Assignment 7
Assignment Set 7 Problem 10.21 In a vapor-compression refrigeration cycle, ammonia exits the evaporator as saturated vapor at -22°C. The refrigerant enters the condenser at 16 bar and 160°C, and saturated liquid exits at 16 bar. There is no significant heat transfer between the compressor and its surroundings, and the refrigerant passes through the evaporator with a negligible change in pressure. If the refrigerating capacity is 150 kW, determine (a) the mass flow rate of the refrigerant, in kg/s. (b) the power input to the compressor, in kW. (c) the coefficient of performance. (d) the isentropic compressor efficiency. (e) the rate of entropy production, in kW/K, for the compressor. Known: Ammonia is the working fluid in a vapor-compression refrigeration system. Data are known at various locations and the refrigerating capacity is given. Find: Determine (a) the mass flow rate of the refrigerant, (b) the compressor power, (c) the coefficient of performance, (d) the isentropic compressor efficiency, and (e) the rate of entropy production for the compressor. Schematic and Known Data: Ɣ A1B; 6Ɣ T $%&# 3 Ɣ $%'()* !""# Ɣ 4 #1.>5./5* $%'()* Ɣ" 7"8'$%&# 2Ɣ 2sƔ Ɣ +,-)./01.' 2)345 Ɣ #1=-*5//1* ?@ 1 9Ɣ s +4)-1*);1* 7$'8'!""# Ɣ $ :);<'2)-1* Ɣ A0. 8'$C&'D? Engineering model: (1) Each component of the cycle is analyzed as a control volume at steady state. (2) There are no pressure drops through the evaporator and condenser. (3) The compressor operates adiabatically. The expansion through the valve is a throttling process. (4) Kinetic and potential energy effects are negligible. Analysis: First, fix each of the principal states: ୩ ୩ State 1: ܶଵ ൌ െʹʹǡ ՜ ݄ଵ ൌ ͳͶͳͷǤͲͺ ୩ ǡݏଵ ൌ ͷǤͶͷ ୩ή ୩ ୩ State 2: ଶ ൌ ͳǡ ܶଶ ൌ ͳͲ ՜ ݄ଶ ൌ ͳͻͺǤͶͷ ୩ ǡ ݏଶ ൌ ͷǤͶͷ ୩ή ୩ State 3: ଷ ൌ ͳǡ ՜ ݄ଷ ൌ ͵ǤͶ ୩ ୩ State 4: ՜ ݄ସ ൌ ݄ଷ ൌ ͵ǤͶ ୩ (a) The mass flow rate is determined using the refrigerating capacity ͳ ܳሶ୧୬ ͳͷͲ ܳሶ୧୬ ൌ ݉ሶሺ݄ଵ െ ݄ସ ሻ ՜ ݉ሶ ൌ ൌ ቮ ቮ ൌ ͲǤͳͶͶͶ ݄ଵ െ ݄ െ Ͷ ሺͳͶͳͷǤͲͺ െ ͵ǤͶሻ ͳ (b) The compressor power is: ܹሶୡ ൌ ݉ሶሺ݄ଶ െ ݄ସ ሻ ൌ ൬ͲǤͳͶͶͶ ͳ ൰ ሺͳͻͺǤͶͷ െ ͳͶͳͷǤͲͺሻ ቮ ቮ ൌ ͷͷǤ͵ ͳ (c) The coefficient of performance is: ܳሶ୧୬ ͳͷͲ ߚൌ ൌ ൌ ʹǤͳ ሶ ܹୡ ͷͷǤ͵ (d) For isentropic compression, ଶ ൌ ͳǡ ݏଶ௦ ൌ ݏଵ Ǥ With this information, ݄ଶ௦ ൌ ͳͷͷǤ͵ͺ . Thus, the isentropic efficiency is: ߟ ൌ ݄௦ଶ െ ݄ଵ ͳͷͷǤ͵ͺ െ ͳͶͳͷǤͲͺ ൌ ൌ ͲǤͺͺͺ ൌ ͺͺǤͺΨ ݄ଶ െ ݄ଵ ͳͻͺǤͶͷ െ ͳͶͳͷǤͲͺ (e) The entropy production for the compressor is: ܳሶ ݀ܵ ൌ ݉ሶሺݏଵ െ ݏଶ ሻ ߪሶୡ୭୫୮ ՜ ߪሶୡ୭୫୮ ൌ ݉ሶሺݏଶ െ ݏଵ ሻ ด ݀ܶ ܶ ᇣᇤᇥ ୀ ୀ ൌ ൭൬ͲǤͳͶͶͶ ! ͳ ൰ ሺͷǤͶͷ െ ͷǤͶͷሻ ൱ቮ ቮ ൌ ͲǤͲͳͶͲ ή ͳ Problem 10.33 An ideal vapor-compression refrigeration cycle is modified to include a counterflow heat exchanger, as shown in Fig. P10.33. Ammonia leaves the evaporator as saturated vapor at 1.0 bar and is heated at constant pressure to 5°C before entering the compressor. Following isentropic compression to 18 bar, the refrigerant passes through the condenser, exiting at 40°C, 18 