U.S. patent number 3,867,811 [Application Number 05/306,557] was granted by the patent office on 1975-02-25 for power modulation of a thermal generator.
This patent grant is currently assigned to Compagnie Francaise de Raffinage. Invention is credited to Raymond Francois Maurice Waeselynck.
United States Patent |
3,867,811 |
Waeselynck |
February 25, 1975 |
POWER MODULATION OF A THERMAL GENERATOR
Abstract
A process for modulating the power of a gas turbine by variation
of the inlet temperature of the working fluid in a compressor
located upstream of a turbine. The compressor and turbine are each
staged and the working fluid is cooled at least before the last
compressor stage by gasification of a liquefied gas. A portion of
the cooling energy produced by expansion of the liquefied gas can
be returned to the liquefied gas in storage to cool the latter.
Inventors: |
Waeselynck; Raymond Francois
Maurice (Paris, FR) |
Assignee: |
Compagnie Francaise de
Raffinage (Paris, FR)
|
Family
ID: |
9086143 |
Appl.
No.: |
05/306,557 |
Filed: |
November 14, 1972 |
Foreign Application Priority Data
|
|
|
|
|
Nov 22, 1971 [FR] |
|
|
71.41723 |
|
Current U.S.
Class: |
60/773; 60/652;
62/50.2; 60/39.17; 60/39.465; 62/46.2; 62/52.1 |
Current CPC
Class: |
F02C
6/14 (20130101); F17C 9/04 (20130101); F02C
7/143 (20130101); F17C 2221/031 (20130101); F17C
2227/0393 (20130101); F17C 2227/0309 (20130101); F17C
2223/0161 (20130101); F17C 2227/0157 (20130101); F17C
2201/0104 (20130101); F17C 2221/033 (20130101); F17C
2201/0128 (20130101); F17C 2223/0123 (20130101) |
Current International
Class: |
F17C
9/04 (20060101); F17C 9/00 (20060101); F02C
6/00 (20060101); F02C 7/12 (20060101); F02C
7/143 (20060101); F02C 6/14 (20060101); F02c
009/14 () |
Field of
Search: |
;60/39.02,39.03,39.18R,39.18B,36,39.71,39.12,39.46,39.17
;62/52,53 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Freeh; William L.
Assistant Examiner: Olsen; Warren
Claims
What is claimed is:
1. A process for modulating the power of a gas turbine by variation
of the inlet temperature of the working fluid in a compressor
located upstream of the gas turbine, said process comprising
forming the compression and turbine steps each in a plurality of
stages, cooling the working fluid before at least the last
compression stage by heat exchange with liquified gas stored in a
tank, producing a further refrigeration of the liquified gas stored
in said tank by supplying at least a part of the liquefied gas
during off-peak hours from said tank to an evaporator wherefrom are
obtained a gas fraction at the top and a cooled liquefied gas
fraction at the bottom, compressing the gas fraction produced in
said evaporator, then condensing the thus compressed gas fraction
by effecting heat exchange thereof with a flow of liquefied gas
coming from said tank and going to cool the working fluid and
introducing the now condensed gas fraction into said flow of
liquefied gas coming from said tank and going to cool the working
fluid, storing the cooled liquefied gas fraction collected in said
evaporator during off-peak hours and utilizing the same during peak
hours together with the liquefied gas from said tank to cool the
working fluid.
2. A process as claimed in claim 1, in which the cooled liquefied
gas fraction collected in said evaporator is stored during off-peak
hours in the same tank used for storing the liquefied gas by
partitioning the tank to prevent mixing of the cooled liquefied gas
fraction with the non-cooled liquefied gas.
3. A process as claimed in claim 1, in which the cooled liquefied
gas fraction collected in asid evaporator is stored during off-peak
hours separately from the tank used for the non-cooled liquefied
gas.
4. A process as claimed in claim 1 wherein the compression of the
working fluid is effected in two stages, the process further
comprising removing water from the working fluid before
introduction into the first compressor stage by cooling said fluid
by spraying at a temperature lower than 0.degree.C with a mixture
of water and anti-freeze and then subsequently separating the
condensed water from the working fluid.
