Lecture 34: Exergy Analysis- Concept

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1 ME 200 Thermodynamics I Lecture 34: Exergy Analysis- Concept Yong Li Shanghai Jiao Tong University Institute of Refrigeration and Cryogenics 800 Dong Chuan Road Shanghai, , P. R. China liyo@sjtu.edu.cn Phone: ; Fax:

2 Previous energy analysis All considered the isentropic process as the goal to strive for. Maximize adiabatic and isentropic efficiency This approach is short sighted for three reasons: 1. It ignores processes where heat transfer is present.(the majority of all practical processes.) 2. It assumes that reversibility can be obtained. 3. It assumes that the exit state of a device can float, i.e., cases where the exit pressure is fixed, but the exit temperature is allowed to fall below the temperature of the surroundings. Not so real! 7.2

3 Example Exergy (Availability) Analysis potential for use, not conserved 7.3

4 Concepts Exergy reference environment and dead state Exergy reference environment:::large enough portion of system (CM1) surroundings such that intensive properties (e.g., T 0, p 0 ) are unaffected by interaction with the system (CM2).» Simple compressible system» ΔU e = T 0 ΔS e - p 0 ΔV e Eq(6.10)» ΔKE = 0, ΔPE=0 Dead state ::: State of system (CM2) when in thermodynamic equilibrium with the environment (T 0 and p 0 )» Still possess energy? T o,p o CM2 Q i Closed System W i CM1 W use 7.4

5 Concepts Defining exergy Exergy- E (J) Systems A B (equilibrium): work Notes:» W c = net useful work of combined system and environment (CM1)!» The goal is to maximize W c! Boundary of the combined system. Exergy/Availability ::: Maximum theoretical work output that could be done by a system if it were to come into equilibrium with its environment! 7.5

6 Exergy Analysis for Closed Systems 1st law Total Energy for CM1: DE Q W c c c 0 Assumptions» Maximize W c final state of CM1 is the dead state» Neglect DKE CM1 and DPE CM1» Sole effect is work out Q c = 0 Wc DEc DU c 7.6

7 Continue Exergy Analysis for Closed Systems The changes in energy of the combined system can be calculated by: DE ( U E) DU c o CM 2 e Constant for environment Substitution into the equation for useful work leads to: W ( E U ) p ( V V ) T DS c 0 CM 2 o 0 0 e W c DE Exergy reference environment ΔU e = T 0 ΔS e - p 0 ΔV e DE ( U E) ( T DS p DV ) c o CM 2 0 e 0 e c 7.7

8 Continue Exergy Analysis for Closed Systems W ( E U ) p ( V V ) T DS Note: ΔV e = ΔV CM2 and c 0 CM 2 o 0 0 e ΔS c = c =ΔS CM1 = ΔS CM2 + Δs e ΔS e = ΔS CM1 ΔS CM2 = ΔS CM1 (S 0 S) CM2 = ΔS CM1 + (S S 0 ) CM2 Then, substituting ΔV e and ΔS e into the equation for useful work: = (V 0 V) CM2 = (V V 0 ) CM2 W c = (E U 0 ) CM2 + p 0 (V V 0 ) CM2 T 0 (S S 0 ) CM2 T 0 ΔS CM1 7.8

9 Continue Exergy Analysis for Closed Systems W c = (E U 0 ) CM2 + p 0 (V V 0 ) CM2 T 0 (S S 0 ) CM2 T 0 ΔS CM1 In order to maximize W c, assume a reversible process for CM1 and thus, ΔS CM1 = 0! In addition, drop the subscript CM2: W rev,c,max = E U 0 + p 0 (V V 0 ) T 0 (S S 0 ) Definition of closed system exergy (availability): E = W rev,c,max E = E U 0 + p 0 (V V 0 ) T 0 (S S 0 ) 7.9

10 Continue Exergy Analysis for Closed Systems In specific terms: e u p v v T s s e o o o o o u V 2 /2 gz u p v v T s s e o o o o o e o o o o o u u p v v T s s V gz 2 /2 Change in Exergy: U U p V V T S S DE = E2-E1 2 1 o 2 1 o

11 Notes for Exergy Analysis It can be used for both adiabatic and non-adiabatic processes. It shows how close a device operating between two fixed end states is to its optimum performance. It identifies the system components most responsible for sub-optimum system performance. 7.11

12 Notes on exergy Exergy is a measure of the departure of the state of a system from that of the environment. Exergy can be regarded as a property of the system, once the environment is specified. Exergy cannot be negative! Exergy is not conserved but is destroyed by irreversibilities. Exergy E does not include chemical availability. Exergy viewed as the maximum theoretical work Exergy can be regarded as the minimum theoretical work input required to bring the system from the dead state to the given state. 7.12

13 change in exergy Closed System Exergy Balance Energy balance Entropy balance Multiply the entropy balance by the temperature T 0 and subtract the resulting expression from the energy balance use the change in exergy closed system exergy balance 7.13

14 Closed System Exergy Balance Obtained by deduction from the energy and entropy balances can be used in place of the entropy balance as an expression of the second law. The exergy balance can be used to determine the locations, types, and magnitudes of energy resource waste 7.14

15 Closed System Exergy Balance destruction of exergy The value of the exergy destruction cannot be negative. It is not a property. Exergy is a property the change in exergy of a system can be positive, negative, or zero 7.15

16 Closed System Exergy Rate Balance For an isolated system, no heat or work interactions with the surroundings occur no transfers of exergy the counterpart of the increase of entropy principle regarded as an alternative statement of the second law 7.16

17 Flow exergy specific flow exergy 7.17

18 Closed System Exergy Rate Balance specific flow exergy Exergy Rate Balance for Control Volumes 7.18

Lecture 29-30: Closed system entropy balance

ME 200 Thermodynamics I Spring 2016 Lecture 29-30: Closed system entropy balance Yong Li Shanghai Jiao Tong University Institute of Refrigeration and Cryogenics 800 Dong Chuan Road Shanghai, 200240, P.