modelado de ciclos de potencia aplicados a micro...
TRANSCRIPT
MODELADO DE CICLOS DE POTENCIA APLICADOS A MICRO-GENERACIÓN RENOVABLE TÉRMICA
JUNIO 2019
Javier Ortega Paredes
DIRECTOR DEL TRABAJO FIN DE GRADO:
Andrés Sebastián Herrera
TRABAJO FIN DE GRADO PARA LA OBTENCIÓN DEL TÍTULO DE GRADUADO EN INGENIERÍA EN TECNOLOGÍAS INDUSTRIALES
0
0
2
2
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2
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44
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66
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88
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1010
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1212
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22
22 24
1.5 2 2.5 3 3.5 4300
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800
900
Cycle efficiency (%)
PRopt (-)
0
0
2
2
2
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40
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42
1.5 2 2.5 3 3.5 4300
400
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600
700
800
900
Cycle efficiency (%)
PRopt (-)
2
10
1010
10
102020
20
2020
30
30
30
3030
40
40
40
4040
50
50
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130
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140
140
150
150
160
160
170
170
180
180
190200
210220
1.5 2 2.5 3 3.5 4300
400
500
600
700
800
900
Work density (kJ/m3)
0
0
50
50
50
50
100
100
100
100100
150
150
150
150150
200
200200
200200
250
250
250
250
300
300
300
300
350
350
350
350
400
400
400
450450
450
500500
500
550550
550
600600
650
650
700
700 750750
800
1.5 2 2.5 3 3.5 4300
400
500
600
700
800
900
Specific work (kJ/kg)
◦
◦
◦
◦
h − s
T − s
h − s
h − s
h − s
Tmax = 300◦
Tmax = 600◦
Tmax = 900◦
◦
Tmax = 225◦
◦
Tmax = 300◦
◦
Tmax = 600◦
◦
Tmax = 900◦
Tmax = 225◦
Tmax = 300◦
Tmax = 600◦
Tmax = 900◦
2
h − s
T − s
h − s
◦
2
◦
ηsC
p1 p2
ηsT
h4 > h2
ε
h − s
h − s
ηCarnot = 1 − Tmin
Tmax
ηciclo = WT − WC
Qin= wT − wC
qin= ηciclo
(ηsC (D), ηsT (D), PR, p1, Tmax, Tmin, , ε
)
max◦
◦max
◦
◦
max◦
◦
◦ ◦◦ ◦
◦3
◦
2
2
◦max
◦
max◦
◦
max◦
2
2
◦
◦
◦ ◦
◦ ◦
◦
2
◦ ◦
◦ ◦
Re = ρuD
μ
◦
◦ ◦
2 6
2
2
2
2
◦
◦
ηsC = h2s − h1h2 − h1
ηsT = h4 − h5h4 − h5s
ε = cp5(T5 − T6)cmin(T5 − T2) cmin = cp2 , cp5
h − s
p1 = p6 = p5 = p5s ≡ pmin
p2 = p2s = p3 = p4 ≡ pmax
T1 ≡ Tmin
T4 ≡ Tmax
p1 p2 T2s
s2s(T2s, p2) − s1(T1, p1) = 0
wC = h2(T2, p2) − h1(T1, p1) = h2s(T2s, p2) − h1(T1, p1)ηsC
T5s
s5s(T5s, p5) − s4(T4, p4) = 0wT = h4(T4, p4) − h5(T5, p5) = ηsT