5. A process as claimed in claim 4 wherein the working fluid coming
out of the first compressor stage is passed through a first cooler,
then through a container where it is freed from traces of water
vapor by spraying, at a temperature lower than 0.degree.C, with a
mixture of water and anti-freeze and subsequently separating the
condensed water from the working fluid and finally passing the
working fluid through a second, main cooler from which it is
discharged at a temperature of about -100.degree.C before being
admitted into the second compressor stage.
6. A process as claimed in claim 1 wherein the compression of the
working fluid is effected in two stages, the working fluid being
passed before being introduced into the first compressor stage
through a container where it is freed from water vapor by cooling
said fluid by spraying the same at a temperature lower than
0.degree.C, with a mixture of water and anti-freeze and
subsequently separating the condensed water from the working fluid,
then passing the working fluid through a main cooler from which it
is discharged at a temperature of about -100.degree.C to be
admitted into the first compressor stage.
7. A process as claimed in claim 6 wherein the working fluid coming
from the first compressor stage is passed through a second main
cooler from which it is discharged at a temperature of about
-100.degree.C before being admitted to the second compressor
stage.
8. A process as claimed in claim 1 wherein the working fluid
compressed in two stages, wherein the first compressor stage
operates at a relatively low compression ratio of about 2.5 and the
second compressor stage compresses the fluid to a higher value
therethan.
9. A process as claimed in claim 1 wherein the liquefied gas is
methane.
Description
BRIEF SUMMARY OF THE INVENTION
This invention relates to a process for increasing the efficiency
of thermal generators, particularly for modulating their power by
use of refrigeration, and to the application of this process, for
example, for indirect electrical power storage.
The advantage of increasing the power of a thermal generator of a
given size and of increasing its efficiency are obvious in
themselves and need not be explained. As for electrical power
storage, it is known that electrical power consumption varies on
the one hand according to the season of the year, and on the other
hand according to the time of day, but power production must
closely follow consumption due to the inability to store
electricity. This requirement causes substantial economic loss as
it entails long periods of reduced output since the size of the
generating installations must correspond to the highest power
demand while such a demand need be actually satisfied only during a
fraction of the operating time.
Indirect electrical power storage installations have already been
realized in the use of artificial lakes in which pumps raise water
during non-peak hours, but these gravitational storage
installations are far from satisfactory, and are only possible in
selected geographical sites.
The invention is based upon the known fact that lowering the
temperature of the cold source of a thermal machine increases its
thermodynamic efficiency and increases the power obtained per unit,
weight or volume of the working fluid. For instance, when the
working fluid is a non condensible gas, by lowering the temperature
of the cold source, the density of the gas going through the cycle
increases and consequently increases the power produced per unit
volume of the working fluid.
An object of the invention is to provide a process in which the
above is utilized in order to increase power production from a
given thermal machine and/or to allow utilization of a smaller
thermal machine to obtain a given power. In other words, the
invention seeks to increase the gross power of thermal machines of
a given size, as well as to improve their utilization and
particularly to increase their efficiency.
The invention contemplates a process in which the output power of
thermal machines can be modulated by refrigeration. The application
of this process permits a more complete and more continuous use of
the power of a thermal power generator, as well as a modulation of
the power output of a thermal machine without changing, at least
within wide limits, the speed of the machine, nor the maximum
temperature in the operating cycle.
According to the invention, it is not necessary to produce the
refrigeration effect near the thermal machine. The refrigeration
machines may therefore be located in any place, particularly in a
place where, due to production, utilization or storage of a
product, the cooling effect is transferred to this product. This
product may undergo, total or partial, transformation, and be
stored near the thermal machine.
Liquefied gases are specific substances for storage of
refrigeration effect and more particularly liquefied natural gases,
liquefied petroleum gases and liquefied gases from the air.
Liquefaction of these gases is effected to facilitate their storage
and transportation, they must be re-gasified before use. This
re-gasification produces a large quantity of cooling energy
hereafter called "frigories" which may be used in numerous
applications, and particularly in power production. Methane is an
example of a gas which is liquefied, transported by ship, stored in
depots, then re-gasified under pressure and distributed through
pipe lines over great distances.
