Transcript HEAT PROCESSES - Czech Technical University in Prague

HP3
HEAT PROCESSES
Application of
Ts,hs,ph diagrams in
refrigeration and
cryogenic cycles.
Enthalpy, entropy,
exergy Balances
Isobaric and isoenthalpic processes, choking and Joule Thomson effect in real gases
(derivation of JT coefficient). Application of JT effect for liquefaction of gases in Linde
process (kryogenics). Enthalpic balances (example: two stage compressor refrigeration,
ph diagrams). Entropy and exergy balances. Exergetic losses: choking and heat
exchangers. Heat processes design based upon entropy generation minimization EGM
Rudolf Žitný, Ústav procesní a
(derivation
ds/dt).
Process
integration.
zpracovatelské
techniky
ČVUT FS
2010
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T-s, h-s, p-h diagrams (application
for refrigeration and cryogenic cycles)
Vapor compression refrigeration uses reverse Rankine cycle. Compressor
increases pressure of refrigerant vapour (ammonia, freons…). Hot vapours are cooled down in condenser.
Liquefied refrigerant expands in the expansion valve (throttle valve) – flash evaporation consumes enthalpy
of evaporation that is removed from the cooled media.
Absorption refrigeration operates also with the reverse Rankine cycle, but compressor is
replaced by an absorber. Refrigerant vapours (e.g. ammonia) are absorbed in liquid (e.g.water) and their
pressure is increased by pump (power of pump is very small because it is only liquid). At this elevated
pressure the refrigerant vapours are desorbed from liquid by supplied heat.
Cryogenics and liquefaction of gases utilise also the expansion valve for temperature
decrease, but unlike the refrigeration techniques the refrigerant vapour and not liquid expands in the throttle
valve (resulting temperature decrease is caused by the Joule Thomson effect that will be described later).
What happened with the refrigerant liquid or vapours when passing
through the throttle valve will be discussed next
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Throttling h=0
Let us assume 1 kg of fluid that flows through a porous plug (or
expansion valve), that reduces pressure from p1 to p2 The duct is
thermally insulated therefore q = 0.
1 kg of fluid is in front of a plug
p1,T1,u1,v1
1 kg of fluid is displaced behind the plug
p2,T2,u2,v2
The first law of thermodynamic describes energy balance of this 1 kg of
fluid taking into account mechanical work done by the fictive pistons
displacing fluid through the plug
0  u2  u1  p1v1  p2 v2  h2  h1
Internal energy change
Mechanical work done by pistons
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Compressor refrigeration
This is the way how your household refrigerator or air conditioning (heat pumpwith exchanged roles of condenser and evaporator) operates
3
T
3
Condenser
2
Compressor
2
Throttle
valve
4
1
1
s
4
Evaporator
p-h diagrams are usually used for the
compressor refrigeration design
Throttling is represented by vertical line in the ph
diagram
p
2
3
1
4
h
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Multistage compr. refrigeration
6
7
m 1
Two stage system with medium pressure vessel and common
refrigerant. Thermal efficiency is increased.
5
6
4
p
3
m 2
3
7
4
2
2
8
8
5
1
1
h
Flowrates in first and second stage are different. Ratio of mass
flowrates follows from the enthalpy balance of the medium pressure
vessel.
 2 (h2  h3 )  m
 1 (h7  h4 )  Q ztraty
0m
For thermally insulated vessel (Q=0) holds
m 2 h4  h7