[h4(T4, p4) − h5s(T5s, p5)
]
T6
h2(T2, p2) + h5(T5, p5) = h6(T6, p6) + h3(T3, p3)
qin = h4(T4, p4) − h3(T3, p3)
ηciclo =˙Wneta
Qin= WT − WC
Qin= wT − wC
qin
p = p(T, ρ)
dh = dh(T, p) = cpdT −[v − T
(∂v
∂T
)p
]dp
ds = ds(T, p) = cp
TdT −
(∂v
∂T
)p
dp
α∗
αr
a(T, ρ) := u(T, ρ) − Ts(T, ρ)
α(τ, δ) = a
RT= α∗(τ, δ) + αr(τ, δ) τ = Tr
Tδ = ρ
ρr
r ρr
(w1, w2, ..., wNc)
α(τ, δ)
h
RT= τ
[(∂α∗
∂τ
)δ
+(
∂αr
∂τ
)δ
]+ δ
(∂αr
∂δ
)τ
+ 1
s
R= τ
[(∂α∗
∂τ
)δ
+(
∂αr
∂τ
)δ
]− α∗ − αr
αr(τ, δ) =A∑
k=1Nkδdkτ tk +
B∑k=A
Nkδdkτ tke−δLk +
+C∑
k=B
Nkδdkτ tke[−ηk(δ−εk)2−βk(τ−γk)2]
αr(τ, δ) =Nc∑i=1
wiαri (τ, δ) +
Nc−1∑i=1
Nc∑j=i+1
wiwjFijαrij(τ, δ)
z
z = p
ρRT= p
δρrRT= 1 + δ
(∂αr
∂δ
)τ
αr =∫ δ
0
z − 1δ
dδ
p = ρRT +(B0RT − A0 − C0
T 2 + D0T 3 − E0
T 4
)ρ2 + (bRT − a − d
T)ρ3 +
+ α(a + C0T 2 )ρ6 + cρ3
T 2 (1 + γρ2)e−γρ2
A0B0 C0 D0 E0 a b c d α γ
z(T, ρ) = z0(T
f, hρ
)
αr(T, ρ) = αr0(T
f, hρ
)
f hf = Tr/Tr0 h = ρr0/ρr
γ cp◦
p = ρRT
dh∗ = dh∗(T, p) = dh∗(T ) = c∗pdT → h∗(T2) − h∗(T1) = c∗
p(T2 − T1)
ds∗ = ds∗(T, p) =c∗
p
TdT − R
pdp → s∗(T2, p2) − h∗(T1, p1) = c∗
p
T2T1
− Rp2p1
z = z(T, p)
�
zz
z = z(T, p)
z(T, p) =Nc∑i=1
wiz�i (T, p) + zM (T, p) =
Nc∑i=1
wiz�i (T, p) + zM
ideal(T, p) + zE(T, p)
zMideal(T, p)
h(T, p) =Nc∑i=1
wih�i (T, p) + hM (T, p) =
Nc∑i=1
wih∗i (T )
s(T, p) =Nc∑i=1
wis�i (T, p) + sM (T, p) =
Nc∑i=1
wis∗i (T, p) −
Nc∑i=1
Riwi wi
h(T2) − h(T1) =Nc∑i=1
wi
(h∗
i (T2) − h∗i (T1)
)=
Nc∑i=1
wic∗pi
(T2 − T1) = cp(T2 − T1)
s(T2, p2) − s(T1, p1) =Nc∑i=1
wi
(s∗
i (T2, p2) − s∗i (T1, p1)
)=
Nc∑i=1
wic∗pi
T2T1
−Nc∑i=1
wiRip2p1
=
= cpT2T1
− Rp2p1
Ri = Ru
Mi
cp∑Nc
i=1 wic∗pi
cp
R
i u
h(T, p) s(T, p)
h = h(T, p) s = s(T, p)
min max
Ai Bi Ci Di
hmin = hmin(T, pmin) = A0 + A1T + A2T 2
hmax = hmax(T, pmax) = B0 + B1T + B2T 2
smin = smin(T, pmin) = C0 + C1T + C2T 2
smax = smax(T, pmax) = D0 + D1T + D2T 2
◦◦
◦◦◦◦◦
300 350 400 450 5000
5
10
15
20
25
30
Cyc
le th
erm
al e
ffici
ency
(%
)
Xenon (noble gases)
Real gasIdeal gasExtrapolated real gas
100 150 200 250 3000
5
10
15
20
Cyc
le th
erm
al e
ffici
ency
(%
)
Isobutane (organic fluids)
Real gasIdeal gasExtrapolated real gas
z = z(x, y, fluido)
2 2 NF = 6◦ ΔTmax = 25◦ NT M = 25 ◦
ΔPR = 0, 25 NP R = 13ΔηsC = 0, 05 NC = 7ΔηsT = 0, 05 NT = 6Δε = 0, 05 Nε = 9
◦
◦◦
◦
◦
z = z(x, y, fluido)
z(1, 1, NF ) z(1, 2, NF ) · · · z(1, NX , NF )
z(2, 1, NF ) z(2, 2, NF ) · · · z(2, NX , NF )
z(NY , 1, NF ) z(NY , 2, NF ) · · · z(NY , NX , NF )
z(1, 1, 2) z(1, 2, 2) · · · z(1, NX , 2)
