lecture 1 slides draravind 22-10-2010...
TRANSCRIPT
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Technische Universität München
EXERGY ANALYSIS
P.V. AravindAssistant Professor, Delft University of Technology
Visiting Lecturer, TU Munich
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Technische Universität München
EXERGY
• definition
• calculation of exergy values (incl. chemical exergy)
• calculation of exergy loss
• exergy efficiencies
• visualization of exergy and exergy loss
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Technische Universität München
EXERGY PURPOSE OF EXERGY ANALYSIS
• to determine exergy losses (true thermodynamic losses) in processes and systems
• minimisation of losses / optimisation of driving forces
THIS COURSE DISCUSSES• the calculation of exergy values:
exergy of heatexergy of a flow of matter: thermo-mechanical exergy
chemical exergy• calculation of exergy losses in open, steady state systems ( )• definition of exergy efficiencies (apparatuses, plants)• visualization of exergy losses and flows in diagrams:
property diagrams (T,s-, h,s-diagrams)exergy flow diagrams (Grassmann-diagrams)value diagrams
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Technische Universität München
DEFINITION OF EXERGY
A MORE COMPREHENSIVE DEFINITION:
EXERGY = the work that can be obtained from an amount of energy
(converted in a well-defined system), under ideal conditions
(applying reversible processes), using the environment only
as a reservoir of heat and matter
GENERAL DEFINITION:
EXERGY = the maximum theoretical work that can be obtained
from an amount of energy
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Technische Universität München
EXERGY ANALYSIS OF OPEN, STEADY STATE, CONSTANT VOLUME SYSTEMS
open, steady state, constant volume systems to determine:
• the exergy of heat
• the exergy of (mass) flows
(work is 100% exergy)
general layout of real systems (open steady state system with constant volume)
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Technische Universität München
EXERGY OF HEATTo calculate the exergy of heat (at temperature T):• make use of a reversible thermal power cycle (closed cycle)• heat is discharged only to the environment (at T0)
maximum theoretical work from a reversible power cycle:
with TH = T and TC = T0:
thus:
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Technische Universität München
EXERGY OF HEAT
exergy of heat:
in general, heat will be transferred to asystem at varying temperatures:
or:
= thermodynamic equivalent temperatureof heat transfer to the cycle
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Technische Universität München
EXERGY OF A FLOW OF MATTERCharacteristics of a system used to determine the exergy of a flow of matter:
• system with only reversible processes
• steady state flow in open system with constant volume
• heat is transferred only to and from the environment at T0
• system brings matter into equilibrium with environment
lay-out of a system that brings an amount of substance (or mass flow) into equilibrium with environment:
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Technische Universität München
equilibrium with environment means (in this case):
• system outlet pressure equals p0
• system outlet temperature equals T0
NB• at system outlet the matter is in
thermo-mechanical equilibrium withthe environment
• chemical composition of matter remains unchanged• therefore the exergy determined in this way is called:
thermo-mechanical exergy
EXERGY OF A FLOW OF MATTER
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Technische Universität München
reversible processes:
heat is supplied at T0: (2)
combining (1) and (2):
DETERMINING THE EXERGY OF A FLOWenergy balance of an open steady state system with constant volume:
as:
and for a flow of mass:
than: (1)
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Technische Universität München
exergy balance of an irreversible systemin steady state:
for the considered system:
can be written:
with:
thus:
EXERGY LOSS OF AN OPEN, STEADY STATE, CONSTANT VOLUME SYSTEM
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Technische Universität München
combining the results from the previous slide gives:
combining these two equations gives:
than the exergy balance becomes:
from the first law it is known that (energy balance of open steady state system):
the entropy balance is:
EXERGY LOSS OF AN OPEN, STEADY STATE, CONSTANT VOLUME SYSTEM
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Technische Universität München
EXERGY EFFICIENCY OF HEAT EXCHANGEpossible definition of heat exchanger efficiency(universal efficiency)
as
thus
correct definition of heat exchanger efficiency (functional efficiency)
note that: and therefore:
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Technische Universität München
EXERGY EFFICIENCY HEAT EXCHANGEuniversal exergy efficiency (should be avoided):
functional (correct) exergy efficiency:
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Technische Universität München
a universal efficiency can be used if a definition of the functional efficiency is not possible (i.e. if no product can be defined)
(universal efficiency):
EXERGY EFFICIENCIESCONCLUSION:only the functional exergy-efficiency is a true thermodynamic efficiency
Exproduct and Exsource have to be specified for each type of system
exergy efficiency:(= functional efficiency)
Exin = exergy of energy flows entering the system Exout = exergy of energy flows leaving the system
note that:
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Technische Universität München
EXERGY EFFICIENCIES OF EXPANSION (TURBINE)AND COMPRESSION (COMPRESSOR)
exergy efficiency of steam turbines:
exergy efficiency of compressors:
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Technische Universität München
with: etc.
EXERGY EFFICIENCY COMBUSTION(adiabatic combustion)
Extm = thermo-mechanical exergyExch = chemical exergy
exergy efficiency of adiabatic combustor:
if fuel and oxidant are supplied at environmental temperature
and the equation simplifies into:
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Technische Universität München
EXERGY EFFICIENCIES
exergy efficiency:(= functional efficiency)
universal efficiency:
however in cases where no product can be defined the universal efficiency enables a thermodynamic comparison of alternative systems
CONCLUSION:the functional efficiency is the only true thermodynamic efficiency
therefore:
definition of exergy efficiencies of specific processes see BB wb4302:course documents/additional information/appendix exergy efficiencies
warning: be very careful with using efficiencies for the assessment ofthe thermodynamic quality of processes or systems!!!
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