An object of the present invention is the specific implementation,
giving a maximum efficiency to the utilization of the frigories
contained in liquefied gas and permitting continuously or
discontinuously to obtain high power and high efficiency in power
generation by means of a gas turbine.
The thermal machine described above effects compression, then
expansion of the working fluid.
The Applicant has established that it is advantageous to perform
the fluid compression in several stages and to cool the working
fluid between stages. Additionally, it is also advantageous to
perform the expansion of the working fluid in several stages.
A further object of the invention is to provide a process for the
modulation of gas turbine power production by variation of the
inlet temperature of the working fluid in a compression device
located ahead of the gas turbine inlet, said process being
characterized in that the working fluid compression and subsequent
expansion are performed in several stages, each compression stage
following a cooling of the working fluid by means of the cold
effect produced during the gasifying of a liquefied gas in a
container connected on the one hand to the liquefied gas storage
tank and on the other hand to a compressor.
The invention will be described hereafter in relation to an
apparatus and method comprising two compression stages and two
expansion stages.
It is necessary to dry to a maximum the inlet air in order to avoid
a quick frosting of the low temperature coolers. This the reason
why, before each stage of air cooling by means of the cooling fluid
(a liquefied gas), the air is first cooled by a coolant consisting
of water and anti-freeze. The air later goes through a separator of
water droplets; the remaining water in the air will be frozen in
the main cooler as very small particles which will be carried along
by the air and will not lie in the main cooler as a film.
The first compressor preferably operates at a rather low
compression ratio to serve the part of a supercharging device
fulfilling two functions:
by variation of its speed, it permits adaptation of the entire
circuit to the conditions of optimum efficiency when the air
temperature varies;
by multiplying the air pressure by the compression ratio, it
permits reduction of the surface area of the cooler located
downstream.
BRIEF DESCRIPTION OF THE DRAWING
The following description will be made with reference to the
appended drawings in which:
FIG. 1 diagrammatically illustrates a circuit for effecting the
process according to the invention by means of a utilization device
for the cold effect which is producted;
FIG. 2 shows another similar circuit according to the
invention;
FIG. 3 shows a device for utilization of the cooling effect by
cooling the liquefied gas and this device can be added to the
utilization devices shown in FIGS. 1 and 2;
FIG. 4 diagrammatically shows another arrangement according to the
invention for utilization of the cooling effect by cooling the
liquefied gas stock; and
FIG. 5 shows a supplementary refrigeration generation devicr whose
cooling effect is used to cool at least a portion of the liquefied
gas stock and this device may be added to the utilization devices
represented in FIGS. 1 and 2.
DETAILED DESCRIPTION
The various figures are simplified in that they do not include
auxiliary equipment such as pumps, etc., the necessity and the use
of which are obvious to those skilled in the art.
With reference to the apparatus of FIG. 1, therein is not
contemplated any cooling of the liquefied storage gas.
Air is introduced through line 1 into a scrubber 2 into which a
coolant consisting of water with added anti-freeze is sprayed by
nozzle device 3. The air is thus cooled to a temperature between
-2.degree.C. and +2.degree.C., at which temperature the greatest
part of the water present in the air is condensed.
The coolant is introduced into the scrubber 2 through a line 4 at a
temperature between -5.degree.C. and -10.degree.C., this
temperature being obtained by passing the coolant, collected by
line 5, through an exchanger 6 supplied with a refrigerating fluid
through circuit or loop 7 connected to the outlet and of a
gasification device of a liquefied gas.
In the upper part of scrubber 2, a cyclone 8 separates any
remaining traces of water droplets from the air.
The air from scrubber 2 is introduced, at a temperature between
-2.degree.C. and +2.degree.C., through line 9 into a compressor C1.
The compressed air is introduced through a line 10 into a cold
water cooler 11 in which water circulates through a line 12. Then,
the air is introduced through line 13 into a scrubber 2' which
operates similar to the scrubber 2 except that it is fed with air
under pressure at a temperature in the neighborhood of 30.degree.C.
Reference characters 3', 5' and 8' in the scrubber 2' designate
structure corresponding to 3, 5 and 8 in the scrubber 2. In the
scrubber 2' the air is substantially dried.
