More Thermodynamic Cycles P M V Subbarao Professor Mechanical Engineering Department The Engineering Systems for High end Extrasomatic Needs… Brayton Cycle for Power Generation 1-2 Adiabatic compression (in a compressor) 2-3 Constant pressure heat addition 3-4 IAdiabaticexpansion (in a turbine) 4-1 Constant pressure heat rejection Thermodynamic Analysis of Adiabatic Compression m 1 h1 m 2 h2 WComp 2 m 1 h1 m 2 h2 m vdp 1 For an infinitesimal compression: h m h dh m vdp m m dh m vdp c p dT vdp Model for infinitesimal Adiabatic Process by a perfect Gas dT 1 dp p T 1 ln T ln p ln C T ln 1 ln C p T p 1 1 ln T ln p ln C 1 C Tp C Finite Compression of Perfect gas 1 Tp pv C C 2 m h1 m h2 m vdp 1 2 dp m h1 m h2 m C 1 1 p p m h1 m h2 m C 1 1 1 p2 p Wcomp m h1 h2 m C 1 p1 1 1 p2 p1 Constant Pressure Heat Addition (combustion) Adiabatic Expansion p Wturb m h3 h4 m C 1 1 1 p4 p3 Cycle Analysis 1 –2 : Specific work input : wcomp h2 h1 c p (T2 T1 ) 2 – 3 : Specific heat input : qin h3 h2 c p (T3 T2 ) 3 – 4 : Specific work output : wtur h3 h4 c p (T3 T4 ) 4 – 1 : Specific heat rejection : qout h4 h1 c p (T4 T1 ) Adiabatic Processes: T2 p2 T1 p1 1 T3 p3 T4 p4 1 wnet wtur wcomp h3 h4 h2 h1 wnet c p (T3 T4 ) (T2 T1 ) wnet T3 c p (T3 ) ( T1 T1 ) 1 T1 ( 1) c p T3 T3 wnet c p (T3 T1 ) T1 qin h3 h2 c p (T3 T1 ) wnet th qin wnet th qin T3 c p (T3 T1 ) T1 c p T3 T1 T3 c p T1 1 c p T3 T1 1 1 1 rp 1 1 Pressure Ratio Vs Efficiency th 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 10 rp 20 30 Reciprocating IC Engine : A Heat Engine Qout Qin Wout Greatness of Heat Engines in i i Qi 1 iWi 1 Qi 1 i Qi 1 iWi 1 iWi 1 out in out • Balance Sheet for A Heat Engine: – All heat inputs consume resources : Total Input Heat : Qin (Cost incurred). – All heat outputs are just mere a loss. – Net work Out put is positive and this is the final benefit : Wnet (Benefit Achieved) – Performance : Benefit to cost ratio (in energy units). Otto’s Engine for Propulsion Modification of Brayton Cycle for Air Craft Propulsion : Invented by Frank Whittle Large Aircrafts : Boeing 747 Physical Properties of Standard Atmosphere Altitude Temperature Pressure (meters) (K) (kPa) 0 288.15 101.3 1,000 281.65 89.87 2,000 275.15 79.49 3,000 268.65 70.10 4,000 262.15 61.64 5,000 255.65 54.02 6,000 249.15 47.18 7,000 242.65 41.06 8,000 236.15 35.59 9,000 229.65 30.74 10,000 223.15 26.43 12,000 216.65 19.33 15,000 216.65 12.04 Air Craft Engine Bleed for Refrigeration System Air Standard Refrigeration Cycle for Aircraft Cooling Air Craft Engine Refrigeration System Air to Cabin Gas Refrigeration Systems •The gas power cycle can be used as refrigeration cycles by simply reversing them. •Of these, the reversed Brayton cycle, which is also known as the gas refrigeration cycle, is used to cool aircraft. • Further Modification this cycle is used to obtain very low (cryogenic) temperatures. •The work output of the turbine can be used to reduce the work input requirements to the compressor. •Thus, the performance index of a gas refrigeration cycle is defined as qL qL COPR wnet , in wcomp , in wturb , out More Cycles for Exotic Needs of Urban World ……. An Urban world that was present till the end of first decade of the 20th century. • Only fresh foods that could be grown locally were available, and they had to be purchased and used on a daily basis. • Meat was bought during the daily trip to the butcher's; the milkman made his rounds every morning. • If you could afford weekly deliveries of ice blocks—harvested in the winter from frozen northern lakes—you could keep some perishable foods around for 2 or 3 days in an icebox. • New York was a virtual ghost town in the summer months. • Homes were built with natural cooling in mind. • Ceilings were high, porches were deep and shaded, and windows were placed to take every possible advantage of cross-ventilation Urban Life after the end of first decade of the 21st century. • Frozen foods of all kinds were available just about anywhere in the world all year round. • The milkman was all but gone and forgotten, and the butcher now did his work behind a counter at the supermarket. • Indeed, many families concentrated the entire week's food shopping into one trip to the market, stocking the refrigerator with perishables that would last a week or more. • New York is a busy town even in the summer months. • Buildings are totally isolated from fresh air. Creation of Artificial Temperature/Quality Why not use the reversed Rankine cycle for Refrigeration ? • Very costly to expand the liquid using a turbine with very low or negligible power output!?! • May become negative under friction. • Cheaper to have irreversible expansion through an expansion valve. Thermodynamics of Ideal VCR Cycle • Ideal Vapor-Compression Refrigeration Cycle • Process Description • 1-2 Adiabatic compression • 2-3 Constant pressure heat rejection in the condenser • 3-4 Throttling in an expansion valve • 4-1 Constant pressure heat addition in the evaporator Performance Index The performance of refrigerators and heat pumps is expressed in terms of coefficient of performance (COP), defined as Desired output Cooling effect QL COPR Required input Work input Wnet ,in Desired output Heating effect QH COPHP Required input Work input Wnet ,in Under the same operating conditions, the COPs are related by COPHP COPR 1 Samsung Split A/c Model No : AQ24UUA Cooling Capacity : 7.03kW Power Consumption (Cooling) : 2,600Watts Refrigerant Type R22 The refrigerant leaves the evaporator at 7.2oC Condenser pressure : 2.71 MPa. Heat Pump Systems