Kĩ thuật lạnh - Chapter 4: Single stage cycle

CHAPTER 4: SINGLE STAGE CYCLE 12/2015 Chapter 4 : Single stage cylce 1 OBJECTIVES Aft thi h t t d ter s c arp er, s u en can : - Analyze and perform cyclic calculations for C t f i ti l d tharno re r gera on cyc e an o ers - Analyze and perform cyclic calculations for t d d i f i tis an ar vapour compress on re r gera on systems A l d t d di d t f- na yze a van age an sa van age o some refrigeration cycles 12/2015 2Chapter 4 : Single stage cylce CONTENTS CARNOT REFRIGERATION CYCLE STANDARD VAPOUR COMPRESSION REFRIGERATION SYSTEM (VCRS) SUBCOOLING AND SUPERHEATING CYCLE LIQUID – SUCTION HEAT EXCHANGER 12/2015 3Chapter 4 : Single stage cylce CONTENTS ACTUAL STANDARD VAPOUR COMPRESSION REFRIGERATION SYSTEM 12/2015 4Chapter 4 : Single stage cylce REFERENCES [1] 4O LESSONS ON REFRIGERATION AND AIR. CONDITIONING FROM IIT KHARAGPUR. ( Useful t i i t i l f h i l i ira n ng ma er a or mec an ca eng neer ng students/college, or reference for engineer ) - Indian I tit t f T h l (IIT)ns u e o ec no ogy [2]. Kỹ thuật lạnh cơ sở - Nguyễn Đức Lợi 12/2015 5Chapter 4 : Single stage cylce CARNOT REFRIGERATION CYCLE 1. Definition: Carnot refrigeration cycle is a completely reversible cycle, hence is used as a model of perfection for a refrigeration cycle operating between a constant temperature heat source and sink. It is used as reference against which the real cycles are compared. 12/2015 6Chapter 4 : Single stage cylce CARNOT REFRIGERATION CYCLE 2. Description : Refer to (page 155, [1]) : P 4 1 i i- rocess - : vapor zat on in evaporator P 1 2 i- rocess - : compress on in compressor P 2 3 d i- rocess - : con ens ng in condenser P 3 4 i i- rocess - : expans on n turbin 12/2015 7Chapter 4 : Single stage cylce CARNOT REFRIGERATION CYCLE qc − qe = wnet 12/2015 8Chapter 4 : Single stage cylce CARNOT REFRIGERATION CYCLE Refer (page 155, [1]) : 12/2015 9Chapter 4 : Single stage cylce CARNOT REFRIGERATION CYCLE The Coefficient of Performance (COP) is given by: - The COP of Carnot refrigeration cycle is a function of evaporator and condenser temperatures only and is independent of the nature of the working substance. - From Carnot’s theorems, for the same heat source and sink temperatures, no irreversible cycle can have COP higher than that of Carnot COP. 12/2015 10Chapter 4 : Single stage cylce CARNOT REFRIGERATION CYCLE 3. Practical difficulties with Carnot refrigeration system: - During process 1-2, a mixture consisting of liquid and vapour have to be compressed isentropically in the compressor -> compressor will be damaged - Using a turbine and extracting work from the system during the isentropic expansion of liquid refrigerant is not economically feasible, particularly in case of small capacity systems. 12/2015 11Chapter 4 : Single stage cylce CARNOT REFRIGERATION CYCLE - This is due to the fact that the specific work output (per kilogram of refrigerant) from the turbine is given by: - The specific volume of liquid is much smaller compared to the specific volume of a vapour/gas, the work output from the turbine in case of the liquid will be small. In addition, the inefficiencies of the turbine -> then the net output will be further 12/2015 12 reduced. Chapter 4 : Single stage cylce Standard Vapour Compression Refrigeration System (VCRS) In practical considerations, the Carnot refrigeration system need to be modified: - Dry compression with a single compressor is possible if the isothermal heat rejection process is replaced by isobaric heat rejection process -The isentropic expansion process can be replaced by an isenthalpic throttling process. 12/2015 13Chapter 4 : Single stage cylce Standard Vapour Compression Refrigeration System (VCRS) This is the theoretical cycle on which the actual vapour compression refrigeration systems are based. 12/2015 14Chapter 4 : Single stage cylce Standard Vapour Compression Refrigeration System (VCRS) Due to these irreversibilities, the cooling effect reduces and work input increases, thus reducing the system COP. This can be explained easily with the help of the cycle diagrams on T-s charts 12/2015 15Chapter 4 : Single stage cylce Standard Vapour Compression Refrigeration System (VCRS) - There is a reduction in refrigeration effect when the isentropic expansion process of Carnot cycle is replaced by isenthalpic throttling process of VCRS cycle, this reduction is equal to the area d-4-4’-c-d (area A2) and is known as throttling loss. - It is easy to show that the loss in refrigeration effect increases as the