The dried air is discharged from scrubber 2' at a temperature
between -2.degree.C and +2.degree.C and is introduced through lines
14 into a main cooler 15. Liquefied gas enters the main cooler
through a line 16 and exits via a line 17 and serves as the
refrigeration fluid in cooler 15. The cold energy in the liquefied
gas is thus utilized to cool the air fed to compressor C.sub.2 and
this increases the efficiency of the compressor and lowers the load
on the turbines hence increasing the available output. The air is
fed from cooler 15 at very low temperature to compressor C.sub.2
where it is compressed and then is passed to a heat recovery device
18 by opening valve 19 and closing valve 20. The air is heated in
recovery device 18 and then passes to a combustion chamber 21
through valve 22 which is opened. A fuel is introduced into the
chamber 21 through line 23. The resulting combustion gas from
chamber 21 is passed to a turbine T.sub.1 through line 24. After a
first stage, a part of the heat content in the gas is recovered by
passing the exhaust gas from T.sub.1 into the heat recovery device
18 (valve 25 being opened and valve 26 being closed). The gas,
after having given up heat in device 18 is admitted into turbine
T.sub.2 through line 27 (valve 28 being opened) and exhaust is
effected through line 30 at atmospheric pressure.
The liquefied gas 31, stored in tank 32, is pumped to the main
cooler 15 through line 16. The gas discharged from line 17 is
supplied either to other gasifiers or to utilization devices or the
gas pipelines.
With reference to FIG. 2 which represents another embodiment of the
process according to the invention employing a device for the
utilization of the refrigeration effect, this embodiment as in FIG.
1 does not include a cooling of the liquefied gas stock.
In the embodiment of FIG. 2, air is introduced through line 1 into
scrubber 2 similar to the scrubber described in FIG. 1, and
reference characters 2-8 in FIG. 2 designate the same parts as in
FIG. 1.
The air in line 50 at a temperature which is between -2.degree.C
and +2.degree.C, is introduced into first main cooler 51. The
liquefied gas refrigeration fluid is fed from tank 32 through line
16 to cooler 51. The cooled air from cooler 51 is introduced into
compressor C1. The compressed air in line 54 passes into second
main cooler 55, the refrigerating fluid of which is liquefied gas
coming from tank 32 through line 16. The air in discharge line 58
from cooler 55 is fed to compressor C2 where it is further
compressed to a maximum value. Turbines T.sub.1 and T.sub.2 are
fed, as in FIG. 1, from the air compressed to a maximum coming from
compressor C2.
The gas coming from the main coolers 51 and 55 is fed through line
17 to other gasifiers or to consumption devices.
The implementation of the process of the invention is accompanied
by an important cooling of the air admitted into compressor C2 or
into compressors C1 and C2, and this enables a high expansion ratio
with a high efficiency and consequently allows installation of the
heat recovery device 18 between turbines T.sub.1 and T.sub.2.
Nevertheless, the two embodiments which have just been described,
need not include heat recovery device 18 in which case the
compressed air from compressor C2 is then directly introduced into
the combustion chamber 21 (valve 20 being opened, and valves 19 and
22 being closed). Furthermore, the exhaust gas from turbine T.sub.1
is directly admitted into turbine T.sub.2 (valves 26 being opened).
It is also possible to place the recuperating device not between
T.sub.1 and T.sub.2 but after T.sub.2, nevertheless, the increase
in compression ratio and efficiency which the invention allows to
obtain, affords the possibility of placing the heat recovery device
after T.sub.1, in which case it is less heavy and less bulky than
if it were placed after T.sub.2 without loss and even with a slight
gain in efficiency.
The magnitude of flow of the liquefied gas into the main coolers of
FIGS. 1 and 2 depends upon the gas demand, and therefore it is not
linked to the operating parameters of the process of the invention.
Nevertheless, this may be the case when the liquefied gas is
methane and generally, a natural gas whose peaks of consumption
correspond to the consumption peaks of the power produced by the
thermal machine. Besides, it is usual in gasifying centers to
maintain the flow of liquefied gas more or less constant
independently of the gas consumption by using gas storage means
such as natural underground reservoirs, gasholders, very long
pipelines under high pressure, etc. The power produced is then that
of a basic power plant.
