Proveden

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HEAT PROCESSES
Thermodynamicsprocesses and cycles
Thermodynamics fundamentals. State variables,
Gibbs phase rule, state equations, internal
energy, enthalpy, entropy. First law and the
second law of thermodynamics. Phase changes and
phase diagrams. Ts and hs diagrams (example Ts
diagrams for air). Thermodynamic cycles Carnot,
Clausius Rankine, Ericson, Stirling,
thermoacoustics.
Rudolf Žitný, Ústav procesní a zpracovatelské
techniky CVUT FS 2010
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FUNDAMENTALS of THERMODYNAMICS
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Estes
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BASIC NOTIONS
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Subsystem flame zone opened

• SYSTEM
• Insulated- without mass or energy transfer
• Closed (without mass transfer)
• Opened (mass and heat transport through
  boundary).
• Thermal units operating in continuous mode (heat
  exchangers, evaporators, driers, tubular
  reactors, burners) are opened systems
• Thermal units operating in a batch mode (some
  chemical reactors) are closed systems

Subsystem candlewick opened
Subsystem candle opened with moving boundary
Subsystem stand closed
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StaTE VARIABLES
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state of system is characterized by

• THERMODYNAMIC STATE VARIABLES related with
  directly measurable mechanical properties
• T K, p PaJ/m3, v m3/kg (temperature,
  pressure, specific volume)

• Thermodynamické state variables related to energy
  (could be derived from T,p,v)
• u J/kg internal energy
• s J/kg/K specific entropy
• h J/kg enthalpy
• g J/kg gibbs energy
• e J/kg exergy

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Gibbs phase rule
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Not all state variables are independent. Number
of independent variables (DOF, Degree Of Freedom)
is given by Gibbs rule
NDOF Ncomponents Nphases 2

• 1 component, 1 phase (e.g.gaseous oxygen)
  NDOF2 . In this case only two state variables
  can be selected arbitrarily, e.g. p,v, or p,T or
  v,T.
• 1 component, 2 phases (e.g. equilibrium mixture
  of water and steam at the state of
  evaporation/condensation). In this case only one
  state variable can be selected, e.g. pressure
  (boiling point temperature is determined by p)

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State EquATIONS p-v-T
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Van der Waals equation isotherms
Critical point, solution of these two equations
give a,b parameters as a function of critical
temperature and critical pressure
Above critical temperature Tc the substance
exists only as a gas (liquefaction is not
possible even at infinitely great pressure)
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PvRT tutorial Baloon
Example Calculate load capacity of a baloon
filled by hot air. D20m, T600C, Te200C, p105
Pa.
M29 (air)
D
m
599 kg
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PvRT tutorial Syringe
Record time change of temperature of air
compressed in syringe.

Thermocouple

P-pressure transducer Kulite XTM 140
Adiabatic change (thermally insulated)

Example V2/V10.5 ?cp/cv1.4 T1300
K T2396 K temperature increase 96 K!!
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PvRT tutorial - expansion
Dynamic inflation test of a viscoelastic pipe
(carried out in our laboratory of cardiovascular
mechanics) was based upon recorded oscillation of
pressure after a sudden release of pressure in a
container. We did not know a reason for a gradual
pressure increase in the end of experiment.
Possible explanation Temperature of
adiabatically expanded air initially drops and
later on slowly increases to the room temperature
(and this is accompanied by a gradual increase of
pressure).
Example p2/p135/600.58 ?cp/cv1.4
T1300 K T2257 K Slow heating (closed
vessel) to the final temperature 300K
tested sample, viscoelastic tube (blood vessel)
In this way only a final value p3 is analysed. It
is necessary to know heat transfer rate (heat
transf.coef.) to calculate the time change of p.
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Internal energy u J/kg
u-all forms of energy of matter inside the system
(J/kg), invariant with respect to coordinate
system (potential energy of height /gh/ and
kinetic energy of motion of the whole system
/½w2/ are not included in the internal energy).
Internal energy is determined by structure,
composition and momentum of all components, i.e.
all atoms and molecules.

