Master in Space Science and Technology
Thermal engineering Isidoro Martínez
Master in Space Science and Technology UPM. Isidoro Martínez
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Thermal engineering •Thermodynamics – Basics • Energy and entropy • Temperature and thermometry • Variables: state properties, process functions • Equations of state, simple processes • Phase change – Applied: • Mixtures. Humid air (air conditioning) • Thermochemistry (combustion) • Heat engines (power generation) • Refrigeration (cold generation) • Thermal effects on materials and processes • Thermofluiddynamic flow 1D…
•Heat transfer (conduction, convection, radiation, heat exchangers) Master in Space Science and Technology, UPM. Isidoro Martínez
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Thermodynamics •
Basic thermodynamics – The science of heat and temperature. Work. Energy. Thermal energy. – Energy and entropy. The isolated system. The traditional Principles – Generalisation (mass, momentum, energy): the science of assets (conservatives do not disappear) and spreads (conservatives tend to disperse) – Type of thermodynamic systems (system, frontier, and surroundings) • Isolated system: Dm=0, DE=0 • Closed system : Dm=0, DE0 • Open system : Dm0, DE0 – Type of thermodynamic variables • Intensive or extensive variables • State or process variables – Type of thermodynamic equations • Balance equations (conservation laws); e.g. DEclose-sys=W+Q • Equations of state (constitutive laws); e.g. pV=mRT • Equilibrium laws: S(U,V,ni)iso-sys(t) Smax e.g. dS/dU|V,ni=uniform… • (Kinetics is beyond classical thermodynamics; e.g. q kT )
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Applied thermodynamics Master in Space Science and Technology, UPM. Isidoro Martínez
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Thermodynamics (cont.) • Basic thermodynamics • Applied thermodynamics – – – – – –
Energy and exergy analysis (minimum expense and maximum benefit) Non-reactive mixtures (properties of real mixtures, ideal mixture model…) Hygrometry (humid air applications: drying, humidification, air conditioning…) Phase transition in mixtures (liquid-vapour equilibrium, solutions…) Reactive mixtures. Thermochemistry. Combustion Heat engines • Gas cycles for reciprocating and rotodynamic engines • Vapour cycles (steam and organic fluid power plants) – Refrigeration, and heat pumps • Cryogenics (cryocoolers, cryostats, cryopreservation…) – Thermal analysis of materials (fixed points, calorimetry, dilatometry…) – Non-equilibrium thermodynamics (thermoelectricity, dissipative structures…) – Environmental thermodynamics (ocean and atmospheric processes…)
Master in Space Science and Technology, UPM. Isidoro Martínez
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Balance equations Magnitude
Accumul . mass dm = momentum d(m v ) =
Production
energy
d(me)
=
0 mg dt 0
entropy exergy
d(ms) d(m)
= =
dSgen T0dSgen
Impermeable flux +0 + FA dt +dW+dQ +dQ/T +dWu+(1T0/T)dQ
Permeable flux
+dme + ve dmepeAe ne dt e+htedme +sedme +edme
with e=u+em=u+gz+v2/2
dW =IFFdx =IFMdq, Wu=W+ p0DV h=u+pv, ht=h+em ds=(du+pdv)/T =(dq+demdf)/T, demdf 0, dSgen0
=e+p0vT0s, =htT0s
Master in Space Science and Technology, UPM. Isidoro Martínez
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Substance data •
Perfect gas model – Ideal gas: pV=mRT or pV=nRuT (R=Ru/M, Ru=8.3 J/(mol·K)) – Energetically linear in temperature: DU=mcvDT –
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Air data: R=287 J/(kg·K) and cp=cv+R=1000 J/(kg·K), or M=0.029 kg/mol and g=cp/cv=1.4
Perfect solid or liquid model – Incompressible, undilatable substance: V=constant (but beware of dilatations!) – Energetically linear in temperature: DU=mcDT –
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Water data: r=1000 kg/m3, c=4200 J(kg·K)
Perfect mixture (homogeneous)
v xi vi , u xiui , s xi si R xi ln xi – Ideal mixture – Energetically linear in temperature: DU=mcvDT *
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*
*
Heterogeneous systems – Phase equilibria of pure substances (Clapeyron’s equation) xV 1 p1* (T ) – Ideal liquid-vapour mixtures (Raoult’s law): x p L1 – Ideal liquid-gas solutions (Henry’s law): cL,s K sdis,cc (T )
•
dp dT
sat
Dh T Dv
cG , s
Real gases. The corresponding state model, and other equations of state. Master in Space Science and Technology, UPM. Isidoro Martínez
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Thermodynamic processes •
Adiabatic non-dissipative process of a perfect gas: dE dQ dW
•
•
mcv dT
mRT dV V
dT R dV 0 Tvg 1 cte., pvg cte., T/p T cv V
g 1 g
cte.