It is possible to accept variations in the supply of liquefied gas
in the main coolers as long as these variations are not too sudden,
as they could then entail damage to the compressors.
Another embodiment of the process according to the present
invention, contemplates cooling the liquefied gas stock or a part
thereof. Three configurations thereof have been represented in
FIGS. 3, 4 and 5.
FIG. 3 shows a configuration which can be used instead of tank 32
of FIGS. 1 and 2 and is additive to the utilization arrangements
represented in FIGS. 1 and 2. The cooled liquid can be mixed in
variable proportions with non-cooled liquid before being introduced
into the air coolers. The supplementary refrigeration effect
produced by the cooling of the liquefied gas stock is stored in the
container used for liquefied gas storage.
Next shall be described the configuration and its operation. To
simplify, there will be distinguished two extreme cases of
operation, one during off peak hours (during which supplementary
refrigeration effect is stored), the other during peak hours
(during which the stored supplementary refrigeration effect is
consumed).
During off peak hours:
A flow of liquefied gas coming from the outlet 60 of tank 61 (valve
62 being opened) is expanded in the evaporator 63. The very cold
liquefied gas collected in line 64 is introduced into the lower
part of tank 61 through line 65 (valve 66 being opened and valve 67
being closed). The cooled liquefied gas introduced through a lower
opening 68 is prevented from mixing with non-cooled liquefied gas
by the presence of partition means, e.g., cylindrical vertical
partition 69 in tank 61.
The flow of liquefied gas to be gasified is withdrawn from tank 61
through the outlet 70. Valve 71 is opened and liquefied gas flows
through line 72 to a condenser 73 (valve 77 being opened) which
condenses the gas compressed in C3 (valves 74 and 75 being opened).
After condensing, this gas is introduced into the flow of liquefied
gas in line 72 (valve 76 being opened). From the outlet of
condenser 73 the liquefied gas is passed through line 16 to the
main cooler 15 (FIG. 1) or to the main coolers 51 and 55 (FIG.
2).
During peak hours:
Compressor C3 does not operate, valves 62, 74, 75, 66, 71, 76 and
77 are closed, valve 67 is opened, so that the flow of liquefied
gas to be gasified totally comes from the opening 68 of tank 61 and
is therefore very cold. Condenser 73 is by-passed during peak hours
by line 78.
The two types of operation which have just been described are
extreme cases, but they are not the only ones: thus, during
non-peak hours, valve 67 may be partially opened, conversely,
during peak hours, valve 71 is generally opened, and additionally,
compressor C3 may be operated.
With reference to FIG. 4 which represents a configuration for
utilizing refrigeration effect including means for generating
supplementary refrigeration effect from the cooling of at least a
part of the liquefied gas stock, the cooled liquid first of all,
passing through a special cooler before being mixed with the
remainder of the liquid introduced into the air coolers. The
cooling effect produced by the cooling of the liquefied gas stock
is stored in the liquefied gas storage container. This
configuration may be used instead of the system constituted by the
tank 32 and the main coolers 51 and 55 represented in FIG. 2.
This configuration and its operation will next be described for the
cases of operation during off peak hours and during peak hours.
During off peak hours:
Operation is very similar to that described with reference to FIG.
3. Valves 62, 74, 75, 76, 77 and 67 are opened, compressor C3 is in
operation, the cooled liquefied gas coming from evaporator 63 is
re-introduced into the tank 61 through the lower opening 68. Valves
79 and 80 are closed. The main coolers 55 and 51 are supplied with
liquefied gas through line 16. The gas coming out of the main
coolers 51 and 55 is supplied through line 17 to other gasifiers or
to consumption means.
During peak hours:
Compressor C3 is not in operation, valves 62, 74, 75, 76, 77 and 67
are closed. Valves 79 and 80 are opened. The cooled liquefied gas
is introduced into a special cooler 82 through line 83, and it is
discharged through line 84 after heat exchange with the air coming
from the main cooler 51. The main coolers 55 and 51 are supplied
with liquefied gas through line 16, the condenser 73 is by-passed
by line 78.