bar. The liquid then passes through the heat exchanger, entering the expansion valve at 18 bar. If the mass flow rate of the refrigerant is 12 kg/min, determine: (a) the refrigeration capacity, in tons of refrigeration. (b) the compressor power input, in kW. (c) the coefficient of performance. (d) the rate of entropy production in the compressor, in kW/K. (e) the rate of exergy destruction in the compressor, in kW. Let T0 = 20°C. Discuss advantages and disadvantages of this arrangement. Known: An ideal vapor-compression refrigeration cycle is modified to include a counterflow heat exchanger between the streams exiting the condenser and evaporator. Ammonia is the working fluid. Data are known at various locations, and the mass flow rate is given. Find: Determine (a) the refrigerating capacity, (b) the compressor power input, (c) the coefficient of performance, (d) the rate of entropy production for the compressor, and (e) the rate of exergy destruction for the compressor. Schematic and Known Data: Ɣ @-A; #-*=2*+28 $6.7)8 Ɣ% T 2Ɣ !" # T4 3 Ɣ 435.!"# (3 5.$6.7)8 $6.7)8 3 4 Ɣ Ɣ Ɣ $:".7)8 1Ɣ Ɣ #-<(82++-8 9# >? 5 Ɣ$ ($.5.$:".7)8 4$.5.9# B2);. &'?C)*D28 (!.5.$6.7)8 s !Ɣ &'()*+,-*. /)012 9Ɣ <ሶ5.$%.EDF<,* (G.5.$:".7)8 &1)(-8);-8 Ɣ @,* H);:./)(-8 ƔG Engineering Model: (1) Each component of the cycle is analyzed as a control volume at steady state. (2) Except for the expansion through the valve, which is a throttling process, all processes of the refrigerant are internally reversible. (3) The compressor and expansion valve operate adiabatically. (4) Kinetic and potential energy effects are negligible. (5) Heat transfer from the outside of the heat exchanger can be neglected. (6) Let T0 = 293 K. Analysis: First, fix each of the principal states. ୩ ୩ State 1: ଵ ൌ ͳǡ ܶଵ ൌ ͷ ՜ ݄ଵ ൌ ͳͶͺ͵Ǥʹͷ ୩ ǡ ݏଵ ൌ Ǥͳ ୩ή ୩ State 2: ଶ ൌ ͳͺǡ ݏଶ ൌ ݏଵ ՜ ݄ଶ ൌ ʹͲʹͷǤͷͶ ୩ ୩ State 3: ଷ ൌ ͳͺǡ ܶଷ ൌ ͶͲ ՜ ݄ଷ ൎ ݄ ሺͶͲሻ ൌ ͵ͳǤ͵ͷ ୩ State 4: Using an energy balance on the heat exchanger control volume: Ͳ ൌ ݉ሶሺ݄ െ ݄ଵ ሻ ݉ሶሺ݄ଷ െ ݄ସ ሻ ՜ ݄ସ ൌ ݄ െ ݄ଵ ݄ଷ ൌ ʹͺǤͷͳ ୩ State 5: ՜ ݄ହ ൌ ݄ସ ൌ ʹͺǤͷͳ ୩ ୩ State 6: ൌ ͳǤͲǡ ՜ ݄ ൌ ͳ͵ͻͺǤͶͳ ୩ (a) The refrigerating capacity is: ୩ ୩ ܳሶ ൌ ݉ሶሺ݄ െ ݄ହ ሻ ൌ ቀͳʹ ୫୧୬ቁ ሺͳ͵ͻͺǤͶͳ െ ʹͺǤͷሻ ୩ ቤ ଵ୲୭୬ ౡె ౣ ଶଵଵ ቤ ൌ ͵ǤʹͶ (b) The compressor power is: ͳ ͳ ൰ ሺʹͲʹͷǤͷͶ െ ͳͶͺ͵Ǥʹͷሻ ฬ ฬቮ ቮ ൌ ͳͲͺǤͷ Ͳ ͳ (c) The coefficient of performance is: ݄ െ ݄ହ ߚൌ ൌ ʹǤͲͷ ݄ଶ െ ݄ଵ (d) As expected with an ideal cycle, the rate of entropy production for the compressor is: ܳሶ Ͳ ൌ ݉ሶሺݏଵ െ ݏଶ ሻ ߪሶୡ୭୫୮ ՜ ߪሶୡ୭୫୮ ൌ ݉ሶሺݏଶ െ ݏଵ ሻ ൌ Ͳ ܶ ด ܹሶ ൌ ݉ሶሺ݄ଶ െ ݄ଵ ሻ ൌ ൬ͳʹ ୀ (e) The rate of exergy destruction for the compressor follows as ሶୢ ൌ ܶ ߪሶୡ୭୫୮ ൌ Ͳ Discussion: The heat exchanger (1) tends to increase the capacity, (2) helps ensure superheated vapor enters the compressor, and (3) increases the average specific volume in the compressor, thereby increasing the power required.
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