Fluid heating or cooling – –
•
dU pdV
At constant volume: Q=DU At constant pressure: Q=DH=D(U+pV)
Adiabatic gas compression or expansion –
Close system: w=Du=cv(T2-T1)
–
Open system: w=Dh=cp(T2-T1)
C
ws h2ts h1t w h2t h1t
PGM
p2t
g 1 g
p1t 1 w PGM 1 T1t T2t T g 1 T2t T1t 1 ws 1 p1t p2t g
Internal energy equation (heating and cooling processes)
DU DE DEm Q Emdf pdV •
One-dimensional flow at steady state
min mout r vA rV •
Dh w q
Thermodynamic processes in engines
w
dp
r
Dem emdf
Master in Space Science and Technology, UPM. Isidoro Martínez
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Phase diagrams (pure substance)
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Normal freezing and boiling points (p0=100 kPa)
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Triple point (for water TTR=273.16 K, pTR=611 Pa)
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Critical point (for water TCR=647.3 K, pTR=22.1 MPa)
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Clapeyron’s equation (for water hSL=334 kJ/kg, hLV=2260 kJ/kg)
dp dT
sat
hV hL T (vV v L )
FG p IJ h FG 1 1 IJ H p K R HT T K
V v L , vV RT / p , hLV const v ln
LV
0
Master in Space Science and Technology, UPM. Isidoro Martínez
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Thermometry • Temperature, the thermal level of a system, can be measured by different primary means: – – – – –
T pV lim The ideal-gas, constant-volume thermometer TTPW p 0 pV TPW The acoustic gas thermometer 1/ 4 The spectral radiation thermometer T M lim The total radiation thermometer TTPW 1 M TPW The electronic noise thermometer
• The temperature unit is chosen such that TTPW 273.16 K
• The Celsius scale is defined by T/ºC T/K-273.15 • Practical thermometers: – Thermoresistances (e.g. Pt100, NTC) – Thermocouples (K,J…). Master in Space Science and Technology, UPM. Isidoro Martínez
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Piezometry •
Pressure (normal surface force per unit normal area), is a scalar magnitude measured by difference (in non-isolated systems; recall free-body force diagrams).
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Gauge and absolute pressure:
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Pressure unit (SI) is the pascal, 1 Pa1 N/m2 (1 bar100 kPa) PLM Hydrostatic equation: p p0 r g z z0 dp r g PGM dp p dz g dz RT Vacuum (practical limit is about 10-8 Pa) Pressure sensors: U-tube, Bourdon tube, diaphragm, piezoelectric…
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Master in Space Science and Technology, UPM. Isidoro Martínez
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Questions (Only one answer is correct) 1.
The mass of air in a 30 litre vessel at 27 ºC and a gauge pressure of 187 kPa is about? a) b) c) d)
2.
When a gas in a 30 litre rigid vessel is heated from 50 ºC to 100 ºC, the pressure ratio: (final/initial): a) b) c) d)
3.
Cannot be compressed Cannot be heated by compression Heat a little bit when compressed, but volume remains the same Heat up and shrink when compressed
The critical temperature of any gas is: a) b) c) d)
5.
