Step 1: Draw a diagram to represent the system. Draw a T-s process diagram to better visualize the processes occurring during the cycle.

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1 ENSC 61 Tutorial, eek#8 Ga Refrigeration Cycle A refrigeration yte ug a the workg fluid, conit of an ideal Brayton cycle run revere with a teperature and preure at the let of the copreor of 37C and 100 kpa. The copreor ha a copreion ratio of 15:1 and ut be upplied to the conditioned pace at 17C. The heat load on the yte i 10 k. a) Calculate the required a flow rate of. b) Calculate the required net-work put. c) Calculate the COP for thi refrigeration yte. d) Calculate the coolg capacity of the yte if the turbe were reoved and replaced with an adiabatic expanion valve (aue tate 1,, 3 and the a flow rate of rea unchanged) Step 1: Draw a diagra to repreent the yte Turbe 3 Copreor net, 1 Draw a T- proce diagra to better viualize the procee occurrg durg the cycle. T 3 1 M. Bahrai ENSC 61 (S 11) Revered Brayton Cycle 1

2 Step : rite out what i required to olve for a) b) net, c) COP R d) Ug COP R i proce poible e) if turbe i reoved and replaced with an adiabatic expanion valve. Step 3: Prepare a property table T(K) P(kPa) Step : State your auption Auption: 1) ke, pe 0 ) cold--tandard auption are applicable 3) teady operatg condition ) copreor and turbe are ientropic 5) heat exchanger are contant preure device Step 5: Solve Part a) The a flow rate of required can be detered by exag a coponent the yte where all the energy tranfer and tate pot are known. In thi cae, the conditioned pace (repreented by the low teperature heat exchanger) fit thee criteria. An energy balance on the conditioned pace i perfored a hown Eq1. h 1 h (Eq1) Iolatg Eq1 for the a flow rate of and recognizg that for an ideal ga the enthalpy i a function of teperature only, Eq1 can be rewritten a Eq. 1 p 1 T h h c T (Eq) M. Bahrai ENSC 61 (S 11) Revered Brayton Cycle

3 The heat load on the yte i given a 10 k. The teperature at the let and outlet of heat exchanger are given the proble tateent a 90K(17C) and 310K(37C) repectively. Fro Table A- for at roo teperature c p = kj/kg*k. Subtitutg thee value to Eq, the required a flow rate of can be detered a hown below. c p T T kj kj [ kg K 98 1 kg Anwer a) Part b) The net work put to the copreor can be detered fro an overall energy balance perfored on the yte a hown Eq3. Alternatively, an energy balance could have been perfored on the copreor., (Eq3) net The low teperature heat tranfer i given the proble tateent a 10 k. The high teperature heat tranfer i till unknown. Perforg an energy balance on the high teperature heat exchanger, Eq i obtaed. ( h ) 3 h (Eq) Aga, recognizg that for an ideal ga the enthalpy i a function of teperature only, Eq can be rewritten a Eq5. c ( T ) 3 T p (Eq5) The a flow rate of wa detered part a) a 0.98 kg/. Fro Table A- for at roo teperature c p = kj/kg*k. The teperature at the let and outlet of the high teperature heat exchanger ut be detered. Sce the copreion proce i odeled a ientropic, the equation that relate the teperature ratio to the preure ratio through k for an ideal ga undergog an ientropic proce can be ued to detere the high teperature heat exchanger let teperature a hown Eq6. M. Bahrai ENSC 61 (S 11) Revered Brayton Cycle 3

4 k 1 P k 0. T T1 310[ 15 K P [ ] (Eq6) Siilarly, the expanion proce i alo odeled a ientropic, and the equation that relate the teperature ratio to the preure ratio through k for an ideal ga undergog an ientropic proce can be ued aga to detere the outlet teperature of the high teperature heat exchanger a hown Eq7. T 90[ T3 68.7[ k 1 0. P k 1 1. P 15 3 (Eq7) Subtitutg the known value to Eq5, the high teperature heat tranfer can be detered a hown below. ( ) kg kj cp T3 T [ kg K 1.7[ k ] The net work put can now be detered ug Eq3 a hown below. net, 1.7[ k ] 10[ k ] 11.7[ k ] Anwer b) Part c) The COP for the refrigerator can be detered ter of the benefit/cot. The benefit thi ituation i the coolg provided by the yte, given a 10 k. The cot thi ituation will be the net work upplied to the yte which wa detered part b) a 11.7 k. Ug thee defition the COP can be calculated a hown below. Benefit 10[ k ] COPR 0.85 Anwer c) Cot 11.7[ k ] net, M. Bahrai ENSC 61 (S 11) Revered Brayton Cycle

5 Part d) The coolg capacity of the odified yte can be detered fro an overall energy balance on the yte a hown Eq8. Alternatively, an energy balance could have been perfored on the conditioned pace. net, (Eq8) Sce the propertie of the yte at location and 3 are aued unchanged, the heat rejected by the yte the high teperature heat exchanger will rea unchanged. If the turbe were replaced with an expanion valve, all of the copreor work would have to be upplied externally. The copreor work can be calculated fro an energy balance over the copreor a hown Eq9. ( h h1) (Eq9) Recognizg that for an ideal ga the enthalpy i a function of teperature only and ubtitutg the other known value to Eq9, the work upplied to the copreor can be detered a hown below. ( ) kg kj cp T T [ kg K 181.[ k ] Subtitutg the known value to Eq8, the coolg capacity can be detered. n 1.7[ k ] 181.[ k ] 159.5[ k ] Anwer d) The refrigerator would no longer reove heat fro the conditioned pace but would upply heat. Therefore, the yte would have no coolg capacity. Step 6: Concludg Reark & Dicuion a) The a flow rate of i 0.98 kg/. b) The net work upplied to the copreor i 11.7 k. c) The COP i d) If the turbe were replaced with an expanion valve the yte would have no coolg capacity. M. Bahrai ENSC 61 (S 11) Revered Brayton Cycle 5

Unit 12 Refrigeration and air standard cycles November 30, 2010

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