m 1 h2  h3
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Refrigerants
 Both the temperature in evaporator and condenser must be between the triple
point and the critical temperatures Ttp< T < Tcrit
Refrigerant
Ttp
oC
Ammonia NH3 -78
CO2
-80
R12
-158
Tcrit
Tbp
pcrit
oC
oC
MPa
132
-33
11
31 sublimate at atmospheric pressure
112
-30
4
 Cooling capacity kJ/m3 determines compressor size (capacity should be as high
as possible).
 Working pressures are usually between 100 kPa and 2 MPa (according to
compressor used).
 Freons are prohibited (R12 is CCl2F2, and aggressive radicals of Fluor destroy
ozonosphere).
Properties of refrigerants are available in databases.
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Cryogenics
Production, transport and storage of liquefied gases.
Gas
Boiling point oC at
He
-270
H2
-250
N2
-200
O2
-180
CH4
-160
atmospheric pressure
Such low temperatures can be achieved by using Joule Thomson effect,
cooling of a real gas during expansions from very high pressure through
throttle valve.
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Joule Thomson effect
What is the temperature of gas after throttling: higher, lower or remains unchanged?
Answer depends upon properties of gas and inlet temperature (Joule Thomson effect)
dh  0  c p dT  (T (
v
) p  v)dp
T
From this equation the Joule Thomson coefficient JT can be expressed as
 JT  (
T
v T v
v
) h  ( ( ) p  1)  (T  1)
p
c p v T
cp
JT coefficient is positive if T>1 (-coefficient of
temperature expansion) and only then the temperature
decreases with the pressure release. Dependence of the
JT coefficient upon temperature is shown in Fig.
It is seen that JT is positive at room temperature for most
gases with the exception of hydrogen and helium (for them
preliminary cooling is necessary). High values of JT are
achieved at low temperatures therefore it is always
desirable to to cool down gases before expansion.
For ideal gas α=1/T
and temperature
remains constant
Cryogenics - Linde
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Linde-Hampson cycle – final cool down using throttling of precooled gas
Liquefactrion
of air
1
2
1
Multistage
compressor with
2
intercoolers
p=200 bar
3
Throttle
valve
p=1 bar
4
5
T
3
Separator
6
6
5
4
s
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Cryogenics -Kapica
Kapica cycle – expansion in turbodetander
1
2
Compressor
2
3
Detander
3
T
4
8
9
5
Throttle
valve
4
7
8
6
5
Separátor
7
s
6
1
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Continuous system-balances
Hockney
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Continuous system-balance
Design of thermal units operating in continuous mode is always based
upon balances
Mass balances (this is quite easy)
Enthalpy balances (power consumption, temperatures… sizing equipment)
Exergetic balances
(enable to estimate measure of irreversibility)
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Enthalpy balance
Similar analysis as in throttling. We assume constant volume of system V. During the
time increment dt the heat dQ is delivered to the system and the technical work dW is
done by the system.
Mass flowrate at inlet
1
p1,u1,dV1
m
dQ
u, V, 
2
m
State at time t
dW
u+du, V,
p2, u2,dV2
+d
State at time t+dt
Technical work of
turbine (e.g.)
dQ  dW  V (u  du)(  d )  Vu  dV11u1  dV2  2u2  p1dV1  p2 dV2
Internal energy change (mass m)
Mechanical work for inlet/outlet
dQ dW
d (u )