The modes of operation which have just been described are extreme
cases and others are possible, e.g., during off peak hours valves
79 and 80 may be partially opened.
With reference to FIG. 5 which represents a configuration for the
generation of supplementary cooling effect from the cooling of at
least a portion of the liquefied gas stock, this configuration may
be added to the configuration of the utilization of refrigeration
effect represented in FIGS. 1 and 2. The supplementary
refrigerating effect produced by cooling of the liquefied gas stock
is stored separately from that used for liquefied gas storage. The
cooled liquid may be either mixed in variable proportions with the
non-cooled liquid before being introduced into the air coolers, or
first introducted into the air cooler.
Next shall be described the configuration and its operation in two
extreme cases:
During off peak hours:
Valves 85, 86, 87, 88 and 89 are opened, compressor C3 is operated.
The liquefied gas coming from tank 32 and passing through valve 85
is expanded in the evaporator 90, a large refrigeration effect is
generated during this expansion which is stored in the evaporator
90 and is not used. The compressed gas coming from C3 is condensed
in the condenser 73, through which passes the flow of liquefied gas
coming from tank 32 through lines 91 and 92. The liquefied gas is
then fed through line 16 to the main cooler (reference character 15
in FIG. 1) or to the main coolers (reference characters 51 and 55
in FIG. 2).
During peak hours:
Valves 85, 86, 87, 88 and 89 are closed, compressor C3 is
stopped.
Distinction must be made as to whether the configuration includes
special cooler 82 or not.
When the configuration includes special cooler 82, it can replace
the system in FIG. 4 including the special cooler 82, the tank 61
and the evaporator 63. The line with valve 93 is omitted, valves 94
and 95 are opened. The special cooler 82 is supplied with cooled
liquefied gas through line 96 to cool the air coming from the main
cooler 51. The resulting very low temperature air is then
introduced into compressor C1.
The liquefied gas is then introduced into the main cooler 55
through line 16 via lines 97, 92 and 78 (condenser 73 is by-passed
by line 78).
When the configuration is not provided with a special cooler 82, it
can replace the system including the tank 61 and the evaporator 63
represented in FIG. 3. The line including valve 93 exists. Lines 96
and 97 as well as valves 94 and 95 are omitted. Valve 93 is opened,
the cooled liquefied gas directly joins the liquefied gas coming
from tank 32 through line 91.
The following examples which are given are not limitative, they
relate to the use of methane as the liquefied gas. Examples I and
II relate to the implementations of the process respectively
represented in FIGS. 1 and 2. Example III relates to the
configuration represented in FIG. 3 for the implementation of the
process in FIG. 1.
The numerical data used in the example are as follows:
the compression of air:
C = 0.246 ; C - c/C = 0.28
Average compressor adiabatic efficiency (adopted for the
simplification) : 0.83
Ambient air temperature : 290.degree. K
For air temperature rise : C = 0.26
Gas turbine inlet temperature: 1,173.degree.K
Gas expansion :
C = 0.26 ; C - c/C = 0.265
Average gas turbine adiabatic efficiency (adopted for the two
bodies) : 0.85
Ratio of gas weight to air weight : 1.015
Recuperation : C = 0.26
Heat recovery efficiency :
Gas inlet temperature - gas exit temperature/Gas inlet temperature
- air inlet temperature = 0.5
All calories are kilog calories.
EXAMPLE I
This example relates to FIG. 1.
