ME 417 Design of Alternative Energy Systems

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1 ME 417 Design of lternative Energy Systems Thermal/Economics ractice roblems 1. company has decided to air condition their manufacturing facility. They are trying to decide between an absorption refrigeration system and a vapor compression refrigeration system. The following economic data is available: bsorption System Vapor Compression System Capital $125,000 $85,000 nnual Operating $15,000 $,000 The life of both systems is estimated to be 15 years and the interest rate for the company is 13%. Using a present value analysis determine which system should be purchased. hat would be the annual operating cost of the vapor compression system needed to make the two systems equivalent in terms of cost? Our present value for either system will be calculated from V cap + op (i, ) where our / function is given by Then and ( ) ( 1+ i) i( 1+ i) 15 ( ) ( ) V 125, , $221,936 ( V) V 85,000 +, $214,248 So the vapor compression system has the lower cost and should be purchased. Since electricity prices have a tendency to increase over time, it might be of interest to determine an operating cost for the vapor compression system that would make its cost equivalent to that of the absorption system. ence we want V V ( ) ( ) $221,936 V 1

2 ME 417 Design of lternative Energy Systems so that ( ) ( V) - ( ) cap op V (i, ) or a 6% increase. V 221,936-85, $21, homeowner is considering replacing their current gas fuel heating system with a solar heating system. Both systems are to last years and the homeowner s interest rate is 8%. The initial cost for the furnaces is $10 and the annual fuel cost $600. Determine the capital cost of the solar system that will make it competitive with the gas fueled system. To determine the acceptable capital cost of our solar system, we will let it be equal to the present value cost of the gas fueled system or ( ) ( V) ( ) + ( ) cap S G cap G op G For i 0.08 and years, we find so that ( ) ( 1+ i) i( 1+ i) ( ) ( ) cap $7091 S (i, ) n experimental research station located in the wilderness must provide its own electricity. Two options are being considered: wind turbine and gasoline powered generator. Determine the energy cost in $/(k hr) for each proposed system. The following conditions apply: System ind Turbine Gasoline Generator Generating ower (k) % Up Time Capital nnual Maintenanc e nnual Operating 15 50% $15,000 $500 $ % $500 $500 $2,500 For the calculation an interest of rate of 15% and a lifetime of years should be used. 2

3 ME 417 Design of lternative Energy Systems For the wind turbine we have: cap (/,0.15,) + m + o i(1+ i) (0.15)(1.15) ( /,i, ) (1+ i) -1 (1.15) -1 (15,000)(0.1598) $ E (power)(up time)(hrs/year) (15)(0.5)(24)(365) 65,700 k hr cost /E ( )/(65,700) $/(k hr) For the gasoline generator we have: cap (/,0.15,) + m + o (500)(0.1598) $ E (power)(up time)(hrs/year) (10)(0.75)(24)(365) 65,700 k hr cost /E ( )/(65,700) $/(k hr) Based on these numbers we would choose the wind turbine system. 4. solar collector receives heat transfer from the sun at a rate of k per m 2 of collector area and provides energy to a storage unit whose temperature remains constant at 500 K. heat engine interacts with the storage unit as its high temperature reservoir, generates 1000 k of work output, and interacts with the surroundings at C as its low temperature reservoir. Determine the minimum theoretical collector area required. e begin by sketching our device interactions igh Temperature eat Reservoir at T (storage unit) eat Engine net L Low Temperature eat Reservoir at T L (surroundings) 3

4 ME 417 Design of lternative Energy Systems The heat transfer from the storage unit is provided the solar collector and is given by (0.315)collector Since we are looking for the minimum collector area, we will assume that the heat engine operates as a Carnot cycle, then T ( 273) 1- L + η th ηcarnot T 500 But by definition we have net η th or solving for the heat transfer 1000 net k η th and solving for the collector area collector 7668 m (0.315) (0.315) 5. In the month of January, a certain dwelling requires 2.4 x 10 6 kj per day to maintain its temperature at C. s a means of proving the required heating, a heat pump cycle is under consideration that would operate between the dwelling and a nearby pond at 10 C. The manufacturer claims that the net work required to operate the heat pump is 1.6 x 10 5 kj per day. Evaluate this claim. gain we begin by sketching our device interactions 4

5 ME 417 Design of lternative Energy Systems igh Temperature eat Reservoir at T (dwelling) eat ump net L Low Temperature eat Reservoir at T L (pond) To evaluate the claim we must compare the operating CO to the Carnot cycle CO for the heat pump 1 1 COCarnot 29.3 T L 1- T 293 The operating CO is given by x 10 CO actual 15 5 net 1.5 x 10 and since CO actual < CO Carnot the claim is possible. 6. n innovative way of power generation involves the utilization of geothermal energy, the energy of hot water that exists naturally underground (hot springs), as the heat source. If a supply of hot water at 140 C is discovered at a location where the environmental temperature is C, determine the maximum thermal efficiency a geothermal plant built at that location can have. If the power output of the plant is to be 5 M, what is the minimum mass flow rate of hot water needed? e begin by sketching our device interactions 5

6 ME 417 Design of lternative Energy Systems Geothermal Source igh Temperature eat Reservoir at T eat Engine net L Environment Low Temperature eat Reservoir at T L The maximum thermal efficiency will occur when the heat engine operates as a Carnot cycle, T ( + 273) η 1- L th η Carnot T ( ) The minimum mass flow rate of hot water corresponds to the maximum thermal efficiency or 5000 ( ) net min 17,8 k ηcarnot erforming a first law analysis on the hot water stream we have m ( hout - hin ) For the minimum flow rate we will assume that the hot water is cooled down to the environment temperature, then -17,8 m c T T (4.1978) 140 ( ) ( ) out 34.2 kg/s in 7. heat pump provides 30,000 Btu/hr to maintain a dwelling at 68 F on a day when the outside temperature is 35 F. The power input to the pump is 1 hp. If electricity costs 8 cents per kilowatt-hour, compare the actual operating cost per day with the minimum theoretical operating cost per day. 6

7 ME 417 Design of lternative Energy Systems e sketch our device interactions Dwelling igh Temperature eat Reservoir at T eat ump net L Outside Low Temperature eat Reservoir at T L The cost is given by (0.08)net For the actual cost we have () act (0.08)(1)( k/hp)(24 hr/day) $1.43 To calculate the minimum cost we will allow the heat pump to operate as a Carnot cycle, so that 1 1 COCarnot 16 T L 1 T 528 Then the minimum possible power input is 30,000 ( ) net min 1875 Btu/hr CO 16 Carnot k and the minimum cost is () min (0.08)(0.5495)(24 hr/day) $1.06 7

2 nd Law of Thermodynamics

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