• Nuclear energy (nucleus) 1017J/kg
• Chemical energy of ionic/covalent bonds in
  molecule 107 J/kg
• Intermolecular VdW forces (phase changes)
  106 J/kg
• Thermal energy (kinetic energy of molecules)
  104 J/kg

Frequently only the following item (thermal
energy) is included into the internal energy
notion (sometimes distinguished as the sensible
internal energy)
It follows from energy balances that the change
of internal energy of a closed system at a
constant volume equals amount of heat delivered
to the system du dq (heat added at isochoric
change)
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Enthalpy h J/kg
hupv enthalpy is always greater than the
internal energy. The added term pv (pressure
multiplied by specific volume) simplifies energy
balancing of continuous systems. The pv term
automatically takes into account mechanical work
(energy) necessary to push/pull the inlet/outlet
material streams to/from the balanced system.
It follows from energy balances that the change
of enthalpy of a closed system at a constant
pressure equals amount of heat delivered to the
system dh dq (heat added at isobaric change)
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Entropy s J/kg/K
Thermodynamic definition of entropy s by Clausius
where ds is the specific entropy change of
system corresponding to the heat dq J/kg added
in a reversible way at temperature T K.
Boltzmanns statistical approach Entropy
represents probability of a macroscopic state
(macrostate is temperature, concentration,).
This probability is proportional to the number of
microstates corresponding to a macrostate (number
of possible configurations, e.g. distribution of
molecules to different energy levels, for given
temperature).
It follows from energy balances that the change
of entropy of a closed system at a constant
temperature equals amount of heat delivered to
the system / T Tds dq (heat added at an
isothermal and reversible change)
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Laws of thermodynamics
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Modigliani
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Laws of thermodynamics
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First law of thermodynamics (conservation of
energy)
dw work done by system
dq heat added to system
expansion work (p.dV) in case of compressible
fluids, surface work (surface tension x increase
of surface), shear stresses x displacement, but
also electrical work (intensity of electric field
x current). Later on we shall use only the p.dV
mechanical expansion work.
dq du dw
Second law of thermodynamics (entropy of closed
insulated system increases)
dq heat added to system is Tds only in the case
of reversible process
Tds ? dq
Combined first and second law of thermodynamics
Tds dupdv
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THERMODYNAMIC relationships
Be careful at interpretation First law of
thermodynamic was presented in the form
corresponding only to reversible changes
(therefore for infinitely slow changes, without
viscous friction, at uniform temperature) This
equation enables to calculate the entropy change
during a reversible process. However, entropy is
a state variable, and its changes are independent
of the way, how the changes were realized (there
are always infinitely many ways how to proceed
from a state 1 to a state 2). So, why not to
select the reversible way even in the case, when
the real process is irreversible? It is always
simpler and results (for example calculated
entropy changes) hold generally even for
irreversible (real) processes. In the following
it will be demonstrated how to calculate internal
energy and enthalpy changes from the measured
changes of temperature, pressure and volume (and
results hold not only for the reversible
processes).
reversible processes are generally defined as
changes of state (1?2) which can be recovered
(2?1) without any change of the system
environment. In an irreversible process it is
also possible to return back (to the initial
state) but heat or work must be added from
environment.
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Example insulated system
Let us consider a perfectly insulated calorimeter
(Deware flask, e.g.) containing a cold metallic
block (temperature Tm) and hot water (Tw).
At a time interval dt the temperature of water Tw
decreases by dTw-dQwm/(mwcpw) and the
temperature Tm increases by dTmdQwm/(mmcpm),
however the sum of inner energies Uummmuwmw
remains, therefore dU0. Volume V is constant and
dV0. Therefore the entropy increase of the
whole system dS should be zero (dS0)
Water Tw300K
dQwm
This conclusion is wrong, because the whole
process is irreversible and dS is actually
positive. So that the previous equation could be
used the whole process must be substituted by an
equivalent but reversible process. For example
the water can be used for heating
Metal Tm273K
of a fictive gas at constant temperature Tw
(reversibly, entropy of water will be decreased
by dQwm/Tw), followed by an adiabatic expansion
cooling down the gas to the temperature Tm
(reversible expansion, not changing the entropy
of gas). The gas then isothermally and reversibly
heats the metallic block, thus increasing its
entropy by dQwm/Tm. Summing the entropy changes
gives
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Energies and Temperature
The temperature increase increases thermal energy
(kinetic energy of molecules). For constant
volume (fixed volume of system) internal energy
change is proportional to the change of
thermodynamic temperature (Kelvins) du cv
dT where cv is specific heat at constant
volume For constant pressure (e.g. atmospheric
pressure) the enthalpy change is also
proportional to the thermodynamic temperature
dh cp dT where cp is specific heat at
constant pressure. Specific heat at a constant
pressure is always greater than the specific heat
at a constant volume (it is always necessary to
supply more heat to increase temperature at
constant pressure, because part of the delivered
energy is converted to the volume increase,
therefore to the mechanical work). Only for
incompressible materials it holds cpcv.
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Energies and Temperature
Internal energy (kinetic energy of translatory
motion) of one monoatomic molecule of an ideal
gas is given by
where k is Boltzmann constant 1.380650410-23
Kinetic energy (1/2mw2) of chaotic thermal motion
is therefore independent of molecular mass
(lighter molecules are moving faster)! Knowing
molecular mass it is therefore possible to
estimate the specific heat capacity cv J/kg/K
theoretically (molar internal energy