evaporator temperature decreases and/or condenser temperature increases. A practical consequence of this is a requirement of 12/2015 16 higher refrigerant mass flow rate. Chapter 4 : Single stage cylce Standard Vapour Compression Refrigeration System (VCRS) The heat rejection in case of VCRS cycle also increases when compared to Carnot cycle. - The heat rejection in case of Carnot cycle (1-2’’-3- 4’) is given by: - In case of VCRS cycle, the heat rejection rate is given by: 12/2015 17Chapter 4 : Single stage cylce Standard Vapour Compression Refrigeration System (VCRS) Hence the increase in heat rejection rate of VCRS compared to Carnot cycle is equal to the area 2’’-2-2’ (area A1). This region is known as superheat horn, and is due to the replacement of isothermal heat rejection process of Carnot cycle by isobaric heat rejection in case of VCRS. 12/2015 18Chapter 4 : Single stage cylce Standard Vapour Compression Refrigeration System (VCRS) 12/2015 19Chapter 4 : Single stage cylce Standard Vapour Compression Refrigeration System (VCRS) The net work input in case of Carnot and VCRS cycles are given by: wnet,Carnot = (qc − qe )Carnot = area 1− 2' '−3 − 4'−1 wnet,VCRS = (qc − qe )VCRS = area 1− 2 − 3 − 4'−c − d − 4 −1 12/2015 20Chapter 4 : Single stage cylce Standard Vapour Compression Refrigeration System (VCRS) The COP of VCRS cycle is given by: Unlike Carnot COP, the cycle efficiency depends very much on the shape of T-s diagram, which in turn depends on the nature of the working fluid. 12/2015 21Chapter 4 : Single stage cylce Standard Vapour Compression Refrigeration System (VCRS) As mentioned before, the losses due to superheat (area A1) and throttling (area A2 ≈ A3) depend very much on the shape of the vapor dome (saturation liquid and vapour curves) on T s diagram. The shape of the saturation curves depends on the nature of refrigerant. 12/2015 22Chapter 4 : Single stage cylce Standard Vapour Compression Refrigeration System (VCRS) T-s diagrams for three different types of refrigerants. 12/2015 23Chapter 4 : Single stage cylce Standard Vapour Compression Refrigeration System (VCRS) Type 1 : Refrigerant such as: Amonia, CO2, H2O. Both the superheat and throttling losses (areas A1 and A3) are significant Type 2 : Refrigerants such as CFC11, CFC12, HFC134a. These refrigerants have small superheat losses (area A1) but large throttling losses (area A3) Type 3 : High molecular weight refrigerants such as CFC113, CFC114, CFC115, iso-butane. Having significant throtting loss; do not have any superheat losses, i.e., when the compression inlet condition is saturated (point 1), then the exit 12/2015 24 condition will be in the 2-phase region -> danger Chapter 4 : Single stage cylce Standard Vapour Compression Refrigeration System (VCRS) The superheat loss increases only the work input to the compressor, it does not effect the refrigeration effect. In heat pumps superheat is not a loss, but a part of the useful heating effect. However, the process of throttling is inherently irreversible, and it increases the work input and also reduces the refrigeration effect. 12/2015 25Chapter 4 : Single stage cylce Standard Vapour Compression Refrigeration System (VCRS) Heat transfer rate at evaporator or refrigeration capacity, is given by: Qe= mr.(h1 - h4 ), (kW) Where : (h1 − h4 ) is known as specific refrigeration effect or simply refrigeration effect, (kJ/kg) Power input to the compressor, is given by: Wc= mr.(h2 - h1 ), (kW) (h2−h1) is known as specific work of compression or simply work of compression, (kJ/kg) 12/2015 26Chapter 4 : Single stage cylce Standard Vapour Compression Refrigeration System (VCRS) Heat transfer rate at condenser, Qc is given by: Qc=mr.(h2- h3 ), (kW) Where: h3 and h2 are the specific enthalpies (kJ/kg) at the exit and inlet to the condenser, respectively. The COP of the system is given by: 12/2015 27Chapter 4 : Single stage cylce Standard Vapour Compression Refrigeration System (VCRS) At any point in the cycle, the mass flow rate of refrigerant can be written in terms of volumetric flow rate and specific volume at that point, i.e., Applying this equation to the inlet condition of the compressor 12/2015 28Chapter 4 : Single stage cylce Standard Vapour Compression Refrigeration System (VCRS) where V1 is the volumetric flow rate at compressor inlet, (m3/s) and v1 is the specific volume at compressor inlet (m3/kg). We can also write, the refrigeration capacity in terms of volumetric flow rate: is called as volumetric refrigeration effect (kJ/m3 of refrigerant). 