z(2, 1, 2) z(2, 2, 2) · · · z(2, NX , 2)
z(NY , 1, 2) z(NY , 2, 2) · · · z(NY , NX , 2)
z(1, 1, 1) z(1, 2, 1) · · · z(1, NX , 1)
z(2, 1, 1) z(2, 2, 1) · · · z(2, NX , 1)
z(NY , 1, 1) z(NY , 2, 1) · · · z(NY , NX , 1)
x(j)
y(i)
2 2NF = 242 2 2 2
◦ ΔTmax = 25◦ NT M = 25◦ ΔTmax = 25◦ NT M = 13
ΔPR = 0, 25 NP R = 13·[1 + ΔηsC (pmin, Tmin, f luido)
]NC = 312
◦
Δpmin = 0, 25 Np = 13
wA = 0, 7 − wB = 0, 3wA = 0, 5 − wB = 0, 5 wA = 0, 3 − wB = 0, 7
◦
(62)
= 15
22
2 22
2 22
2 2
◦
◦ ◦ 5 ·3 = 15
pmin 24 · 13 = 312
[ΔηsC ] =
⎡⎢⎢⎢⎢⎢⎢⎢⎣
ΔηsC (1, 1) ΔηsC (1, 2) · · · ΔηsC (1, 13)
ΔηsC (2, 1) ΔηsC (2, 2) · · · ΔηsC (2, 13)
ΔηsC (24, 1) ΔηsC (24, 2) · · · ΔηsC (24, 13)
⎤⎥⎥⎥⎥⎥⎥⎥⎦
− x ypmin Tmax −
2 2NF = 242 2 2 2
◦ ΔTmax = 25◦ NT M = 25◦ ΔTmax = 25◦ NT M = 13
ΔPR = 0, 25 NP R = 13
◦
Δpmin = 0, 25 Np = 13
◦
2 2NF = 242 2 2 2
◦ ΔTmax = 25◦ NT M = 25◦ ΔTmax = 25◦ NT M = 13
ΔPR = 0, 25 NP R = 13
◦
Δpmin = 0, 25 Np = 13
◦
− −
ηciclo = ηciclo
(PR, Tmax, pmin, ηsC , ηsT , Tmin, ε,
)
(∂ηciclo
∂PR∗
)Tmax,pmin,ηsC
,ηsT,Tmin,ε,
= 0
Tmax
ηciclo(i, jP Ropt , k)
[PRopt]
[ηmaxciclo] =
⎡⎢⎢⎢⎢⎢⎢⎢⎣
ηciclo(1, jP Ropt , 1) ηciclo(2, jP Ropt , 1) · · · ηciclo(25, jP Ropt , 1)
ηciclo(1, jP Ropt , 2) ηciclo(2, jP Ropt , 2) · · · ηciclo(25, jP Ropt , 2)
ηciclo(1, jP Ropt , 6) ηciclo(2, jP Ropt , 6) · · · ηciclo(25, jP Ropt , 6)
⎤⎥⎥⎥⎥⎥⎥⎥⎦
[PRopt] =
⎡⎢⎢⎢⎢⎢⎢⎢⎣
PR(1, jP Ropt , 1) PR(2, jP Ropt , 1) · · · PR(25, jP Ropt , 1)
PR(1, jP Ropt , 2) PR(2, jP Ropt , 2) · · · PR(25, jP Ropt , 2)
PR(1, jP Ropt , 6) PR(2, jP Ropt , 6) · · · PR(25, jP Ropt , 6)
⎤⎥⎥⎥⎥⎥⎥⎥⎦
Tmax PRopt
− pmin, Tmin, ε −
ηmaxciclo(Tmax, , ηsC , ηsT )
PRopt Tmax pmin
PRopt ηmaxciclo(pmin, Tmax, )
PRopt(pmin, Tmax, )
PRopt
PRopt
2 PRopt
022
24
4
4
6
6
6
88
8
10
10
12
12
14
14
16
18
20
2 3 4
400
600
800
022
24
4
4
6
6
6
88
8
10
10
1212
1414
16
18
2 3 4
400
600
800
22
244
4
66
6
8
8
10
10
12
14
2 3 4
400
600
800
0
0
2
2
2
4
4
4
6
6
6
8
8
8
10
10
10
1212
14
14 16
16
18
18
20
22
24
2 3 4
400
600
800
0
0
2
2
2
4
4
4
6
6
6
8
8
8
10
10
10
1212
14
14 16
16
18
18
20
22
24
2 3 4
400
600
800
0
0
2
2
2
4
4
4
6
6
6
8
8
8
10
10
10
121214
14 16
16
18
18
20
22
24
2 3 4
400
600
800
0
5
10
15
20
25
Cyc
le th
erm
al e
ffici
ency
(%
)
0246
6
8
8
8
10
10
10
10
12
12
12
14
14
14
16
16
16
18
18
18
20
20
20
22
22
22
24
24
24
26
26
28
28
30
30
32
32
34
34
36
38
2 3 4
400
600
800
02468
8
8
8
10
10
10
10
12
12
12
14
14
14
16
16
16
18
18
18
20
20
20
22
22
22
24
24
26
26
28
28
30
30
32
32
34
34
36
38