, therefore molar heat capacity
. Specific heat capacity is
where M is molecular mass kg/mol. For
helium (M0.004) thus calculated specific heat
capacity cv12.5/0.0043125 J/kg/K. The tabulated
cp value at 300K is cp5193 J/kg/K. This agrees
quite well, because cp-cvR/M8.314/0.0042078
J/kg/K, see the Mayers equation). For more
complicated molecules the equipartition principle
can be applied, stating that any mode of motion
(translational, vibrational, rotational) has the
same energy kT/2 (monoatomic gas has 3
translational modes in the x,y,z directions,
therefore u3kT/2).
According to the equipartition theorem the
specific heat capacities are constants
independent of temperature. This is not quite
true especially at low temperatures, when cv
decreases and in this case quantum mechanics
must be applied. At low temperatures (lt100 K)
only three translational degrees of freedom are
excited (cv3/2R), at higher temperatures two
additional rotational degrees increase cv to 5/2R
(for diatomic molecules N2, H2, O2) and
contribution of vibrational degrees of freedom is
significant at even higher temperatures (gt500 K).
In water rotational and vibrational degrees of
freedom are excited at very low temperatures.
This nice animated gif (molecule of a peptide
with atoms C,N,O,H) is captured from Wikipedia.org
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u(T,v) internal energy change
How to evaluate internal energy change? Previous
relationship ducvdT holds only at a constant
volume. However, according to Gibbs rule the du
should depend upon a pair of state variables (for
a one phase system). So how to calculate du as
soon as not only the temperature (dT) but also
the specific volume (dv) are changing? Solution
is based upon the 1st law of thermodynamic (for
reversible changes) where du is expressed in
terms dT and dv (this is what we need),
coefficient at dT is known (cv), however entropy
appears at the dv term. It is not possible to
measure entropy directly (so how to evaluate
ds/dv?), but it is possible to use Maxwell
relationships, stating for example that Instead
of exact derivation I can give you only an idea
based upon dimensional analysis dimension of s/v
is Pa/K and this is just the dimension of p/T!
So there is the final result
cv
ds
This term is zero for ideal gas (pvRT)
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h(T,p) enthalpy changes
The same approach can be applied for the enthalpy
change. So far we can calculate only the enthalpy
change at constant pressure (dhcpdT). Using
definition hupv and the first law of
thermodynamics And the same problem how to
express the entropy term ds/dp by something that
is directly measurable. Dimensional analysis s/p
has dimension J/(kg.K.Pa)m3/(kg.K) and this is
dimension of v/T. Corresponding Maxwells
relationship is After substuting we arrive to
the final expression for enthalpy
change Negative sign in the Maxwell equation
is probably confusing, and cannot be derived from
dimensional analysis. Correct derivation is
presented in the following slide.
cp
Tds
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Maxwell relationships
Basic idea consists in design of a state function
with total differential depending only upon dT
and dp . Such a function is Gibbs energy g
(previously free enthalpy) Notice the fact,
that using this combination of enthalpy and
entropy (h-Ts) the differentials dh and ds are
mutually cancelled. Comparing coefficients at dp
and dT the partial derivatives of Gibbs energy
can be expressed as Because the mixed
derivatives equal, the Maxwell equation follows
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s(T,v) s(T,p) entropy changes
Changes of entropy follow from previous equations
for internal energy and enthalpy
changes Special case for IDEAL GAS (pvRmT,
where Rm is individual gas constant) Please
notice the difference between universal and
individual gas constant. And the difference
between molar and specific volume.
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u,h,s finite changes (without phase changes or
reactions)
Previous equations describe only differential
changes. Finite changes must be calculated by
their integration. This integration can be
carried out analytically for constant values of
heat capacities cp, cp and for state equation of
ideal gas
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u,h,s finite changes during phase changes
During phase changes (evaporation, condensation,
melting,) both temperature T and pressure p
remain constant. Only specific volume varies and
the enthalpy/entropy changes depend upon only one
state variable (for example temperature). These
functions are tabulated (e.g. ?h-enthalpy of
evaporation) as a function of temperature (see
table for evaporation of water), or approximated
by correlation
T0C pPa ?hkJ/kg
0 593 2538
50 12335 2404
100 101384 2255
200 1559120 1898
300 8498611 1373
Tc647 K, T1373 K, r2255 kJ/kg, n0.38 for water
Pressure corresponding to the phase change
temperature is calculated from Antoines equation
C-46 K, B3816.44, A23.1964 for water
Entropy change is calculated directly from the
enthalpy change
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h,s during phase changes (phase diagram p-T)
Melting ?hSLgt0, ?sSLgt0,,
Evaporation ?hLGgt0, ?sLGgt0,
Sublimation ?hSGgt0, ?sSGgt0,
Phase transition lines in the p-T diagram are
described by the Clausius Clapeyron equation
?hLG
Specific volume changes, e.g. vG-vL
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h finite changes EXAMPLE