A. In the absence of exchanger (18)
Compression: air admitted at + 2.degree.C (i.e., 275.degree.K) -
total compression ratio : 34
First compression body (C1) : compression ratio : 2.5
Compression work
T'.sub.c = 0.246 275/0.83 [(2.5).sup.0.28 -1]
T'.sub.c = 0.246 .times. 94.5 calories
Air temperature after compression:
275 + 94.5 = 369.5.degree.K
Second compression body (C2) : compression ratio :
34.3/2.5 = 13.7
Air temperature at the inlet after cooling : 173.degree.K
Compression work:
T".sub.c = 0.246 173/0.83 [(13.7).sup.0.28 -1]
T".sub.c = 0.246 .times. 223.5 calories
Air Temperature after compression:
173 + 223.5 = 396.5.degree.K
Total compression work:
T.sub.c = T'.sub.c + T".sub.c = 0.426 .times. 318 calories, = 78.5
calories
Air temperature rise
q = 0.26 (1173 - 396.5) = 0.26 .times. 776.5 calories = 202
calories
Expansion: total expansion ratio:
34.3/1.08 = 31.7
First expansion body (T.sub.1): Expansion ratio : 12.68
Expansion work :
T'.sub.t = 1.015 .times. 0.26 .times. 0.85 .times. 1173 [ 1 -
1/(12.68).sup.0.265 ]= 1.015 .times. 0.26 .times. 490 calories
Gas temperature after expansion : 1173 - 490 = 683.degree.K
Second expansion body (T.sub.2) - Expansion ratio 31.7/12.68 =
2.5
Expansion work :
T".sub.t = 1.015 .times. 0.26 .times. 0.85 .times. 683 [1 -
1/(2.5).sup.0.265 ]= 1.015 .times. 0.26 .times. 124.5 calories
Gas temperature after expansion :
683 - 124.5 = 558.5.degree.K
Total expansion work :
T.sub.t = T'.sub.t + T".sub.t = 1.015 .times. 0.246 .times. (490 +
124.5) = 1.015 .times. 0.246 .times. 614.5 calories = 162.5
calories
Useful work:
t.sub.u = T.sub.t - T.sub.c = 162.5 - 78.5 = 84 calories per kilog
of air
Efficiency : .rho. = t.sub.u /Q = 82.4/202 = 0.408
B. In the presence of the exchanger (18)
Recuperator: gas temperature before recuperator 18 and before
second expansion in T.sub.2 : 683.degree.K
Air temperature after compression: 396.5.degree.K
Gas temperature drop in the exchanger:
0.5 (683 - 396.5) = 143.5.degree.K
Heat recovery calories:
143.5 .times. 0.26 = 37.5 calories
Necessary heat for air temperature rise :
202 - 37.5 = 164.5 calories
Second expansion : temperature after exchanger :
683 - 143.5 = 549.5.degree.K
Expansion work :
T".sub.t = 1.015 .times. 0.26 .times. 0.85 .times. 549.5 [1 -
1/(2.5).sup.0.26 ]
T".sub.t = 1.015 .times. 0.26 .times. 100
Total expansion work :
T.sub.t = 1.015 .times. 0.26 (490 + 100) = 155.9 calories
Useful work : t.sub.u = (155.9 - 78.5) 0.98
T.sub.u = 77.4 .times. 0.98 = 75.8 calories per kilog of air
Efficiency : .rho. = 75.8/161.5 = 0.46
example ii
this example relates to FIG. 2.
A. In the absence of the recuperator 18
Compression : air admitted at - 100.degree.C (i.e., 173.degree.K) -
Total compression ratio : 35
First body (C1) compression ratio : 2.5
Compression work
T'.sub.c = 0.246 .times. 173/0.83 [ (2.5).sup.0.28 -1 ] = 0.246
.times. 60.5
Air temperature after compression:
173 + 60.5 = 233.5.degree.K
Second body (C2) compression ratio: 35/2.5 = 14
Air temperature on inlet after cooling: 173.degree.K
Compression work:
T".sub.c = 0.246 .times. 173/0.83 .times. [ (14).sup.0.28 -1 ] =
0.246 .times. 225
Air temperature after compression: 173 + 225 = 398.degree.K
Total compression work:
T.sub.c = 0.246 (60.5 + 225) = 70.1 calories
Air temperature rise:
q = 0.26 (1173 - 398) = 0.26 .times. 775 = 202 calories
Expansion:
total expansion ratio: 35/1.08 = 32.3
First body T.sub.1): expansion ratio: 32.3/2.5 = 12.9
Expansion work:
T'.sub.t = 1.015 .times. 0.26 .times. 0.85 .times. 1173 [ 1-
1/(12.9).sup.0.265 ] = 1.015 .times. 0.26 .times. 492
Gas temperature after expansion : 1175 - 492 = 681.degree.K
Second body (T.sub.2): expansion ratio: 2.5
