evaporator temperature of Te,a and a condenser/absorber

temperature of Ta. The isenstropic efficiency of the compressor (is) is given by the equation

All the temperatures used in the above equations are absolute temperatures. Based on thisinformation, find: a) Expression for overall COP (COPoverall) in terms of COPVCRS and COPVARS,b) power input to compressor and required steam flow rate in generator in kg/h, and c) totalentropy rate of the cascade system assuming a condensing temperature of 10oC in the cascadecondenser.

(6+8+6 = 20 marks)

Common data: 1 TR = 3.517 kW, specific heat of liquid water = 4.18 kJ/kg.K

---End of the paper ---

10TR at 18oC

To ambient at38

oC

To ambient at38

oC

Saturated steam at125

oC

Wc

Evaporator

Cascade condenser

CondenserGenerator

Absorber


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Date : Time : 2 hours Full Marks : 60 No. of students : 50

Mid-Semester 2011 Mechanical Engineering Subject No. ME60085

Subject name: Refrigeration Systems

Answer any 4 questions

Make suitable assumptions wherever necessary and state them clearly

1a) An engineer wishes to design a domestic refrigerator whose energy consumption is less thanor equal to 1 kWh per day. On an average the refrigerator compressor runs for 10 hours a dayand the average refrigeration load is 150 W. The average refrigerated space and external ambient

temperatures are 20oC and 35oC, respectively. To achieve the design goal of 1 kWh per day,what should be the maximum allowable entropy generation rate of the refrigerator (in W/K)?

(5)

1b) Saturated liquid water at 25

o

C is throttled in a valve so that its pressure drops by 1 kPa. Findthe dryness fraction (quality) of water at the exit of the valve assuming an average latent heat ofvaporization of 2450 kJ/kg, average liquid specific heat of 4.19 kJ/kg.K and an average vapourspecific heat of 1.9 kJ/kg.K. The following equation relates the saturation pressure, psat (in kPa)with temperature, T (in K) of water.

Assuming the water vapour to behave as an ideal gas, find the void fraction (volume occupied bythe vapour to the total volume) at the exit of the valve. Take the density of liquid water as 998

kg/m3

. (6+4 = 10)

2a) Find the stroke length and bore of a reciprocating compressor used in a window air conditionerof 1.5 TR cooling capacity from the following data. Evaporator pressure = 625.5 kPa, condenserpressure = 2147 kPa, refrigeration effect=154 kJ/kg, density of vapour at compressor inlet = 23.41kg/m3, index of compression, k = 1.101, clearance ratio = 0.04, number of cylinders = 2, RPM =2950. Assume the actual volumetric efficiency to be 80 % of the clearance volumetric efficiencyand use a suitable stroke length-to-bore ratio. If the design frictional mean effective pressure of thecompressor is 0.5 bar, what is the indicated power input to the compressor? The shaft power inputto the compressor at design conditions is 1.75 kW. (6+4 = 10)

2b) Explain what practical reasons encourage the designers to design reciprocating compressorsthat operate at high RPM? What are the advantages and disadvantages of running thecompressor at high RPM? (5)

3a) Using suitable equations and velocity diagrams, explain why compared to a backward curvedblade, a forward curved blade is more compact but less efficient and may also lead to overloadingof the compressor motor. (9)

3b) The specific work input to a single stage centrifugal compressor is 21 kJ/kg. The impeller usesa radial curved blade (blade angle = 90o) and rotates at 6000 RPM and is designed such that theimpeller reaction is 0.3 (i.e., 30 % of the power input is used to increase the pressure inside the

impeller, while the rest is used to increase the kinetic energy of the refrigerant). Find the requiredimpeller diameter and absolute, tangential and normal velocities of the refrigerant at the impellerexit. (6)


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24

4a) Take a small element L of an adiabatic capillary tube in two-phase region and write therelevant mass, momentum and energy balance equations. Assume steady and homogeneous

flow. Explain how the length L can be determined if all the relevant parameters and properties ofrefrigerant at the inlet, and the temperature at the outlet of the element are given. Assume that allsaturated properties of the refrigerant are known from property data.

(5+5 = 10)

4b) With the help of suitable diagrams explain why capillary tubes are most widely used in smallcapacity refrigeration and air conditioning systems but not in larger capacity systems.