• There are infinitely many ways how to proceed
  from the state 1 to the state 2. For example
• Red way increases first the pressure to the final
  value and continues by heating. Water boils at
  120C (Antoines equation).
• Compression ?hcompres0
• Liquid water ?hcpL.120 for cpL4.21
• Evaporation ?hLG2203 J/kg (from table)
• Steam ?hcpG.380, cpG2.07
• Taken together ?h3495 J/kg
• Green way holds initial pressure when heating up
  to final temperature and isothermal compression
  follows.
• Liquid water ?hcpL.100 for cpL4.20
• Evaporation ?hLG2255 J/kg (from table)
• Steam ?hcpG.400, cpG2.05
• Isothermal compression ?hcompres0
• Sum (1-4) gives the same result ?h3495 J/kg

Final state T2500C, p22bar
Initial state T10C, p11bar
1200C
1000C
Remark cp depends upon temperature (use tables)
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s finite changes EXAMPLE
Entropy change follows directly from definition
Final state T280C, p21bar
Initial state T120C, p11bar
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SUMMARY
State equation p,v,T. Ideal gas pVnRT (n-number
of moles, R8.314 J/mol.K) First law of
thermodynamics (and entropy change) Internal
energy increment (ducv.dT for constant volume
dv0) Enthalpy increment (dhcp.dT for
constant pressure dp0)

These terms are zero for ideal gas (pvRT)
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Check units
It is always useful to check units all terms in
equations must have the same dimension. Examples
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Important values
cvcp ice 2 kJ/(kg.K) cvcp water 4.2
kJ/(kg.K) cp steam 2 kJ/(kg.K) cp air
1 kJ/(kg.K) ?henthalpyof
evaporation water 2.2 MJ/kg R 8.314
kJ/(kmol.K) Rm water 8.314/18 0.462 kJ/(kg.K)
Example Density of steam at 200 oC and pressure
1 bar.
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THERMODYNAMICDIAGRAMS
Delvaux
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DIAGRAM T-s
isobars
Critical point
isochors
Left curve-liquid
Right curve-saturated steam
Implementation of previous equations in the T-s
diagram with isobars and isochoric lines.
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DIAGRAM h-s
Critical point
Left curve liquid
Right curve saturated steam
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Thermodynamic processes

• Basic processes in thermal apparatuses are
• Isobaric dp0 (heat exchangers, ducts, continuous
  reactors)
• Isoentropic ds0 (adiabatic-thermally insulated
  apparatus, ideal flow without friction, enthalpy
  changes are fully converted to mechanical energy
  compressors, turbines, nozzles)
• Isoenthalpic dh0 (also adiabatic without heat
  exchange with environment, but no mechanical work
  is done and pressure energy is dissipated to
  heat throttling in reduction valves)