V
 m 2 (u2  p2 v2 )  m 1 (u1  p1v1 )
dt
dt
dt
d (u )
Q  W  V
 m 2 h2  m 1h1
dt
Exergetic balances
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Exergy e [J/kg] is maximum technical work obtainable by transition to the
state of environment having infinitely large thermal capacity (e.g. an
ocean having temperature Te that remains constant even if heat is
supplied or removed from the ocean) .
Steady state enthalpy balance
(for 1 kg of matter)
T
0  hin  hout  q  w
1
Isoentropic
expansion
0  h1  he T e( s1  se )  e
Exergy
e
Heat absorbed in ocean
s
Exergetic loss analysis of
continuous systems enables to
find out “weak points” from the
point of view of large irreversible
losses.
e  h1  he T e( s1  se )
ein  eout  hin  hout T e( sin  sout )
losses due to
irreversibility
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Exergetic balances examples
Throttle valve
h1  h2
e  Te s
Tds  dh  vdp
vdp
dp
ds  
 R
T
p
e  Te R ln
p2
p1
Heat exchanger
T1
Heat dq is removed from hot stream at temperature T1 and
transferred to cold stream at T2. Entropy of the hot stream
decreases and entropy of the cold stream increases
ds1  
dq
T2
Heat transfer surface
T  T2
dq
dq
ds2 
ds  ds1  ds2  dq 1
T1
T2
T1T2
Assuming no heat losses (dh=0) the exergy losses
are
T T
de1  Te ds  Te dq
1
T1T2
2
Exergetic balances example
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Heat exchanger water/water, mass flowrate in both streams 1 kg/s, hot stream is
cooled down from 95 to 900C, cold stream is heated from 40 to 450C.
Heat exchanger can be substituted by HEAT PUMP and TURBINE Carnot cycles
T 0C
T 0C
95
95
90
90
T [0C]
3.7kW
1kW
45
45
40
40
h [kJ/kg]
s[kJ/kg/K]
40
167.45
0.5721
45
188.35
0.6383
90
376.94
1.1925
95
397.99
1.25
Te=27
Te=27
0.58 0.64
H=21kW
1.2 1.25
s
Net profit would be 2.7kW of mechanical energy, the same as the exergetic
loss of heat exchanger
T T
50
E  QTe
H
TH TC
C
 21 300 
365  315
2.7kW
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EGM Entropy Generation Minimization
There are always many different design parameters of apparatuses for thermal
unit operations (diameters of pipes, fins,…) satisfying specification, e.g. required
duty, maximal pressures, temperatures… Optimum is always a compromise,
typically trade off between heat transfer and pressure drop (if you increase
velocity in a heat exchanger the heat transfer coefficients increase, but at the
same time also pressure loss increases). And it is difficult to balance quite
different phenomena: thermodynamics and hydraulics. Frequently the
specification of free design parameters is a matter of experience, but…
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EGM Entropy Generation Minimization
EGM is a design concept based upon minimization of irreversible processes. It
is a new philosophy: reversible processes are good, irreversible wrong.
As a measure of irreversibility the rate of entropy generation in a system is
considered. Entropy increase is caused by heat transfer from high to low
temperatures (this is always irreversible process) and also by hydrodynamics,
by frictional losses (conversion of mechanical energy to heat by friction is also
irreversible). These two causes can be summarized for the case of continuous
fluid flow (general temperature and flow velocity distribution in space) as
S gen
Rate of entropy
increase in unit
volume W
3
m K
T 2  : u
 (
) 
T
T
Irreversibility due to heat
conduction.  is thermal
conductivity. See also
previous expression
T T
ds  dq 1 2
T1T2
Scalar product of viscous
stress tensor  and
gradient of velocity u is
power dissipated to heat
in unit volume
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EGM Entropy Generation Minimization
Previous equation needs explanation. Let us assume a rod of cross section A,
thickness dx, made from material with thermal conductivity .
T
T+dT
Q   AT   A
Sin  
x
x+dx
 A dT
dSvolumeAdx
Sout  
 A dT
T  dT dx
dT 1
1
 Sout  Sin   A
( 
)
dx T T  dT
 Adx dT 2
 dT 2

(
)
dS

( )
gen
2
2
T
dx
T dx
T dx
dSvolumeAdx
dT
dx
Heat flux is directly
proportional to temperature
gradient
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EGM Entropy Generation Minimization
Example:
Internal flow in a heat exchanger pipe: Given fluid (viscosity , thermal conductivity …),
mass flowrate through a pipe ( m ), and heat flux q’ corresponding to 1 meter of pipe, find out the
diameter of pipe D giving minimum generated entropy. Rate of entropy generation related to unit length
of a pipe is the sum of entropy changes in fluid and environment (in the pipe wall):
q’
m
D
T+T wall temperature
Tfluid temperature
x
Entropy
increase in fluid
Entropy decrease
of environment
Entropy production in
system: pipe+environment
ds
q'
S 'gen  m 
dx T  T
Enthalpy balance mdh  q ' dx
Tds  dh  vdp
ds 1 dh v dp q '
1 dp




dx T dx T dx mT T dx
S 'gen 
Remark: You can alternatively derive the same result
from previous EGM expression, knowing that the
 p / 
dissipated power [W]  Vp  m
q ' m dp
q'
q ' T
m dp




T T dx T  T T (T  T ) T dx
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EGM Entropy Generation Minimization
For circular pipe (q’ is related to unit length of pipe)
q'
q'
T 