2 3 4
400
600
800
2
4
4
4
6
6
6
8
8
810
10
10
1212
12
1414
14
1616 18
18
20
20
22
22
24
24
26
28
30
2 3 4
400
600
800
0
0
2
2
4
4
6
6
8
8
10
10
12
12
14
14
16
16
18
18
18
20
20
20
22
22
22
24
24
24
26
26
26
28
28
28
30
30
30
32
32
34
34
36
36
3838 40
42
2 3 4
400
600
800
0
0
2
2
4
4
6
6
8
8
10
10
12
12
14
14
16
16
18
18
18 20
20
20
22
22
22
24
24
24
26
26
26
28
28
28
30
30
30
32
32
34
34
36
36
3838 40
42
2 3 4
400
600
800
0
0
2
2
4
4
6
6
8
8
10
10
12
12
14
14
16
16
18
18
18
20
20
20
22
22
22
24
24
24
26
26
26
28
28
28
30
30
30
32
32
34
34
36
36
3838 40
42
2 3 4
400
600
800
0
5
10
15
20
25
30
35
40
Cyc
le th
erm
al e
ffici
ency
(%
)
− −
010
10
2020
20
3030
30
40
40
50
50
60
60
70
70
80
80
90
90
100
100 110120
130140 150
2 3 4
400
600
800
0
10
10
2020
20
3030
30
40
40
50
50
60
60
70
70
80
80
90
90
100
110120
130140
2 3 4
400
600
800
1010
10
2020
20
30
30
40
40
50
50
60
60
70
70
80
90 100110
2 3 4
400
600
800
0
0
10
10
10
20
20
20
30
30
40
40
50
50
60
60 70
2 3 4
400
600
800
0
0
50
50
100
100
100
150
150
150
200
200
200
250
250
300
300
350
350
400
400
450
450
500
500
550
550
600
600 650700
750
2 3 4
400
600
800
0
0
2
2
4
4
4
6
6
6
8
8
10
10
12
12
14
14
16
16
18
18
20
22 24
2 3 4
400
600
800
0
100
200
300
400
500
600
700
800
Cyc
le s
peci
fic w
ork
(kJ/
kg)
2
2
01010
10
2020
20
3030 40
40
50
50
60
60
70
70
80
80
90
90
100110
120130
140150
160
2 3 4
400
600
800
01010
10
2020
20
3030 40
40
50
50
60
60
70
70
80
80
90
90
100110
120130
140150
160170
2 3 4
400
600
800
10
10
1020
20
20
30
30
30
40
40
50
50
60
60
70
70
80
80
90
90
100
100
110
110
120130140150160170180190200
2 3 4
400
600
800
0
0
10
10
10
20
20
20
30
30
40
40
50
50
60
60
70
80
90100
110120
2 3 4
400
600
800
0
0
10
10
10
20
20
20
30
30
40
40
50
50
60
60
70
80
90100
110
2 3 4
400
600
800
0
0
10
10
10
20
20
20
30
30
40
40
50
50
60
60
70
70
80
90100
110120
2 3 4
400
600
800
0
50
100
150
200
Cyc
le w
ork
dens
ity (
kJ/m
3)
Tmax◦
2
Tmax = 900◦
2
22
PRopt
PRopt
Tmax = 300◦
2
0
0
24
68
0.6 0.65 0.7 0.75 0.80.5
0.6
0.7
0.8
0
0
24
68
0.6 0.65 0.7 0.75 0.80.5
0.6
0.7
0.8
02
46
8
0.6 0.65 0.7 0.75 0.80.5
0.6
0.7
0.8
02
46
8
0.6 0.65 0.7 0.75 0.80.5
0.6
0.7
0.8
02
46
8
0.6 0.65 0.7 0.75 0.80.5
0.6
0.7
0.8
02
46
8
0.6 0.65 0.7 0.75 0.80.5
0.6
0.7
0.8
0
2
4
6
8
10
12
Cyc
le th
erm
al e
ffici
ency
(%
)
Tmax = 300◦
0
0
2
2
4
4
6
6
8
8
10
10
12
12
14
14
16
1618
2022
2426
0.6 0.65 0.7 0.75 0.80.5
0.6
0.7
0.8
0
0
2
2
4
4
6
6
8
8
10
10
12
12
14
14
16
1618
2022
2426