Doubles Is closer to 1 than to 2. Depends on initial volume Depends on heating speed
Liquids: a) b) c) d)
4.
1g 10 g 100 g 1000 g..
The temperature below which the gas cannot exist as a liquid -273.16 ºC The temperature above which the gas cannot be liquefied The temperature at which solid, liquid, and gas coexist
In a refrigerator, the amount of heat extracted from the cold side: a) b) c) d)
Cannot be larger than the work consumed Cannot be larger than the heat rejected to the hot side Is inversely proportional to the temperature of the cold side Is proportional to the temperature of the cold side.
Master in Space Science and Technology, UPM. Isidoro Martínez
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Questions (Only one answer is correct) 6.
Which of the following assertions is correct? a) b) c) d)
7.
The variation of entropy in a gas when it is compressed in a reversible way is: a) b) c) d)
8.
Is always positive Is dimensionless Is different in the Kelvin and Celsius temperature scales Is three times the linear coefficient value.
It is not possible to boil an egg in the Everest because: a) b) c) d)
10.
Less than zero Equal to zero Greater than zero It depends on the process.
The volumetric coefficient of thermal expansion: a) b) c) d)
9.
Heat is proportional to temperature Heat is a body’s thermal energy Net heat is converted to net work in a heat engine The algebraic sum of received heats in an interaction of two bodies must be null.
The air is too cold to boil water Air pressure is too low for stoves to burn Boiling water is not hot enough Water cannot be boiled at high altitudes.
When a combustion takes place inside a rigid and adiabatic vessel: a) b) c) d)
Internal energy increases Internal energy variation is null Energy is not conserved Heat flows out.
Master in Space Science and Technology, UPM. Isidoro Martínez
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Exercises 1.
A U-tube is made by joining two 1 m vertical glass-tubes of 3 mm bore (6 mm external diameter) with a short tube at the bottom. Water is poured until the liquid fills 600 mm in each column. Then, one end is closed. Find: 1. 2.
2.
3. 4.
An aluminium block of 54.5 g, heated in boiling water, is put in a calorimeter with 150 cm3 of water at 22 ºC, with the thermometer attaining a maximum of 27.5 ºC after a while. Find the thermal capacity of aluminium. How many ice cubes of 33 g each, at -20 ºC, are required to cool 1 litre of tea from 100 ºC to 0 ºC? Carbon dioxide is trapped inside a vertical cylinder 25 cm in diameter by a piston that holds internal pressure at 120 kPa. The plunger is initially 0.5 m from the cylinder bottom, and the gas is at 15 ºC. Thence, an electrical heater inside is plugged to 220 V, and the volume increases by 50% after 3 minutes. Neglecting heat losses through all walls, and piston friction, find: 1. 2.
5.
The change in menisci height due to an ambient pressure change, (∂z/∂pamb), with application to Dp=1 kPa. The change in menisci height due to an ambient temperature change, (∂z/∂Tamb), with application to DT=5 ºC.
The energy balance for the gas and for the heater. The final temperature and work delivered or received by the gas.
Find the air stagnation temperature on leading edges of an aircraft flying at 2000 km/h in air at -60 ºC. Master in Space Science and Technology, UPM. Isidoro Martínez
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Master in Space Science and Technology
Thermal engineering Isidoro Martínez
Master in Space Science and Technology UPM. Isidoro Martínez
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Thermal engineering •Thermodynamics –Basic (energy and entropy, state properties, state equations, simple processes, phase changes) –Applied (mixtures, liquid-vapour equilibrium, air conditioning, thermochemistry, power and cold generation, materials processes)
•Heat transfer – – – – – – –
Thermal conduction (solids…) Thermal convection (fluids…) Thermal radiation (vacuum…) Heat exchangers Heat generation (electrical heaters…) Thermal control systems Combined heat and mass transfer (evaporative cooling, ablation…)
Master in Space Science and Technology, UPM. Isidoro Martínez
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Heat transfer •
What is heat (i.e. heat flow, heat transfer)? – First law: heat is non-work energy-transfer through an impermeable surf.