 D  Nu
dp
u2 
4m 2 
m2

2f
2f(
)
 32 f
2
dx
D
D  D
 2 D5
Nusselt
number
Fanning friction
factor
And substituting to the previous equation
S 'gen
Nusselt number Nu and
Fanning friction factor f must
be evaluated for
laminar/turbulent flow regime
q '2
32m3 f

 2 2 5
2
T Nu   TD
Minimisation of Sgen gives the optimal value of Reynolds number
Reopt 
uD

 2.02Pr 0.07 (
mq ' 
 5T
See the paper Exergy analysis… by A.Bejan
)0.36
This result holds for turbulent
flow 2500<Re<1e6 and Pr>0.5
(almost any fluids)
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EGM Entropy Generation Minimization
Similar analysis can be applied for external flows (flows around
sphere, cylinder, fins…). Assuming constant temperature of body TB
and constant temperature T and velocity u of fluid far from the
surface, the total entropy generation rate can be expressed as
S gen
Q(TB  T ) FDu


TBT
T
FD is drag force
therefore FDu is
power dissipated to
heat
Need to know more about EGM? Read the book Entropy Generation
Minimization by Adrian Bejan, Frank A. Kulacki (Editor) Crc Press (Oct 1995)
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EGM Entropy Generation Minimization Papers
Susan W. Stewart, Samuel V. Shelton: Finned-tube condenser design optimization using
thermoeconomic isolation. Applied Thermal Engineering 30 (2010) 2096-2102
Using a detailed system model as a comparison, this study shows that isolating the condenser component and optimizing
it independently by minimizing the entropy generation in the condenser component alone, also known as thermoeconomic
isolation, can be a practical way to design the condenser for optimum air-conditioning system efficiency. This study is
accomplished by comparing the optimum design determined by maximizing the entire system’s COP, an undisputed
method, with the optimum design determined by minimizing the entropy generation in the isolated condenser component,
with consistent constraints used for the two methods. The resulting optimum designs from the isolated model produced a
COP within 0.6%e1.7% of the designs found by optimizing the COP using an entire system model.
A good review of EGM applications (references on papers applying entropy minimization
to counter flow HE, cross flow HE, shell&tube HE, finned tube condensers, wavy plate HE, offset strip HE)
A model of an air-conditioning system using R-410a as the working fluid was developed in EngineeringEquation
Solver (EES) [33]. This model includes a detailed simulation of the components of the air-conditioning system for
various designs, including the compressor, finned-tube condenser, evaporator, and expansion valve.
The paper doesn’t discuss details of EGM, for me it is only an indicator
of the fact that the EGM concept gives similar results as the analysis
based upon COP method.
Optimized geometrical
parameters
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EGM Entropy Generation Minimization Papers
Jiangfeng Guo, Lin Cheng, Mingtian Xu:Optimization design of shell-and-tube heat exchanger by
entropy generation minimization and genetic algorithm. Applied Thermal Engineering 29 (2009) 2954–
2960
In the present work, a new shell-and-tube heat exchanger optimization design approach is developed, wherein the
dimensionless entropy generation rate obtained by scaling the entropy generation on the ratio of the heat transfer rate to the
inlet temperature of cold fluid is employed as the objective function, some geometrical parameters of the shell-and-tube heat
exchanger are taken as the design variables and the genetic algorithm is applied to solve the associated optimization
problem. It is shown that for the case that the heat duty is given, not only can the optimization design increase the heat
exchanger effectiveness significantly, but also decrease the pumping power dramatically. In the case that the heat transfer
area is fixed, the benefit from the increase of the heat exchanger effectiveness is much more than the increasing cost of the
pumping power.
the entropy increase
by heat transfer
the entropy generation number
defined by Bejan suffers from the
‘entropy generation paradox’, while
the modified entropy generation
number avoids such a paradox.
the entropy
increase by friction
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EGM Entropy Generation Minimization Papers
Lina Zhang,Chun xin Yang, Jian hui Zhou : A distributed parameter model and its application in
optimizing the plate-fin heat exchanger based on the minimum entropy generation. International Journal
of Thermal Sciences 49(2010) 1427-1436
Temperatures and pressures are
calculated in each 3D cell
numerically
Different optimization methods, for