Expansion work:
T".sub.t = 1.015 .times. 0.26 .times. 681 [ 1- 1/(2.5).sup.0.265 ]
= 1.015 .times. 0.26 .times. 124 calories
Gas temperature after expansion: 681 - 124 = 557.degree.K
Total expansion work:
T.sub.t = 1.015 .times. 0.26 (492 + 124) = 1.015 .times. 0.26
.times. 616
T.sub.t = 163 calories
Useful work:
t.sub.u = (T.sub.t - T.sub.c) 0.96 = (163 - 70.1) 0.98 = 91
calories per kilog of air
Efficiency: 91/202 = 0.45
b. in the presence of the recuperator 18
Recuperator: gas temperature before recuperation and before second
expansion in T.sub.2 : 681.degree.K
Air temperature after compression: 398.degree.K
Gas temperature drop in the exchanger:
0.5 (681 - 398) = 141.5.degree.K
Recovery of heat in calories:
141.5 .times. 0.26 = 37 calories
Necessary heat for air temperature rise:
202 - 37 = 165 calories
Second expansion: gas temperature after recuperation:
681 - 141.5 = 539.5.degree.K
Expansion work:
T".sub.t = 1.015 .times. 0.26 .times. 0.85 .times. 539.5 1-
[1/(2.5).sup.0.265 ] = 1.015 .times. 0.26 .times. 98.2 calories
Gas temperature after expansion: 539.5 - 98.2 = 441.3.degree.K
Total expansion work: T.sub.t = 1.015 .times. 0.26 (492 + 98.2) =
156 calories
Useful work: t.sub.u = (156 - 70.1) 0.98 = 84.2 calories per kilog
of air
Efficieny: .rho. = 84.2/165 = 0.51
example iii
the air temperature at the inlet of the first compressor body,
which in the case of Example I in the absence of the recuperator
18, was equal to 275.degree.K, is lowered by 40.degree.C and is
equal to 233.degree.K during operation in peak hours. Let us assume
for the time being that the opening of the gas turbine circuit is
not modified, nor is the revolution speed of the two compression
devices.
On the one hand, the density of the inlet air is increased
according to the ratio of the absolute temperatures = 275/233.
On the other hand, the compression ratio of the first body rises
from 2.5 to P.sub.1 /P.sub.o so that:
(P.sub.1 /P.sub.o).sup.0.28 -1 =[(2.5).sup.0.28 -1] .times. 275/233
= 0.29 .times. 275/233 = 0.342
without change in the compression work per kilog of air as opening
and speed remain constant. We deduce therefrom:
P.sub.1 /P.sub.o = 2.87 and the pressure at the gas turbine inlet
goes from 31.7 .times. P.sub.o to 31.7 P.sub.o .times. 2.87/2.5 =
36.4
To enable this new flow of gas to pass into the turbine, it would
be necessary to increase the pressure at the inlet by the ratio
275/233 = 1.18 and not by the ratio 2.87/2.5 = 1.147. This
adaptation requires that the speed of the first compression body be
increased by the ratio .sqroot.1.18/1.147, that is to say about 1.5
percent. The expansion ratio is then increased by the ratio 1.18 as
air densities.
For the remainder of the calculations, we shall neglect this slight
adaptation which would only improve the useful work ratio per kilog
of air.
If, therefore, we do not change the speed nor the opening, the
total compression work is not modified and remains equal to 78.5
calories. The expansion work is slightly increased and the useful
work per kilog of air goes from 84 to 85.9 calories.
The total useful work is thus increased in the ratio 85.9/84
multiplied by the ratio in weight of air flows, that is to say,
finally, in the ratio:
85.9/84 .times. 275/233 = 1.21
The peak power is thus increased by 21 percent.
Efficiency is itself improved in the ratio 85.9/84 and goes from
0.408 to 0.408 .times. 85.9/84 = 0.416.
It would of course be possible to lower the air temperature below
-40.degree.C at the inlet of the first compression body by
increasing the refrigerating machine power. The available power
during peak hours would thus be increased.
* * * * *