Q DE W DE pdV Wdis DH Vdp Wdis mcDT PIS,non-dis – Second law: heat tends to equilibrate the temperature field.
sgen •
T q T2
What is heat flux (i.e. heat flow rate, heat transfer rate)?
dQ dT Q mc dt dt •
KADT PSM,non-dis
Heat transfer is the flow of thermal energy driven by thermal nonequilibrium (i.e. the effect of a non-uniform temperature field), commonly measured as a heat flux (vector field). Master in Space Science and Technology, UPM. Isidoro Martínez
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Heat transfer modes •
How is heat flux density modelled?
conduction q k T Q q K DT convection q h T T A 4 4 radiation q T T – The 3 ways to change Q: K, A, and DT. – K is thermal conductance coeff. (or heat transfer coeff.), k is conductivity, h is convective coeff., is emissivity. – Field or interface variables? – Vector or scalar equations? – Linear or non-linear equations? – Material or configuration properties? – Which emissivity? This form only applies to bodies in large enclosures. Master in Space Science and Technology, UPM. Isidoro Martínez
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Heat conduction •
Physical transport mechanism –Short-range atomic interactions (collision of particles in fluids, or phonon waves in solids), supplemented with free-electron flow in metals.
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Fourier’s law (1822)
q kT •
Heat equation
dH dt
Q p
rc V
T dV q ndA dV q dV dV t A V V V
k 0 T rc q k 2T , or t V 0
T a 2T t rc
–with the initial and boundary conditions particular to each problem. Master in Space Science and Technology, UPM. Isidoro Martínez
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Thermal conductivity
Table 1. Representative thermal conductivity values k [W/(m·K)] Comments Order of magnitude for solids 10 (good conductors) In metals, Lorentz's law (1881), k/(T)=constant 1 (bad conductors) Aluminium 200 Duralumin has k=174 W/(m·K), increasing to k=188 W/(m·K) at 500 K. Iron and steel 50 (carbon steel) Increases with temperature. 20 (stainless steel) Decreases with alloying Order of magnitude for liquids 1 (inorganic) Poor conductors (except liquid metals). 0.1 (organic) Water 0.6 Ice has k=2.3 W/(m·K), 2 Order of magnitude for gases 10 Very poor thermal conductors. KTG predicts k/(rc)a=Di=10-5 m2/s Air 0.024 Super insulators must be air evacuated. 2
Master in Space Science and Technology, UPM. Isidoro Martínez
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Simple heat conduction cases •
One-dimensional steady cases – Planar – Cylindrical – Spherical
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•
Q kA
T1 T2 L12
Q k 2 L Q k 4 R1R2
T1 T2 R2 R1
T1 T2 R ln 2 R1
Composite wall (planar multilayer) T T T T T T q K DT k12 2 1 k23 3 2 ... n 1 Li L12 L23 k i Unsteady case. Relaxation time: Bi 1 r cL2 Dt k hL Dt mcDT / Q Bi Bi 1 r cV kS Dt hA Master in Space Science and Technology, UPM. Isidoro Martínez
K
1 Li k i
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Multiple path in heat conduction • Multidimensional analysis – Analytical, e.g. separation of variables, conduction shape factors, – Numerical, finite differences, lumped network, finite elements
• Parallel thermal resistances – Example: honeycomb panel made of ribbon (thickness d), cell size s:
DT Qx kFx Ax x Lx Qy kFy Ay Qz kFz Az
DTy Ly DTz Lz
Master in Space Science and Technology, UPM. Isidoro Martínez
3d with Fx 2 s d with Fy s 8d with Fz 3 s 21
Heat convection • Newton’s law and physical mechanism q h T T knT • •
hDT k
DT
d
Nu
hL f Re,Pr... k
W/(m2·K)
e.g. in air flow, h=a+bvwind, with a=3 and b=3 J/(m3·K) e.g. plate (