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Thermodynamic processes
STEAM expansion in a turbine the enthalpy
decrease is transformed to kinetic energy,
entropy is almost constant (slight increase
corresponds to friction)
h
T
Expansion of saturated steam in a nozzle the same
as turbine (purpose convert enthalpy to kinetic
energy of jet)
s
s
Steam compression power consumption of compressor
is given by enthalpy increase
Throttling of steam in a valve or in a porous
plug. Enthalpy remains constant while pressure
decreases. See next lecture Joule Thomson effect.
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Thermodynamic processes
Superheater of steam. Pressure only slightly
decreases (friction), temperature and enthalpy
increases. Heat delivered to steam is the
enthalpy increase (isobaric process). The heat is
also hatched area in the Ts diagram (integral of
dqTds).
Boiler (evaporation at the boiling point
temperatrure) constant temperature, pressure.
Density decreases, enthalpy and entropy
increases. Hatched area is the enthalpy of
evaporation.
Mixing of condensate and superheated steam
purpose of mixing is to generate a saturated
steam from a superheated steam. Resulting state
is determined by masses of condensate and steam
(lever rule).
37
Thermodynamic cycles
Periodically repeating processes with working
fluid (water, hydrocarbons, CO2,) when heat is
supplied to the fluid in the first phase of the
process followed by the second phase of heat
removal (final state of the working medium is the
same as the initial one, therefore the cycle can
be repeated infinitely many times). Because more
heat is supplied in the first phase than in the
second phase, the difference is the mechanical
work done by the working medium in a turbine
(e.g.). It follows from the first law of
thermodynamics.
38
Thermodynamic cycles
Carnot cycle Mechanical work
3
Clausius Rankine cycle Cycle makes use phase
changes. Example POWERPLANTS. 1-2 feed pump
2-3 boiler and heat
exchangers 3-4 turbine
and generator 4-5
condenser
T
2
4
1
s
Ericsson cycle John Ericsson designed (200 years
ago) several interesting cycles working with only
gaseous phase. Reversed cycle (counterclock
orientation) is applied in air conditioning see
Brayton cycle shown in diagrams.
3
2
1
4
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Thermodynamic cycles
H. Chen et al. / Renewable and Sustainable Energy
Reviews 14 (2010) 30593067
ORC Organic Rankine Cycles supercritical
Rankine cycle (CO2)
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Stirling machine
Engine (work produced)
Stirling cycle Gas cycle having thermodynamic
efficiency of Carnot cycle. Can be used as engine
or heat pump (Stirling machines fy.Philips are
used in cryogenics). Efficiency can be increased
by heat regenerator (usually a porous insert in
the displacement channel capable to absorb heat
from the flowing gas).

1. Compression 1-2 and transport of cool gas to
   heater 2-3
2. Expansion of hot gas
   3-4
3. Displacement of gas from hot to cool section 4-1
4. Compression (1-2)

ß-Stirling
Refrigeration (work consumed)
?-Stirling with regenerator
41
Thermoacoustical engine
Thermoacoustic analogy of Stirling
engine Very simple design can be seen on
Internet video engines. Cylinder can be a glass
test tube with inserted porous layer (stack).
Besides toys there exist applications with rather
great power driven by solar energy or there exist
equipments for cryogenics liquefaction of
natural gas.
Standing waves mutually shifted pressure and
velocity waves (90o)
Wave equation for pressure, velocity. C is speed
of sound
Mechanical design is simple, unlike theoretical
description (N.Rott published series of papers
Thermally driven acoustic oscillations,
I.,II.,III.,IV.,V. in Journal of Applied
Mathematics and Physics in years 1969,1973,
1975,1976). Standing temperature and pressure
waves generated inside the cylinder are mutually
shifted (phase shift is similar to the Stirling
engine, where compression/expansion phases are
shifted with respect to the heating/cooling
phase). Solution of oscillating pressure,
temperature and gas velocity is frequently
realized by Computer Fluid Dynamics codes
(Fluent).
Travelling waves mode in phase pressure and
velocity waves
Travelling waves analogy with Stirling
42
Thermoacoustics
Phenomena and principles of thermoacoustics are
more than hundred years old.
Singing Rijke tube Rijke P.L. Annalen der Physik
107 (1859), 339
Sondhauss tube Sondhauss C. Annalen der Physik 79
(1850), 1
Taconis oscillations Taconis K.W. Physica 15
(1949) 738
Thin tube
Thin tube inserted into a cryogenic liquid
Heated bulb
Liquid helium

• Lord Rayleigh authorLord Rayleigh titleThe
  explanation of certain acoustical phenomena
  journalNature (London) year1878 volume18
  pages319321 formulated principles as follows
  
• thermoacoustic oscillations are generated as soon
  as
• Heat is supplied to the gas at a place of
  greatest condensation (maximum density)
• Heat is removed at a place of maximum rarefaction
  (minimum pressure)