(5)

5a) An R134a based refrigeration system has a design cooling capacity of 1.5 kW when operatingas a single stage saturated cycle between an evaporator temperature of 2oC and a condensingtemperature of 38oC. A hot gas bypass valve shown in the figure is used to control the capacitywhile maintaining the operating conditions and mass flow rate through the compressor same.What should be the refrigerant flow rate through the hot gas bypass valve (HGB) if the requiredcapacity at off-design condition is 0.6 kW? What are the dryness fraction (x) values at evaporator

inlet for design and off-design conditions? Is this method of capacity control efficient? Justify youranswer with suitable reasons. Use the refrigerant property data given below:

t (oC) p (kPa) x h (kJ/kg) s (kJ/kg.K)

2 314.8 0 54.55 0.2141

2 314.8 1 251.6 0.9303

38 963.7 0 105.3 0.3855

- 963.7 - 274.9 0.9303

(4+2+3 = 9)

5b) Draw the T-s and p-h diagrams of a single stage vapour compression refrigeration cycle thatuses a zeotropic mixture as refrigerant. Explain with suitable equations under what conditions azeotropic mixture offers better performance compared to a pure fluid. What are the problems withzeotropic mixtures?

(2+3+1 = 6)

Common data: 1 TR 3.517 kW

Universal gas constant = 8.314 kJ/kmol.K

End of the paper

(HGB)

te=2oC

tc=38oC

Hot gas bypass system


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Department of Mechanical Engineering

Time : 3 hours Full Marks : 100 No. of students : 50

End-Semester 2011 Subject name: Refrigeration Systems Subject No. ME60085

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Answer any 5 questions

1a) A R502 based, 2-stage refrigeration system with a flash chamber is shown below. As shown, the lowand high temperature evaporators which operate at evaporator temperatures of 38oC and 0oC haverefrigeration capacities of 12 kW and 30 kW, respectively. Refrigerant condenses at a temperature of 45oC.The refrigerant at the exit of evaporators, condenser and flash chamber may be assumed to be saturated.The compression in low and high stage compressors may be assumed to be reversible and adiabatic. Inaddition, refrigerant vapour may be treated as an ideal gas with a molecular weight of 111.6 kg/kmol and anaverage specific heat of 0.8 kJ/kg.K. The isentropic index of compression (k) may be taken as 1.09. Usingthe property data given below, find the COP of the system.

(12)

t, oC P, kPa x h, kJ/kg s, kJ/kg

38 141.5 0 2.273 0.00890538 141.5 1 171.4 0.7281

0 573 0 42.22 0.16480 573 1 188.9 0.7017

45 1880 0 96.94 0.346345 1880 1 203.5 0.6814

1b) If the above system maintains a frozen food chamber at

32oC and a fresh food chamber at 5oC while rejecting heat tothe surroundings which is at 38oC, find the total entropygeneration rate of the system and cycle efficiency (=ratio ofactual COP to reversible cycle COP). (8)

2) A 4-pass, horizontal, shell-and-tube R22 condenser has 60 copper tubes of 14 mm inner diameter (di)and 18 mm outer diameter (do). The thermal conductivity of copper (kcopper) is 385 W/m.K. Cooling waterflows through the tubes while the refrigerant condenses on the outside of the tubes. The outer surface ofthe tubes is provided with integral fins such that the ratio of outer-to-inner heat transfer area is 1.5. Thecooling water flow rate through the condenser is 5 litres per second. The inlet and outlet temperatures ofthe cooling water are 27oC and 33oC, respectively, while the refrigerant condenses at 38oC. The fouling

factor on waterside is 176 X 10 6 m2.K/W, while that on the refrigerant side is negligible. The 60 tubes arearranged in 14 vertical columns. Find the length of the tubes required to meet the requirement. Assume

suitable temperature difference (t) between the refrigerant and tube wall and verify the correctness of theassumed value at the end (you need not repeat the calculations). Use the following correlations for heat

transfer coefficients on water (hw) and refrigerant (hr) sides. The mean properties of water and refrigerantare given below.