0.6 0.65 0.7 0.75 0.80.5
0.6
0.7
0.8
0
0
2
2
4
4
6
6
8
8
10
10
12
12
14
1416
1820
22
0.6 0.65 0.7 0.75 0.80.5
0.6
0.7
0.8
0
0
2
2
4
4
6
6
8
8
10
10
12
12
14
14
16
16
18
18
20
2022
2426
28
0.6 0.65 0.7 0.75 0.80.5
0.6
0.7
0.8
0
0
2
2
4
4
6
6
8
8
10
10
12
12
14
14
16
16
18
18
20
2022
2426
28
0.6 0.65 0.7 0.75 0.80.5
0.6
0.7
0.8
0
0
2
2
4
4
6
6
8
8
10
10
12
12
14
14
16
16
18
18
20
2022
2426
28
0.6 0.65 0.7 0.75 0.80.5
0.6
0.7
0.8
0
5
10
15
20
25
30C
ycle
ther
mal
effi
cien
cy (
%)
Tmax = 600◦
02
4
4
6
6
8
8
10
10
12
12
14
14
16
16
18
18
20
20
22
22
24
24
26
26 28 30 32 34 36
0.6 0.65 0.7 0.75 0.80.5
0.6
0.7
0.8
02
4
4
6
6
8
8
10
10
12
12
14
14
16
16
18
18
20
20
22
22
24
24
26
26 28 30 32 34 36
0.6 0.65 0.7 0.75 0.80.5
0.6
0.7
0.8
0246
8
8
10
10
12
12
14
14
16
16
18
18
20
20
22
22 24
26
28
0.6 0.65 0.7 0.75 0.80.5
0.6
0.7
0.8
02468
10
10
12
12
14
14
16
16
18
18
20
20
22
22
24
24
26
26
28
28
30
30
32
34 36 38 40
0.6 0.65 0.7 0.75 0.80.5
0.6
0.7
0.8
0246
810
10
12
12
14
14
16
16
18
18
20
20
22
22
24
24
26
26
28
28
30
30
32
34 36 38 40
0.6 0.65 0.7 0.75 0.80.5
0.6
0.7
0.8
02468
10
10
12
12
14
14
16
16
18
18
20
20
22
22
24
24
26
26
28
28
30
30
32
34 36 38 40
0.6 0.65 0.7 0.75 0.80.5
0.6
0.7
0.8
0
5
10
15
20
25
30
35
40
Cyc
le th
erm
al e
ffici
ency
(%
)
Tmax = 900◦
0.5 0.6 0.7 0.8 0.90
10
20
30
40
0.5 0.6 0.7 0.8 0.90
10
20
30
40
0.5 0.6 0.7 0.8 0.90
10
20
30
40
0.5 0.6 0.7 0.8 0.90
10
20
30
40
0.5 0.6 0.7 0.8 0.90
10
20
30
40
0.5 0.6 0.7 0.8 0.90
10
20
30
40
2 ◦
ηsT = 0, 85
ηsT = cte ηsC = cte
2 ◦◦
◦ 2◦
2
6 88 1010 1212
14
1416
16
18
18
20
20
22
22
24
24
26
26
28
28
30
3234
3638
0.6 0.7 0.8 0.9 1
400
600
800
6 88 1010 1212
14
1416
16
18
18
20
20
22
22
24
24
26
26
28
28
30
3234
3638
0.6 0.7 0.8 0.9 1
400
600
800
8 10
1012
12
14
14
16
16
18
18
20
22
0.6 0.7 0.8 0.9 1
400
600
800
22 44 66 88 1010 1212 1414 1616 18
1820
2022
22
24
24
26
26
28
28
30
30
32
32
34
34
3638
40424446
48
0.6 0.7 0.8 0.9 1
400
600
800
22 44 66 88 1010 1212 1414 1616 18
1820
2022
22
24
24
26
26
28
28
30
30
32
32
34
34
3638
40424446
48
0.6 0.7 0.8 0.9 1
400
600
800
22 44 66 88 1010 1212 1414 1616 18
1820
2022
22
24
24
26
26
28
28
30
30
32
32
34
34
3638
404244
4648
0.6 0.7 0.8 0.9 1
400
600
800
0
5
10
15
20
25
30
35
40
45
50
55
Cyc
le th
erm
al e
ffici
ency
(%
)
100
125150
150
175
175
200
200
225
225
250
250
275
275
300
300
325
325
350375400425450
0.6 0.7 0.8 0.9 1
400
600
800
100
125
125
150
150
175
175
200
200
225
225
250
250
275
275
300
