Prototype
Vortex
Thermodynamic Calculation Method
s4 = s3
z4
4
VORTEX
SOLAR
CHIMNEY
q34 = 0
w34 =0
h3 - h4 = gz4
Warm
water inlet
T=SST
p3 = p2
T3 = SST - A
U3 = 100 - B
z3 = 0
Nozzles Rotor
1
2
3
s2 = s1
z2 = z1 = 0
COOLING
TOWER
TURBINE
w12 = h1 - h2
q12 = 0
Cooled water
return
q23 = h3 - h2
w23 = 0
Vortex Engine Ideal Process Calculations.
Heat source
None
26°C water
at P2
36°C dry
heat at P2
40°C dry
heat at P1
Air properties:
P1 (kPa)
T1 (°C)
r1 = r2 (g kg-1)
U1 (%)
s1 = s2 (J K-1 kg-1)
h1 (J kg-1)
101.1
25.8
16.87
80.0
241.0
68913
101.1
25.8
16.87
80.0
241.0
68913
101.1
25.8
16.87
80.0
241.0
68913
101.1
33.6
16.87
50.1
267.7
76992
P2 = P3 (kPa)
P12
T2 (°c)
U2 (%)
h2 (J kg-1)
101.1
0
25.8
80.0
68913
97.72
3.38
22.92
92.3
65943
97.70
3.40
22.91
92.3
65916
97.73
3.37
30.6
57.6
73941
T3 (°c)
U3 (%)
r3 = r4 (g kg-1)
h3 = 3 = 4 (J kg-1)
s3 = s4 (J K-1 kg-1)
25.8
80
16.87
68913
241.0
24.5
97
19.57
74433
269.7
30.7
57.4
16.87
74003
268.0
30.6
57.6
16.87
73941
267.7
P4 (kPa)
T4 (°c)
z4 (m)
h4 (J kg-1)
10.0
-87.1
16570
-96209
10.0
-80.92
16570
-91130
10.0
-82.2
16570
-91150
10.0
-82.3
16570
-91180
Heat Input (J kg-1)
Q = h3 - h2
0
8504
8072
8079
Work (J kg-1)
W = h1 - h2
0
2984
2996
3048
Velocity (m s-1)
v = (2 W )0.5
0
77.2
77.4
78.1
Efficiency (%)
n (%) = W12/Q23
n (%) = 1 – T4/T3
n/a
n/a
35.1
35.4
37.1
37.2
37.7
37.8
Hurricane Isabel effect on sea surface temperature as observed from satellite
Source: http://www.meted.ucar.edu/npoess/microwave_topics/overview/print.htm#s3p7
A hurricane viewed as a Carnot cycle
Efficiency
n = 1 – Tc / Th = 1 – 200/300 = 33%
Source Divine Wind by Kerry Emanuel
Gravity Power Cycle
Brayton gas-turbine power cycle
Atmospheric work production process
Energy conservation in an open system
Reversible and Irreversible Expansion
Latch #2
Piston
Latch #1
Valve
#1
Base pressure
100 kPa
Rising Air
Column
Ambient Air
Column
Automat
in vacuum
Valve
#2
Cylinder
and Piston
Base Pressure
95 kPa
Constrained reversible expansion - Work is produced - No Latch
1. Start with piston at bottom of the cylinder, open valve #1,
2. Automat raises piston and let 1 kg of air at 100 kPa in cylinder,
3. Close valve #1,
4. Automat raises piston until cylinder pressure decreases to 95 kPa,
5. Open valve #2,
6. Automat pushes piston to the bottom of the cylinder.
The air temperature decreases.
Unconstrained irreversible expansion - No work is produced - Two Latches
1-3. As above except after step 3. set latch #1 and #2,
set latch #2 so that the final pressure is 95 kPa,
4. Automat lets go of the piston,
5. Let go latch #1, piston snaps against latch #2 without doing any work,
6. Automat pushes piston to the bottom of the cylinder.
The air temperature does not decrease.
Cooling Towers
Mechanical Draft: $15 million 40 m tall
mechanical draft tower uses 1% to 4%
of power output to drive fans. (uses
energy)
Natural Draft: doesn’t need
fans but is 150 m tall and
costs $60 million. (saves
energy)
Vortex
Starting
Heat
Source
Sub-atmospheric
Heater
(cooling tower)
Cylindrical
wall
Deflector
Restrictor
or Turbine
Vortex Cooling Tower: $15 million 40 m
tall to function like a natural draft
tower. (produces energy!)