Refrigerant side: ; waterside:

In the above equations, Nis the number of tubes per column and Redis the Reynolds number based oninner diameter diand gis the acceleration due to gravity (9.81 m/s

2)

Refrigerant at 38oC: hfg = 168.8 kJ/kg; f = 1138 kg/m3, kf = 0.08 W/m.K, f = 0.000144 kg/m.s

Water at 30oC:w = 996 kg/m3, kw = 0.6 W/m.K, w = 0.0008 kg/m.s, cpw = 4.18 kJ/kg.K, Prw= 5.535

(20)3a) Explain with the help of neat diagrams how boiling of refrigerant in a fin-and-tube type evaporator differsfrom boiling in a shell-and-tube evaporator with refrigerant boiling on the shell side. (6)


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3b) For the same tube dimensions and operating pressure and temperature, explain why pressure dropduring refrigerant evaporation is higher compared to that in condensation. (4)

3c) In a shell-and-tube type evaporator, refrigerant boils at 4oC outside a tube of length 3.0 m and outerdiameter 10 mm, while water flows through the tube. The tube wall which is 0.5 mm thick is made of highthermal conductivity material such that its resistance to heat transfer is negligible. The average heattransfer coefficient on water side is 6000 W/m2.K, while the average heat transfer coefficient on refrigerant

side (hr in W/m2.K) is given by the relation, , where t is the average temperature

difference between the refrigerant and the tube surface (in K). Water enters the tube at a velocity of 1.5 m/sand a temperature of 15oC. Find the heat transfer rate between water and refrigerant and temperature ofwater at the outlet of the tube. For calculating heat transfer rate from water to refrigerant, use arithmeticaverage temperature difference instead of the logarithmic average temperature difference. Assume thedensity of water to be 1000 kg/m3 and its specific heat to be 4.19 kJ/kg.K. Assume a suitable initial guessvalue for tand carry out at least two iterations. (10)

4a) In a R134a refrigeration system the condenser is kept at ground level, whereas the expansion deviceand evaporator are located at a height of 15 m from the condenser. The condenser pressure is 1450 kPa. Ifthe frictional pressure drop in the pipeline connecting the condenser to expansion device is 30 kPa, find theminimum degree of subcooling required at condenser exit so that only liquid enters the expansion device.The density of R134a liquid may be taken as 1083 kg/m3 and the acceleration due to gravity is 9.81 m/s2.

Assume that the connecting pipeline does not exchange heat with the surroundings. Use the followingequation which relates saturation pressure of R134a with temperature.

(6)

; where psat is in kPa and T is in K

4b) The inlet pressure of an R134a evaporator is 140 kPa. A designer wishes to maintain a superheat of 5K at the evaporator exit and selects an internally equalized thermostatic expansion valve assuming that therefrigerant pressure drop across evaporator is negligible. What should be the spring pressure for thiscondition? Readings show that there is a pressure drop of 20 kPa across the evaporator. Under theseconditions, what is the actual degree of superheat at evaporator exit? What type of TEV should be selectedto meet the requirement of 5K and what should be the correct spring pressure? Use the equation given

above for relating saturation pressure of R134a to temperature. (8)

4c) Using fundamental mass, momentum and energy balance equations show that for a given inlet

conditions, the refrigeration capacity of an expansion valve, , where c is a constant and p is the

pressure drop across the valve. State the assumptions made while arriving at the above expression.(6)

5a) A H2O-LiBr based single stage vapour absorption refrigeration operates at an evaporator temperatureof 10oC (psat = 1.23 kPa) and a condensing temperature of 40

oC (psat = 7.38 kPa). The correspondingtemperatures of solution at the exit of absorber and generator are: 30oC and 100oC, respectively. Theconcentration of weak and strong solutions at the exits of absorber and generator are 0.5 and 0.664,

respectively. The enthalpy of weak and strong solutions at the exits of absorber and generator are 168

kJ/kg and 52 kJ/kg, respectively. The average density and specific heat of solution are 1200 kg/m3 and2.0 kJ/kg.K, respectively, while the effectiveness of solution heat exchanger is 0.52. If under full loadconditions, the mass flow rate of weak solution through the solution pump is 1.2 kg/s, find a) refrigerationcapacity at full load, b) COP and, c) solution pump power assuming a pumping efficiency of 70 %. Theenthalpy of water vapour (hv) and liquid water (hf) are given by: , where

enthalpy is in kJ/kg and temperature t is in oC.(12)

5b) Find entropy generation rate in the evaporator, condenser, refrigerant expansion device and solutioncircuit for the above system, if saturated steam at 120oC is condensed in the generator to provide thenecessary heat input to the system, the system rejects heat to surroundings which are at 28oC and theevaporator maintains an air conditioned space at 25oC. Take the saturated liquid water entropy values at

10o

C and 40o

C as 0.1508 kJ/kg.K and 0.5729 kJ/kg.K, respectively. (8)


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Old Question Papers 2006-11-2