300
325
325
350375400425450
0.6 0.7 0.8 0.9 1
400
600
800
100
125
125
150
150
175
175
200
200
225
225
250
250
275
275
300
300
325
325
350
350
375
375
400425450475500
0.6 0.7 0.8 0.9 1
400
600
800
75
75
100
100
125
125
150
150
175
200
0.6 0.7 0.8 0.9 1
400
600
800
700700
800
800
900
900
1000
1000
1100
1100
1200
1200
1300
1300
1400
1400
1500
1500
1600
17001800190020002100
0.6 0.7 0.8 0.9 1
400
600
800
20
25
25
30
30
35
35
40
40
45
45
50
50
5560
65
0.6 0.7 0.8 0.9 1
400
600
800
0
500
1000
1500
2000
Hea
t sou
rce
ther
mal
ene
rgy
(kJ/
kg)
120
130
140
140
150
150
160
160
170
170
180
180
190
190
200
200
210
21022023024025
0
260
270
0.6 0.7 0.8 0.9 1
400
600
800
120
130
140
140
150
150
160
160
170
170
180
180
190
190
200
200
210
210
220
23024025026
0
270
0.6 0.7 0.8 0.9 1
400
600
800
160180200
220
220
240
240
260
260
280
280
300
300
320
320
340
340
360
360380400420440460
0.6 0.7 0.8 0.9 1
400
600
800
110
110
120
120
130
130
140
140
150
160
170
180
0.6 0.7 0.8 0.9 1
400
600
800
110
110
120
120
130
130
140
140
150
160
170
180
0.6 0.7 0.8 0.9 1
400
600
800
110
110
120
120
130
130
140
140
150
150
160
170
180
0.6 0.7 0.8 0.9 1
400
600
800
0
50
100
150
200
250
300
350
400
450
500
Hea
t sou
rce
ther
mal
ene
rgy
dens
ity (
kJ/m
3)
◦
◦
2
−◦ −
1 1.5 2 2.5 3 3.5 40.65
0.66
0.67
0.68
0.69
0.7
0.71
0.72
0.73
1 1.5 2 2.5 3 3.5 40.685
0.69
0.695
0.7
0.705
0.71
0.715
0.72
0.725
0.73
wA = 0, 5 − wB = 0, 5
−−
00 1122334
4
55
66
1 2 3 4
400
600
800
00 1122334
4
55
66
1 2 3 4
400
600
800
001122
33
44
1 2 3 4
400
600
800
00 11 22 33 445
56
67
78
8
1 2 3 4
400
600
800
00 11 22 33 44 55 6
6 7
7 8
1 2 3 4
400
600
800
00 11 2233445566
77
88
1 2 3 4
400
600
800
0
1
2
3
4
5
6
7
8
9
Cyc
le th
erm
al e
ffici
ency
(%
)
◦
2
00 112233
44
55
1 2 3 4
400
600
800
00 11223344
55
1 2 3 4
400
600
800
00 11 223344
55
1 2 3 4
400
600
800
00 11223344
55
1 2 3 4
400
600
800
00 11 22334455
6
1 2 3 4
400
600
800
00 11 22 33445566
1 2 3 4
400
600
800
00 11 22 33 44 556677
1 2 3 4
400
600
800
00 11 22 33 44556677
1 2 3 4
400
600
800
00 11 22 33445566
7
1 2 3 4
400
600
800
0
1
2
3
4
5
6
7
8
Cyc
le th
erm
al e
ffici
ency
(%
)
00 11 22 3344556
6
77
1 2 3 4
400
600
800
00 1122334455
66
77
1 2 3 4
400
600
800
00 11223344
55
66
7
1 2 3 4
400
600
800
00 11 223344556677
88
1 2 3 4
400
600
800
00 11 2233445566
77
88
1 2 3 4
400
600
800
00 11 2233445566
77
88
1 2 3 4
400
600
800
0
1
2
3
4
5
6
7
8
Cyc
le th
erm
al e
ffici
ency
(%
)
2◦
◦◦
◦0
0
0
0.15
0.15
0.30.3 0.