example genetic algorithms are used in
the EGM (multi variable minimization of
Sgen).
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Process Integration Pinch Analysis and Targeting
Exergetic analysis enables to identify units (boilers, reactors, heat
exchangers, furnaces,…) responsible for major irreversible losses in
complicated systems (e.g. processing plants of chemical industry).
EGM is concentrated to the engineering design of individual apparatuses.
Process integration is technology of a preliminary design of complicated
systems (network of heat exchangers) aimed to “optimal” arrangement of
thermal units from the point of view of process heat utilisation (internal heat
transfer between sources and sinks) and minimization of irreversible heat
transfer. Key feature is PINCH analysis (it has nothing to do with dogs).
Pinch is a critical point in the network of heat exchanger characterised by
the smallest temperature difference (approach) between the hot and cold
streams. Tells nothing to you, is it confusing? Read e.g. the short and easy
paper Gavin P. Towler: Integrated process design for improved energy efficiency. Renewable
Energy, Volume 9, Issues 1-4, September-December 1996, Pages 1076-1080
Need to know more about the process integration? Read papers from Bodo
Linnhoff, father of this technology (UMIST Manchester) or the paper of his colleague Klemesh
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Process Integration Pinch Analysis and Targeting
System is described as a list of apparatuses (reactors, separators, distillation
columns, furnaces,…, so far without heat exchangers) connected by streams.
Temperatures and flowrates at entries and outlets of apparatuses are specified
according to process requirements.
First step of process integration consists in generation of a table of process
streams. Each stream is characterized by mass flowrate [kg/s], heat capacity,
inlet and outlet temperatures and enthalpy flows H [W] which must be added to
heated cold streams or rejected from hot streams.
Streams are plotted in graph T,H as vectors (lines if the heat capacity of stream
is constant). Vectors of hot streams are added together (by adding enthalpy
flow changes) giving composite curve
T
T
1
2
1+2
H
H
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Process Integration Pinch Analysis and Targeting
Composite curve of hot and cold streams in T-H diagram (plot of composite curves is
obtained by summing enthalpy changes in the table of process streams)
Hot service requirement
T [C]
Pinch
point
Streams below pinch
H
C
Streams above pinch
Heat utilised by heat exchangers
Cold service requirement
H [W]
The composite curves can be freely shifted in
horizontal direction because H represents
only enthalpy flow changes. Moving for
example the composite curve of cold
streams to the right increases temperature
difference between the streams (heat
transfer surface of the heat exchangers
transferring enthalpy from hot to cold
streams will be smaller), but at the same
time demands on hot and cold service
increases.
Process integration aims to find out a
compromise between the amount of utilised
processed heat and investment (heat
transfer surface of HE). This optimum
determines position of pinch point.
Pinch point divides process streams to streams
above and bellow pinch and according to
this the following simple design rules can be
expressed:
1.
Never use hot service bellow pinch
2.
Never use cold service above pinch
3.
Never transfer heat across the pinch
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Process Integration Pinch Analysis and Targeting
Grand Composite Curve (GCC). GCC serves for alocation of hot/cold services to
different utility levels (with the aim to satisfy the process requirement by the lowest
possible quality of heat, e.g. using cooling water instead of refrigeration).
GCC is created from the composite curve by increasing the cold composite temperature by ½ DTmin and
decreasing the hot composite temperature by ½ DTmin
Hot service requirement
T [C]
T [C]
DTmin
Only a part of hot service is
supplied by high pressure steam
Part of hot service delivered by
medium pressure steam
H [W]
Cold service requirement
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Process Integration Pinch Analysis and Targeting
Try on line web application (written by undergraduate student J.S.Umbach university of Illinois, Chicago 2010)
Composite curves
Grand composite curves
(exchanged axis – enthalpy flow vertical, temperatures and shifted temperatures on horizontal axis,
please note that the GCC are simplified – only the composite cold curve is shifted up by DTmin=10)