Vortex Engine
LMM
Atmospheric Vortex Engine
2
Vortex
Arena
Water cooler
and Air heater
Warm water
Turbine &
generator
Warm air
Ambient air
Cool water
Illustration by:
Charles Floyd
Wet cooling tower AVE – Side view
Capacity approximately 200 MW
Willis Island sounding and updraft temperatures
Pressure (kPa)
20
40
4
Updraft
SST approach 1°C
Humidity 90%
SST = 30.4 °C
0
Sounding
Temperature
Constant Entropy
Updrafts
Udraft of unheated
surface air
60
Heating and humidification
in exchanger
80
100
-100
Turbine Outlet Pressure = 83.5 kPa
Base Pessure = 100.3 kPa
-80
-60
-40
Constant Entropy
Expansion in Turbine
2
3
1
-20
Temperature (°C)
0
20
40
Effect of entrainment and ambient
relative humidity on updraft buoyancy
60
95%
at P<80
Ambient
Relative
Humidities
Pressure (kPa)
70
Updrafts with app. 10%
entrainment per kPa
80%
at P<80
80
50%
at P<80
Updraft with
no entrainment
50%
at P<93
90
100
-1
0
1
2
3
Virtual Temperature Excess (K)
4
Subsidence warming and radiative cooling
Q
Radiative
cooling
1
P1 T1
M
P2 T2
Dry Adiabatic
Subsidence
9.8 C/km
P1
P
2
Environment
Temperature
Lapse rate
6.5 C/km
3
Radiative cooling
1.5 C/day
2
Air column
with subsiding
layer
T1
T2
T3
Hurricane Isabel Intensity SST 25 to 26.5 C
Temperature approach 1 C - Relative humidity 97%
Surface air properties: P1 = 101.1 kPa, T1 = 27.8 °C, U1 = 80, r1 = r2 = 19.06 g kg-1, h1 = 76572 J kg-1,
-1
-1
s1 = s2 = 266.8 J K kg .
Eyewall SST (°c)
25.0
25.5
26.0
26.5
P2 = P3 (kPa)
T2 (°c)
U2 (%)
-1
h2 (J kg )
99.14
26.12
86.8
74830
97.72
24.90
92.2
73557
96.01
23.41
99.3
72005
94.36
22.72
101.75
70490
T3 (°c)
U3 (%)
r3 = r4 (g kg-1)
h3 = h4 + (1+r4) gz
s3 = s4 (J K-1 kg-1)
24
97
18.69
71686
256.2
24.5
97
19.57
74434
269.7
25.0
97
20.55
77459
285.2
25.5
97
21.57
80590
300.8
P4 (kPa)
T4 (°c)
15.0
-61.45
10.0
-80.92
10.0
-77.72
10.0
-74.42
T4V (°c)
T4A (°c)
z4 (m)
-1
h4 (J kg )
-65.32
-62.9
14220
-70275
-84.69
-80.1
16570
-91130
-81.65
-80.1
16570
-88264
-78.61
-80.1
16570
-85299
P12
W = h 1 - h2
v = (m/s)
1.96
1742
59.0
3.38
3015
77.6
5.09
4567
95.6
6.74
6081
110.3
n (%) = W12/Q23r
n (%) = 1 – T4/T3
n/a
28.8
base
35.4
33.9
33.5
33.2
33.5
Typical Energy Calculations – SST 30.4 C
Vortex solar chimney energy calculations for a range of temperature and humidity approach to sea surface
temperature (SST). Ambient surface air conditions: P1 = 100.3 kPa, T1 = 29.4 °C, U1 = 77.5%, r1 = r2 = 20.50
g kg-1, s1 = s2 = 287.0 J kg-1 K-1, h1 = 81920 J kg-1. Heights based on 17 January 1999, 0000Z Willis Island
sounding. Approach based on SST = 30.4 °C.
Properties
Case 0
q23 = 0
Case 1
A=3, B=10
Case 2
A=1, B=10
Case 3
A=1, B=5
Case 4
A=0, B=0
P2 = P3 (kPa)
P1 - P2 (kPa)
T2 (°C)
U2 (%)
h2 (J kg-1)
95.80
4.50
25.47
94
77820
91.38
8.92
23.10
103
73670
83.42
16.88
19.99
115
65720
81.02
19.28
18.99
119
63200
74.62
25.68
16.14
131
56150
T3 = SST – A (°C)
U3 = 100 – B (%)
-1
r3 = r4 (g kg )
-1
h3 (J kg )
-1
-1
s3 = s4 (J K kg )
25.47
94
20.50
77820
287.0
27.4
90
23.25
86840
331.3
29.4
90
28.87
103320
413.5
29.4
95
31.43
109840
444.1
30.4
100
38.35
128590
531.1
P4 (kPa)
T4 (°C)
z4 (m)
h4 (J kg-1)
h4+gz4(1+r4)
10
-77.39
16570
-87890
77820
10.0
-68.01
16570
-79330
86840
7.0
-69.91
18580
-84020
103320
7.0
-63.21
18580
-77970
109840
5.0
-62.77
20560
-80630
128590
q23 = h3-h2 (J kg-1)
w12 = h1-h2 (J kg-1)
vx (m s-1)
0
4090
90
13170
8250
128
37590
16190
180
46650
18720
193
72440
25770
227
n/a
n/a
n/a
n/a
4050
n/a
n/a
32.8%
base
base
base
base
n/a
512
1000
28.1%
n/a
n/a
n/a
28.2%

w12/T3
w12/U3
w12/r3
w12/q23
32