45
0.45 0.6
0.75
1 2 3 4100
150
200
250
300
350
400
0
0
0.15
0.150.3
0.3
0.45
0.45
0.6
1 2 3 4100
150
200
250
300
350
400
0
00.15
0.150.3
0.30.45
0.450.6
0.6
0.75
0.75
0.9
0.9
1.05
1.05 1.21.35
1 2 3 4100
150
200
250
300
350
400
0
0.5
1
1.5
Cyc
le th
erm
al e
ffici
ency
(%
)
◦ ◦
◦
2◦
◦
00
22446688
101012121414161618
1820
20
1 2 3 4
400
600
800
00
22446688
101012121414161618
1820
20
1 2 3 4
400
600
800
00
2244668
810
1012
1214
1416
1618
18
1 2 3 4
400
600
800
00224466 88
10101212141416161818202022222424
26
1 2 3 4
400
600
800
002
24
4 66 88 10
10 1212 1414 1616 1818 2020 2222 24
24
1 2 3 4
400
600
800
0022446688
10101212141416161818202022222424
2626
1 2 3 4
400
600
800
0
5
10
15
20
25
Cyc
le th
erm
al e
ffici
ency
(%
)
PRopt
◦
◦ 2
0022446688
10101212141416161818
1 2 3 4
400
600
800
0022446688
10101212141416161818
1 2 3 4
400
600
800
0022446688
10101212141416161818
20
1 2 3 4
400
600
800
0022446688
10101212141416161818
1 2 3 4
400
600
800
002244 6688
1010121214141616181820
1 2 3 4
400
600
800
0022 4466 88
1010 12121414161618182020
1 2 3 4
400
600
800
002244 66 88 1010 1212 1414 1616 1818 20202222
1 2 3 4
400
600
800
0022 44 66 88 1010 1212 1414 1616
18182020
2222
1 2 3 4
400
600
800
0022 44 6688 1010 1212
141416161818202022
1 2 3 4
400
600
800
0
5
10
15
20
25
Cyc
le th
erm
al e
ffici
ency
(%
)
002244 6688
10101212141416
1618
1820
2022
22
1 2 3 4
400
600
800
0022446688
1010121214141616181820
2022
1 2 3 4
400
600
800
00
22446688
101012121414161618182020
22
1 2 3 4
400
600
800
0022446688
10101212141416161818202022222424
26
1 2 3 4
400
600
800
0022446688
10101212141416161818202022222424
26
1 2 3 4
400
600
800
0022446688
10101212141416161818202022222424
26
1 2 3 4
400
600
800
0
5
10
15
20
25
Cyc
le th
erm
al e
ffici
ency
(%
)
PRopt
◦
0
0
0
1
1
2
2
3
3
4
45 6 7
1 2 3 4100
150
200
250
300
350
400
0
0
0.5
0.51
1
1.5
1.5
2
2 2.5 3 3.5
1 2 3 4100
150
200
250
300
350
400
0
01
12
23
3
4
4
5
5
6
6
7
7
8
8 9 10 11 12
1 2 3 4100
150
200
250
300
350
400
0
2
4
6
8
10
12
Cyc
le th
erm
al e
ffici
ency
(%
)
◦ ◦
Tmax = 225◦
Tmax = 300◦
Tmax = 600◦
Tmax = 900◦
◦
◦
pmin PRopt
◦
2.6 2.8 3 3.2 3.4 3.6 3.8
600
800
1000
1200
1
2
3
4
2.4 2.6 2.8 3 3.2 3.4 3.6
600
800
1000
1200
1
2
3
4
2.6 2.8 3 3.2 3.4 3.6 3.8
600
800
1000
1200
1
2
3
4
5
6
2.4 2.6 2.8 3 3.2 3.4 3.6
600
800
1000
1200
1
2
3
4
5
6
Tmax − pmin
Tmax = 225◦
Micro 1 Micro 2 Micro 30
2
4
6
8
10
12
14
Micro 1 Micro 2 Micro 30
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Minimum efficiency Maximum efficiency
Tmax = 225◦
◦
◦
Air
Helium
Nitrog
en CO 2
Argon
Xenon
Isobu
tane
Propa
neR12
50
5
10
15
20
1
1.5
2
2.5
3
3.5
4
MICRO
1
MICRO
2
MICRO
3
Air
Helium
Nitrog
en CO 2
Argon
Xenon
Isobu
tane
Propa
neR12
5
1
1.5
2
2.5
3
3.5
4
4.5
1
1.5
2
2.5
3
3.5
4
MICRO
1
MICRO
2
MICRO
3
◦
2
Tmax = 225◦
3 3.5 4
600
800
1000
1200
1400
1
2
3
4
5
6
2.5 3 3.5
600
800
1000
1200
1400
1
2
3
4
5
6
0.66 0.68 0.7 0.72 0.74 0.76 0.78100
120
140
160
180
1
2
3
4
5
6
0.55 0.6 0.65 0.7100
120
140
160
180
1
2
3
4
5
6
2
pmin =2, 75
Tmax = 300◦
Micro 1 Micro 2 Micro 30
2
4
6
8
10
12
14
16
18
Micro 1 Micro 2 Micro 30
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Minimum efficiency Maximum efficiency
Tmax = 300◦
2
◦
Air
Helium