12/2015 29Chapter 4 : Single stage cylce SUBCOOLING AND SUPERHEATING CYCLE 1.Definition : Refer to page 175,[1] In actual refrigeration cycles, the temperature of the heat sink will be several degrees lower than the condensing temperature to facilitate heat transfer. Hence it is possible to cool the refrigerant liquid in the condenser to a few degrees lower than the condensing temperature by adding extra area for heat transfer. In such a case, the exit condition of the condenser will be in the subcooled liquid region. 12/2015 30Chapter 4 : Single stage cylce SUBCOOLING AND SUPERHEATING CYCLE - Similarly, the temperature of heat source will be a few degrees higher than the evaporator temperature, hence the vapour at the exit of the evaporator can be superheated by a few degrees. - If the superheating of refrigerant takes place due to heat transfer with the refrigerated space (low temperature heat source) then it is called as useful superheating as it increases the refrigeration effect. 12/2015 31Chapter 4 : Single stage cylce SUBCOOLING AND SUPERHEATING CYCLE - It is possible for the refrigerant vapour to become superheated by exchanging heat with the surroundings as it flows through the connecting pipelines. Such a superheating is called as useless superheating as it does not increase refrigeration effect. 12/2015 32Chapter 4 : Single stage cylce SUBCOOLING AND SUPERHEATING CYCLE + Advantage of subcooling cycle : 12/2015 33Chapter 4 : Single stage cylce SUBCOOLING AND SUPERHEATING CYCLE - Increases the refrigeration effect by reducing the throttling loss at no additional specific work input. - Without subcooling the throttling loss is equal to the hatched area b-4’-4-c. - With subcooling the throttling loss is given by the area a-4”-4’-b. -The refrigeration effect increases by an amount equal to (h4-h4’) = (h3-h3’). - Less vapour at the inlet to the evaporator 12/2015 34Chapter 4 : Single stage cylce SUBCOOLING AND SUPERHEATING CYCLE + Advantage of superheating cycle : It prevents the entry of liquid droplets into the compressor + Disadvantage of superheating : In case of useful superheating increase - Useful superheating increases both the refrigeration effect as well as the work of compression. - The COP (ratio of refrigeration effect and work of compression) may or may not increase with superheat, depending mainly upon the nature of the 12/2015 35 working fluid Chapter 4 : Single stage cylce SUBCOOLING AND SUPERHEATING CYCLE 12/2015 36Chapter 4 : Single stage cylce LIQUID-SUCTION HEAT-EXCHANGER CYCLE 1. Definition : A LSHX is a counterflow heat exchanger in which the warm refrigerant liquid from the condenser exchanges heat with the cool refrigerant vapour from the evaporator. 12/2015 37Chapter 4 : Single stage cylce LIQUID-SUCTION HEAT-EXCHANGER CYCLE 12/2015 38Chapter 4 : Single stage cylce LIQUID-SUCTION HEAT-EXCHANGER CYCLE 12/2015 39Chapter 4 : Single stage cylce LIQUID-SUCTION HEAT-EXCHANGER CYCLE 12/2015 40Chapter 4 : Single stage cylce LIQUID-SUCTION HEAT-EXCHANGER CYCLE 2. Refrigeration cycle calculations : If we assume that there is no heat exchange between the surroundings and the LSHX and negligible kinetic and potential energy changes across the LSHX, then, the heat transferred between the refrigerant liquid and vapour in the LSHX, QLSHX is given by: 12/2015 41Chapter 4 : Single stage cylce LIQUID-SUCTION HEAT-EXCHANGER CYCLE If we take average values of specific heats for the vapour and liquid, then we can write the above equation as; cp,l (T3 − T4 ) = cp,v (T1 − T6 ) since the specific heat of liquid (cp l) is larger, than that of vapour (cp,v), i.e., cp,l > cp,l, we can write: (T3 − T4 ) < (T1 − T6 ) This means that, the degree of subcooling (T3- T4) will always be less than the degree of superheating, (T1-T6). 12/2015 42Chapter 4 : Single stage cylce LIQUID-SUCTION HEAT-EXCHANGER CYCLE If we define the effectiveness of the LSHX, εLSHX as the ratio of actual heat transfer rate in the LSHX to maximum possible heat transfer rate If we have a perfect LSHX with 100 percent effectiveness (εLSHX = 1.0), the temperature of the refrigerant vapour at the exit of LSHX will be equal to the condensing temperature, Tc, i.e., (T1 =T3 = Tc ) 12/2015 43Chapter 4 : Single stage cylce LIQUID-SUCTION HEAT-EXCHANGER CYCLE 3. Effect of superheat on system COP: - When the refrigerant is superheated usefully (either in the LSHX or the evaporator itself), the refrigeration effect increases. - The work of compression also increases, primarily due to increase in specific volume of the