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Introduction​ ​:

Power​ ​cycles 

An​ ​important​ ​application​ ​of​ ​thermodynamics​ ​is​ ​the​ ​analysis​ ​of​ ​power​ ​cycles through​ ​which​ ​the​ ​energy​ ​absorbed​ ​as​ ​heat​ ​can​ ​be​ ​continuously​ ​converted​ ​into mechanical​ ​work​ ​.​ ​A​ ​thermodynamics​ ​analysis​ ​of​ ​the​ ​heat​ ​engine​ ​cycles provides​ ​valuable​ ​information​ ​regarding​ ​the​ ​design​ ​of​ ​new​ ​cycles​ ​or​ ​for improving​ ​the​ ​existing​ ​cycles.

These​ ​four​ ​processes​ ​make​ ​a​ ​cycle.. 1.Compression 2.​ ​Heat​ ​Addition 3.Expansion 4.Heat​ ​rejection 1.Compression​ ​and​ ​expansion​ ​are​ ​opposite​ ​to​ ​each​ ​other,​ ​Whereas​ ​heat addition​ ​and​ ​heat​ ​removal​ ​are​ ​opposite​ ​to​ ​each​ ​other. 1.Compression​ ​process​ ​in​ ​all​ ​cycles​ ​is​ ​isentropic​ ​Compression,​ ​because​ ​it​ ​is ideal​ ​process​ ​for​ ​the​ ​compression.​ ​An​ ​isentropic​ ​compression​ ​process​ ​can​ ​be shown​ ​on​ ​P-V​ ​and​ ​T-S​ ​diagram​ ​as​ ​below.

Prepared​ ​by​ ​Reliance​ ​Academy​ ​Kolhapur​ ​ ​Email:​ ​[email protected]

WWW.MECHDIPLOMA.COM 3.​ ​Expansion​ ​process​ ​in​ ​all​ ​cycles​ ​is​ ​also​ ​isentopic​ ​expansion..

3.​ ​The​ ​difference​ ​among​ ​the​ ​various​ ​cycles​ ​is​ ​the​ ​process​ ​by​ ​which​ ​heat​ ​is added​ ​or​ ​rejected​ ​from​ ​the​ ​system.​ ​Heat​ ​addition​ ​may​ ​be​ ​isothermal,​ ​constant volume,constant​ ​pressure​ ​or​ ​combinations.​ ​This​ ​makes​ ​the​ ​different​ ​cycles. 5​ ​cycles  Cycle...  Process  .  1-2   {comp}  ​ ​ ​ ​ ​ ​ ​ ​ ​2-3  {Heat​ ​ad}  3-4  {expans.} 

Carnot  Cycle 

Otto  cycle 

Brayton  cycle 

Diesel  cycle 

Dual​ ​cycle 

Isentropic  Isentropic  Isentropic  Isentropic  Isentropic  compr.  compr.  compr.  compr.  compr.  Isothermal  Const.Vol 

Const​ ​Pr 

Const​ ​Pr 

Const.vol  +  Const.​ ​Pr 

Isentropic   Isentropic   Isentropic   Isentropic   Isentropic   exp.  exp.  exp.  exp.  exp. 

4-1  Isothermal  Const​ ​vol  {Heat​ ​rej.) 

Const​ ​pr 

Const​ ​vol 

Const​ ​vol 

     

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WWW.MECHDIPLOMA.COM OTTO​ ​cycle    The​ ​air-standard-Otto​ ​cycles​ ​is​ ​the​ ​idealized​ ​cycle​ ​for​ ​the​ ​idealized​ ​cycle  for​ ​the​ ​spark-ignition​ ​internal​ ​combustion​ ​engines​ ​.This​ ​cycles​ ​is​ ​shown  above​ ​on​ ​p-v​ ​and​ ​T-s​ ​diagrams​ ​.The​ ​otto​ ​cycle​ ​1-2-3-4​ ​consist​ ​of​ ​following  four​ ​process​ ​:  Process​ ​1-2​ ​;​ ​Reversible​ ​adiabatic​ ​compression​ ​of​ ​air  Process​ ​2-3:​ ​Heat​ ​addition​ ​at​ ​constant​ ​volume  Process​ ​3-4​ ​:​ ​Reversible​ ​adiabatic​ ​expansion​ ​of​ ​air  Process​ ​4-1​ ​:​ ​Heat​ ​rejection​ ​at​ ​constant​ ​volume             

Where​ ​r=​ ​compression​ ​ratio​ ​=V1/V2 γ = ratio​ ​of​ ​specific​ ​heats

Prepared​ ​by​ ​Reliance​ ​Academy​ ​Kolhapur​ ​ ​Email:​ ​[email protected]

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From​ ​the​ ​above​ ​equation,​ ​it​ ​can​ ​be​ ​observed​ ​that​ ​the  efficiency​ ​of​ ​the​ ​Otto​ ​cycle​ ​is​ ​mainly​ ​the​ ​function​ ​of  compression​ ​ration​ ​for​ ​the​ ​given​ ​ratio​ ​of​ ​ ​Cp​ ​and​ ​Cv.          Diesel​ ​cycle  Air​ ​standard​ ​diesel​ ​cycle​ ​is​ ​a​ ​idealized​ ​cycle​ ​for​ ​diesel  engines.​ ​It​ ​is​ ​as​ ​shown​ ​on​ ​P-V​ ​diagram​ ​and​ ​T-s​ ​Diagram,  the​ ​processes​ ​in​ ​the​ ​cycle​ ​are​ ​as​ ​follows​ ​:   