Nitrog
en CO 2
Argon
Xenon
0
5
10
15
20
25
30
35
1
1.5
2
2.5
3
3.5
4
MICRO
1
MICRO
2
MICRO
3
Air
Helium
Nitrog
en CO 2
Argon
Xenon
1
1.5
2
2.5
3
3.5
4
1
1.5
2
2.5
3
3.5
4
MICRO
1
MICRO
2
MICRO
3
◦
2
2
2
2
2 2
Tmax = 600◦
Micro 1 Micro 2 Micro 30
5
10
15
20
25
30
35
40
Micro 1 Micro 2 Micro 30
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Minimum efficiency Maximum efficiency
Tmax = 600◦
2
2
◦
◦
2
2
Air
Helium
Nitrog
en CO 2
Argon
Xenon
0
10
20
30
40
50
1
1.5
2
2.5
3
3.5
4
MICRO
1
MICRO
2
MICRO
3
Air
Helium
Nitrog
en CO 2
Argon
Xenon
1
1.5
2
2.5
3
3.5
4
1
1.5
2
2.5
3
3.5
4
MICRO
1
MICRO
2
MICRO
3
◦
2 2
Tmax = 900◦
Micro 1 Micro 2 Micro 30
10
20
30
40
50
Micro 1 Micro 2 Micro 30
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Minimum efficiency Maximum efficiency
Tmax = 900◦
2
pmin = 4
◦
◦
◦◦ ◦
◦
2
◦◦
2
2
2
◦ ◦◦
PRopt
Branch Name Duration Start End
Fase previa del proyecto 14 days 25/09/2018 12/10/2018
Reunión inicial 1 day 25/09/2018 25/09/2018
Declaración de objetivos 13 days 26/09/2018 12/10/2018
Estudio del Estado del Arte 13 days 26/09/2018 12/10/2018
Modelo base y caso Nominal 39 days 15/10/2018 06/12/2018
Modelado del ciclo base 7 days 15/10/2018 23/10/2018
Simulaciones del caso Nominal 26 days 19/10/2018 23/11/2018
Optimización del caso Nominal 9 days 26/11/2018 06/12/2018
Estudio de mezclas 63 days 12/11/2018 06/02/2019
Estado del Arte en mezclas 9 days 12/11/2018 22/11/2018
Estudio de modelos simplificados 10 days 23/11/2018 06/12/2018
Aplicación al caso Nominal 44 days 07/12/2018 06/02/2019
Estudio de los casos Micro 75 days 05/12/2018 19/03/2019
Simulación de los casos Micro 56 days 05/12/2018 20/02/2019
Optimización de los casos Micro 19 days 21/02/2019 19/03/2019
Estudio de los fluidos orgánicos 17 days 20/03/2019 11/04/2019
Estudio de los modelos simplificados 9 days 20/03/2019 01/04/2019
Aplicación a los casos Micro 8 days 02/04/2019 11/04/2019
Generación de resultados 124 days 24/10/2018 15/04/2019
Resultados de simulación 119 days 24/10/2018 08/04/2019
Análisis de resultados 5 days 09/04/2019 15/04/2019
Redacción de la memoria 49 days 16/04/2019 21/06/2019
Redacción del trabajo 44 days 16/04/2019 14/06/2019
Revisión del tutor 5 days 17/06/2019 21/06/2019
Preparación de la defensa ante tribunal 16 days 26/06/2019 17/07/2019
Elaboración de la presentación 15 days 26/06/2019 16/07/2019
Fin del proyecto 1 day 17/07/2019 17/07/2019
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Task Name
Fase previa del proyecto
Reunión inicial
Declaración de objetivos
Estudio del Estado del Arte
Modelo base y caso Nominal
Modelado del ciclo base
Simulaciones del caso Nominal
Optimización del caso Nominal
Estudio de mezclas
Estado del Arte en mezclas
Estudio de modelos simplificados
Aplicación al caso Nominal
Estudio de los casos Micro
Simulación de los casos Micro
Optimización de los casos Micro
Estudio de los fluidos orgánicos
Estudio de los modelos simplificados
Aplicación a los casos Micro
Generación de resultados
Resultados de simulación
Análisis de resultados
Redacción de la memoria
Redacción del trabajo
Revisión del tutor
Preparación de la defensa ante tribunal
Elaboración de la presentación
Fin del proyecto