refrigerant due to superheat 12/2015 44Chapter 4 : Single stage cylce Actual Standard Vapour Compression Refrigeration System The cycles considered so far are internally reversible and no change of refrigerant state takes place in the connecting pipelines. However, in actual VCRS several irreversibilities exist. These are due to: - Pressure drops in evaporator, condenser and LSHX - Pressure drop across suction and discharge valves of the compressor - Heat transfer in compressor - Pressure drop and heat transfer in connecting 12/2015 45 pipe lines Chapter 4 : Single stage cylce Actual Standard Vapour Compression Refrigeration System The cycles considered so far are internally reversible and no change of refrigerant state takes place in the connecting pipelines. However, in actual VCRS several irreversibilities exist. These are due to: - Pressure drops in evaporator, condenser and LSHX - Pressure drop across suction and discharge valves of the compressor - Heat transfer in compressor - Pressure drop and heat transfer in connecting 12/2015 46 pipe lines Chapter 4 : Single stage cylce Actual Standard Vapour Compression Refrigeration System - The pressure drop in the evaporator, in the suction line and across the suction valve has a significant effect on system performance because suction side pressure drop increases the specific volume at suction, compression ratio and discharge temperature increase -> reduction in system capacity, increase in power input and also affect the life of the compressor due to higher discharge temperature -> this pressure drop should be as small as possible for good performance. 12/2015 47- Chapter 4 : Single stage cylce Actual Standard Vapour Compression Refrigeration System - The pressure drop depends on the refrigerant velocity, length of refrigerant tubing and layout (bends, joints etc.). Pressure drop can be reduced by reducing refrigerant velocity (e.g. by increasing the inner diameter of the refrigerant tubes). However, this affects the heat transfer coefficient in evaporator and the carring of the lubricating oil back to the compressor - Pressure drops across the valves of the compressor increase the work of compression and reduce the volumetric efficiency of the compressor. 12/2015 48 Hence they should be as small as possible. Chapter 4 : Single stage cylce Actual Standard Vapour Compression Refrigeration System - Heat transfer in the suction line is detrimental as it reduces the density of refrigerant vapour and increases the discharge temperature of the compressor. Hence, the suction lines are normally insulated to minimize heat transfer. - Actual systems there are the presence of foreign matter : lubricating oil, water, air, particulate matter inside the system. - We can’t avoid the presence of oil in system but we must return oil to compressor properly 12/2015 49Chapter 4 : Single stage cylce Actual Standard Vapour Compression Refrigeration System 12/2015 50Chapter 4 : Single stage cylce Actual Standard Vapour Compression Refrigeration System Exercise : In a R22 based refrigeration system, a liquid-to- suction heat exchanger (LSHX) with an effectiveness of 0.65 is used. The evaporating and condensing temperatures are 7.2oC and 54.4oC respectively. Assuming the compression process to be isentropic, find: a) Specific refrigeration effect, b) Volumic refrigeration effect, c) Specific work of compression d) COP of the system, 12/2015 51Chapter 4 : Single stage cylce Actual Standard Vapour Compression Refrigeration System e) Temperature of vapour at the exit of the compressor Comment on the use of LSHX by comparing the performance of the system with a SSS cycle operating between the same evaporator and condensing temperatures. 12/2015 52Chapter 4 : Single stage cylce Actual Standard Vapour Compression Refrigeration System 12/2015 53Chapter 4 : Single stage cylce Actual Standard Vapour Compression Refrigeration System e) Temperature of vapour at the exit of the compressor Comment on the use of LSHX by comparing the performance of the system with a SSS cycle operating between the same evaporator and condensing temperatures. 12/2015 54Chapter 4 : Single stage cylce Actual Standard Vapour Compression Refrigeration System 12/2015 55Chapter 4 : Single stage cylce Actual Standard Vapour Compression Refrigeration System 12/2015 56Chapter 4 : Single stage cylce Actual Standard Vapour Compression Refrigeration System 12/2015 57Chapter 4 : Single stage cylce Actual Standard Vapour Compression Refrigeration System 12/2015 58Chapter 4 : Single stage cylce