43
Thermoacoustics
Scott Backhaus and Greg Swift New varieties of
thermoacoustic engines, 2002
Thermoacoustic machines can operate either as
heat pumps (usually refrigerators) when forced
oscillations are driven by an oscillating
membrane (usually loadspeaker), or as an engine
(prime mover) that turns heat into mechanical
energy (sound). Spontaneous oscillations (engine
mode) exist only if the axial temperature
gradient in stack is high enough so that the
Rayleigh criterion will be satisfied (see fig.
showing axial gradient ?Tstack in a stack and
?Tcrit in a gas parcel oscillating in the
x-direction at a large distance from the wall of
stack).
?-frequency, ?-therm.expansion 1/K, p-mean
pressure amplitude, u-mean velocity amplitude,
?-mean density
Babaei H.,Siddiqui K. Design and optimisation of
thermoacoustic devices. Energy Conversion and
Management, 49 (2008), 3585-3598
Engine (oscillations generated if
)
Refrigerator (heat pump if
)
T
Heat supplied to gas parcel at max.density
stack
Hot HE
Cold HE
Hot HE
loadspeaker
Critical gradient ?Tcrit (insulated parcel)
Piston or piezocrystal
Axial temperature of stack ?Tstack
Heat removed from gas to stack
x
Gas parcel oscillating back and forth in
accordance with pressure (motion left
increasing pressure compression gas
temperature increases - heat is removed from gas
to stack and work is consumed by gas parcel)
44
Thermoacoustics
How to understand the expression for the critical
axial temperature gradient?
?-frequency, ?-therm.expansion 1/K, p-mean
pressure amplitude, u-mean velocity amplitude,
?-mean density
?T describes temperature difference during
pressure oscillation of a thermally insulated gas
parcel (adiabatic compression/expansion)
Mean velocity of gas parcel times time of period
For ideal gas thermal expansion coefficient ?1/T
T
For adiabatic compression T?s0
?T temperature change during adiabatic
compression of gas parcel
?x displacement of a gas parcel during one
oscillation
45
Thermoacoustics - modelling
Theoretical background of thermoacoustics
developed by Nicolas Rott and published as a
serie of articles (Thermally driven acoustic
oscillations) in Journal of Applied Mathematics
and Physics is not freely available in Internet,
on contrary to the recent PhD thesis Mathematical
Aspects of Thermoacoustics 2009 (Eidhoven) or the
Technical Research Institute of Sweden report
written by Freddy Rietdijk Thermoacoustic
refrigeration using a standing-wave device 2010.
Some papers are available from Science direct,
for example
This paper presents analytical solution of
oscillating velocity, pressure and temperature
field in a tube (capillary of a stack). The
solution is almost the same as that derived by
Nicolas Rott
Continuity equation relating axial (u1) and
transversal (v1) velocities and density ?. ? is
prescribed frequency and a is speed of sound, L
is length of tube
Momentum balance for axial velocity (pressure is
independent of radius and radial velocity profile
is expressed in terms of bessel function J0). ?v
is viscous penetration depth (therefore
velocities are not exactly in phase with
oscillation of pressure).
Enthalpy balance of gaseous layer. The first RHS
term corresponds to the time derivative of
pressure. Only the radial heat transport
characterised by the thermal penetration depth ?t
is important. Penetration depth shifts
temperature oscillations.
Enthalpy balance in the wall of stack must be
solved too (stack represents an regenerator). ?s
is the penetration depth in solid material of
wall.
State equation of ideal gas (after expansion,
index 1 means the first term of expansion)
46
Thermoacoustics
CFD combustion thermoacoustics Low computational
cost CFD analysis of thermoacoustic
oscillationsApplied Thermal Engineering, Volume
30, Issues 6-7, May 2010, Pages 544-552Andrea
Toffolo, Massimo Masi, Andrea Lazzaretto
Timing of the pressure fluctuation due to the
acoustic mode at 36 Hz and of the heat released
by the fuel injected through the main radial
holes (if the heat is released in the gray zones,
the necessary condition stated by Rayleigh
criterion is satisfied and thermoacoustic
oscillations at this frequency are likely to
grow).
47
Magnetic refrigeration
Application of magnetic field upon ferromagnetic
material causes orientation of magnetic spin of
molecules therefore decreases the magnetic