Process​ ​1-2​ ​:​ ​Reversible​ ​adiabatic​ ​compression Process​ ​2-3​ ​;​ ​Constant​ ​Pressure​ ​heat​ ​addition Process​ ​3-5​ ​:​ ​Reversible​ ​adiabatic​ ​compression Process​ ​4-1;​ ​Constant​ ​volume​ ​heat​ ​rejection Air​ ​Standard​ ​efficiency​ ​of​ ​diesel​ ​cycle

Prepared​ ​by​ ​Reliance​ ​Academy​ ​Kolhapur​ ​ ​Email:​ ​[email protected]

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Limited​ ​pressure​ ​cycle​ ​or​ ​Dual​ ​cycle  This​ ​cycle​ ​has​ ​heat​ ​addition​ ​split​ ​into​ ​two​ ​processes,​ ​part​ ​is​ ​at​ ​constant​ ​volume​ ​and​ ​remaining part​ ​is​ ​at​ ​constant​ ​pressure.​ ​Thus​ ​this​ ​cycle​ ​combines​ ​the​ ​advantages​ ​of​ ​both​ ​Diesel​ ​cycle​ ​and​ ​Otto cycle.Hence​ ​the​ ​process​ ​of​ ​heat​ ​addition​ ​2-3​ ​is​ ​split​ ​into​ ​two​ ​processes,​ ​as​ ​2-3’​ ​&​ ​3’-3. This​ ​cyles​ ​is​ ​very​ ​close​ ​to​ ​the​ ​actual​ ​cycle​ ​because​ ​the​ ​heat​ ​addition​ ​in​ ​actual​ ​engines​ ​does not​ ​occur​ ​exactly​ ​at​ ​constant​ ​volume​ ​or​ ​at​ ​constant​ ​pressure​ ​but​ ​it​ ​is​ ​a​ ​combination​ ​of​ ​both.

Process​ ​1-2:​ ​Reversible​ ​adiabatic(Isentropic)​ ​compression Process​ ​2-3’:​ ​Constant​ ​Volume​ ​heat​ ​addition Process​ ​3’-3:​ ​Constant​ ​Pressure​ ​heat​ ​addition Process​ ​3-4:​ ​Reversible​ ​adiabatic(Isentropic)​ ​expansion Process​ ​4-1:​ ​Constant​ ​volume​ ​heat​ ​rejection

Prepared​ ​by​ ​Reliance​ ​Academy​ ​Kolhapur​ ​ ​Email:​ ​[email protected]

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Carnot​ ​cycle 

Carnot​ ​cycle​ ​is​ ​ideal​ ​cycle​ ​in​ ​which​ ​heat​ ​addition​ ​and​ ​heat​ ​rejection​ ​is​ ​carried out​ ​at​ ​constant​ ​temperature(isothermal​ ​process).​ ​Actually​ ​it​ ​is​ ​not​ ​practically possible​ ​to​ ​carry​ ​out​ ​the​ ​heat​ ​addition​ ​and​ ​rejection​ ​at​ ​constant temperature..Carnot​ ​cycle​ ​is​ ​used​ ​for​ ​comparing​ ​the​ ​actual​ ​cycles. Process​ ​1-2​ ​Isentropic​ ​compression Process​ ​2-3​ ​Isothermal​ ​heat​ ​addition Process​ ​3-4​ ​isentropic​ ​expansion Process​ ​4-1​ ​isothermal​ ​heat​ ​rejection

Prepared​ ​by​ ​Reliance​ ​Academy​ ​Kolhapur​ ​ ​Email:​ ​[email protected]

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Brayton​ ​Cycle(Constant​ ​pressure​ ​closed​ ​cycle):

Process​ ​1-2​ ​Isentropic​ ​compression Process​ ​2-3​ ​Constant​ ​pressure​ ​heat​ ​addition Process​ ​3-4​ ​isentropic​ ​expansion Process​ ​4-1​ ​Constant​ ​pressure​ ​heat​ ​rejection ​ ​ ​ ​ ​ ​The​ ​Brayton​ ​cycle​ ​is​ ​a​ ​theoretical​ ​cycle​ ​for​ ​simple​ ​gas​ ​turbine.​ ​This​ ​cycle​ ​consists​ ​of two​ ​isentropic​ ​and​ ​two​ ​constant​ ​ ​pressure​ ​processes.​ ​The​ ​cycle​ ​is​ ​similar​ ​to​ ​the​ ​diesel cycle​ ​in​ ​compression​ ​and​ ​heat​ ​addition.​ ​The​ ​isentropic​ ​expansion​ ​of​ ​the​ ​diesel​ ​cycle​ ​is further​ ​extended​ ​followed​ ​by​ ​constant​ ​pressure​ ​heat​ ​rejection. The​ ​efficiency​ ​of​ ​the​ ​ideal​ ​Brayton​ ​cycle​ ​is​ ​given​ ​by

Prepared​ ​by​ ​Reliance​ ​Academy​ ​Kolhapur​ ​ ​Email:​ ​[email protected]