entropy. Total entropy (sum of magnetisation
entropy and lattice entropy, thermal vibration of
molecules in a crystal lattice) remains constant
assuming a thermally insulated (adiabatic)
system, therefore the magnetic entropy decrease
must be compensated by the thermal entropy (and
temperature) increase. The first law of
thermodynamic can be formulated in terms of
internal energy as
(?o magnetic permeability of vacuum, H intensity
of magnetic field T,? specific magnetisation)
For constant volume the relationship between
entropy, temperature and H is
For most materials magnetisation decreases with
temperature therefore d?/dTlt0 and matter heats
when H increases.
This equation enables to construct the T-s
diagrams and demonstrate thermodynamic cycles of
refrigeration.
48
Magnetic refrigeration
Principle of Active Magnetic Regenerator (AMR)
cycle.
49
Magnetic refrigeration
Romero Gómez, J., Ferreiro Garcia, R., Carbia
Carril, J., Romero Gómez, M., Experimental
analysis of a reciprocating magnetic
refrigeration prototype, International Journal of
Refrigeration (2013)
The working principle is as follows during the
first semicycle of operation one of the
regenerators (2) is subjected to the magnetic
field action generated by the permanent magnets
(6). As a consequence of this field, the material
contained in this part of the regenerator
undergoes the MCE. The HTF, consisting of glycol
water, is pumped via the circulation pump (4)
through the servo-valve (5a) activated during the
first semi-cycle to absorb the heat generated by
the magnetocaloric material whilst it is cooled.
The heat absorbed from the magnetocaloric
material is ceded to the environment in the
HHEX(1). Once the heat is ceded, the HTF is
returned through the other regenerator. Upon
contact with the magnetocaloric material, whose
temperature has decreased as a result of being
removed in the previous semi-cycle from the
presence of the magnetic field, the HTF is
cooled. The cooled HTF passes through the
two-position three-way valve (5b) toward the
CHEX(3). Once the first semi-cycle is finished,
the valve positions change simultaneously (5a)
and (5b) whilst the AMR moves (2) within the
magnetic field, thus inverting the flow direction
of the circulating HTF.
(1) HHEX, (2)mobile AMR, (2a) regenerator A, (2b)
regenerator B, (3) CHEX, (4) pump, (5a), (5b)
solenoid valve, (6) static NdFeB magnets, (7)
motor, (8) magnet fixed to yoke to compensate F,
(9) magnet fixed to the AMR, (10) AMR
displacement guide
50
Magnetic refrigeration
Romero Gómez, J., Ferreiro Garcia, R., Carbia
Carril, J., Romero Gómez, M., A review of room
temperature linear reciprocating magnetic
refrigerators. Renewable and Sustainable Energy
Reviews, Volume 21, May 2013, Pages 1-12
AMR cycle cannot be described by Ts diagrams.
Rotary AMR
Reciprocating AMR
51
Magnetic refrigeration
H.R.E.H. Bouchekara, A. Kedous-Lebouc, J.P.
Yonnet Design of a new magnetic refrigeration
field source running with rotating bar-shaped
magnets. International Journal of Refrigeration
35 (2012) 115-121
A Halbach magnet array is an arrangement of
permanent magnets to increase the magnetic field
on one side of the array while canceling it on
the other side
This paper is only a theoretical analysis
calculated by MATLAB. Permanent magnets NdFeB
(Neodymium-Iron-Boron alloy, diameter of 7 rods
is 20 mm, magnetic induction 1.4T). Active blocks
are Gadolinium.
52
Laser cooling
Ruan X.L. et al. Entropy and efficiency in laser
cooling solids. Physical Review B, 75 (2007),
214304
A phonon is a quantum of collective excitation in
a periodic, elastic arrangement of atoms or
molecules in condensed matter.
Chu, Steven, Science 253, 861-866, 1991 Lasers
to achieve extremely low temperatures has
advanced to the point that temperatures of 10-9 K
have been reached. Idea of Doppler effect
atom Na moving with velocity about 570 m/s at
300K
laser should be tuned below the resonance
frequency (difference ?f should be the Doppler
frequency given by velocity of atom)
collision with photon from behind has too low
energy
53
EXAM
HP2
Thermodynamic cycles. Heat pumps and Heat engines
54
What is important (at least for exam)
HP2
regenerator
T
STIRLING
displacing piston
Thermoacoustic standing wave
compression/expansion wave stack
s
Thermoacoustic travelling wave
regenerator
AMR Active Magnetic Refrigerator