US2407166A - Heat cycle - Google Patents

Description

p 1946 I JQKREITNER ETAL\ 2,407,166

HEAT CYCLE Filed Nov. 8, 1941 2 Sheets-Sheet 1 Fi .1. Fig.2

Sepia 9 1946 J. KREHTNER EAL. 7,

HEAT CYCLE Filed Nov. 8, 1941 ZSheets-Sheet 2 IN VEN TORS KIAMW.

Patented Sept. 3, 1946 HEAT CYCLE Johann Kreitner, New York, and Frederick Nettel, Manhasset, N. Y.

' Application November 8, 1941, Serial No. 418,288

Claims.

The present inventiondeals with heat cycles for power production in heat enginesof any type, with preferred application to power systemsof the continuous combustion type. Its object is to improve the thermal overall efiiciency beyond" that of any known heat cycle which is practically realizable withlpresent'means. I

Ever since the conception of the theoretical reversible cycle by Carnot as the one yielding the highest possible thermal efliciency, efforts have been made to reproduce it in practical power plants, or to approximate it.

For well known reasons power plants with water vapor as working medium can never achieve this. Gaseous working fluids are basically better suited. But also there the Carnot cycle, represented by a rectangle in the T-S diagram, meets unsurmountable difliculties if it is to utilize tem perature ranges as available today, for example between deg. C. and 650deg: C. for plant's of the continuous combustion type, and between 15 deg. C, and about 1200 deg. C. for plants of the intermittent combustion type. To reach these temperatures, the isentropic sides of the Carnot rectangle lead to extremely high compression end pressures and/or extremely. low expansion end pressures, that is, into pressure ratios which cannot be managed with existing compressing means. For example a Carnot cycle for the first mentioned temperature range would require a compression ratio well over 1:100, and for the second mentioned temperature rangeof well over 1:700.

Thus the practical utilization of the technologically available temperature range requires cycles with isobaric heating, which permits to reach the top temperature without involving extreme top pressures.

Amongst these isobaric cycles the simples in comparatively small output per weight unit of working fluid, and is accordingly sensitive to the internal losses of the practical compression and expansion means and in conduits. I I

This results in compartively lowpractical thermal overall efllciencies for the Brayton cycle, par- 2 ticularly in plants of the continuous combustion type.

It is known in the art to improve upon the Brayton cycle by reducing the compression work through inter-cooling, and/or by increasing the expansion work through re-heating. Both intercooling and reheating have been proposed either uniformly distributed over the whole compression and expansion, or concentrated in a definite number of individual points substantially uniformly distributed over the whole compression and expansion, respectively. In both methods it was the declared purposes of these measures to approach, as closely as practically possible, isothermic expansion and/or compression, thus aiming at an ideal cycle which had been conceived already by Ericsson. This Ericsson cycle is represented in a T-S diagram by a quadrilateral with two isothermic and two isobaric sides, thus involving the sequence of isothermic cooled com pression, isobaric heating, isothermic heated expansion, and isobaric rejection, or re-cooling in the case of a closed cycle. The Ericsson, or double-isothermal cycle, offers considerable difficulties in practical execution due to the great amount of intercooling and re-heating throughout the compression and expansion, respectively, but it represents according to the teachings of the present art, the highest refinement of the fisobaric cycles. i

It is also known in the art to combine isothermal compression with isentropic-expansion or vice versa, which measures, however, do not leadto improved efiiciencies.

The present invention consists in the realization that there exists a cycle, so to speak, in between the Braytonand the Ericsson cycles, which requires less inter-cooling and re-heating than the latter, yet is superior in efficiency to either of them. H

In the drawings, Fig. 1 represents a temperature-entropy diagram of the Brayton cycle; Fig.

In the Fig. 1 the Brayton cycle, in Fig. 2 the Ericsson cycle, and in Fig. 3 the new cycle are shown in the usual T-S diagrams, each'within the same temperature rangeTi same pressure range m p2.

. T2 and the In Fig. 1, the quadrilateral l l--l2l3-|4 represents the Brayton cycle, in Fig. 2, the quadrilateral 2I22 23-24 represents the Ericsson cycle; in Fig. 3, the hexagon 3l32-33-34- 35-35 represents the fundamental theoretical form of the new cycle, which for the purposes of this specification may be referred to hereafter as Hexagon cycle. It consists of an isothermic compression 31-32., an isentropic compression 3233, an isobaric heating 3334, an isothermic expansion 3435, an isentropic expansion 3536,

and isobaric rejection, or re-cooling in the caseof a closed cycle, 363l. Dotted lines in Fig. 3 show the corresponding Brayton cycle 3l-32- 3435', and the corresponding Ericsson cycle 3l-32"34-35".

The isobaric heating 33-44 of the Hexagon cycle may be carried out solely by direct or indirect transfer of fuel combustion heat to the compressed working fluid, or partly by regeneration of waste heat from the exhaust gases past point 36, as in the case of other cycles. The efficiency of such regenerative heat transfer is determined by the ratio of the transferred heat to the enthalpy difference between points 38 and 33.

The means for the practical execution of the Hexagon cycle are basically the same as for the Ericsson cycle; the difference consists in restricting the inter-cooling to the first part of the compression, and the re-heating to the first part of the expansion. The uncooled part of the compression shall, according to this invention, cover at least forty per cent of the pressure diiierence between the highest and lowest pressure in the system. Thus the practical execution becomes simpler. Yet the efliciency is superior to both the Brayton and the Ericsson cycles- In a comparative numerical example, calculated for identical conditions, the thermal efiiciency of the three cycles is as follows:

All figures of the above table are calculated for temperature limits 15 deg. C. and 650 deg. 0., pressure limits 1 and 6 at absolute, and 85 per cent internal efficiency for compression and expansion. The accuracy of the computation can be easily verified by anyone skilled in the art.

The above figures, which represent. practical working conditions, clearly demonstrate that the Hexagon cycle combines simplification in practical execution with a marked improvement in efliciency over what the art has so far known.

In actual execution the efiiciency difference between the Hexagon cycle and the Ericsson cycle will be still larger than that shown in the above table, in which the pressure losses in the systems have not been taken into account. Nearisothermic compression and expansion, however, if practically carried out, involve pressure losses in the corresponding cooling and heating means, which lower the efficiency. Since the Hexagon cycle needs materially less cooling and heating that the Ericsson cycle, the detrimental influence of these pressure losses is correspondingly smaller in the Hexagon cycle.

Fig. 4 shows a Hexagon cycle such as assumed for the mentionedcomputation. The second part of the compression, 4243, and of the expansion,

45-46, are not strictly isentropic any more, but somewhat inclined due to the 15 per cent internal losses in the compression and expansion means.

The Figures 3 and 4 represent, so to speak, schematic forms of the new cycle, with six corners. These are, however, not essential for the present invention. In practical execution some of the corners may be rounded off or disappear altogether; in Fig. 4 this isshown by dotted lines 42' and 45 for the corners 42 and 45, indicating that there must not necessarily exist a definite demarcation between an isothermal and an isentropic, or near-isentropic, part of the compression and expansion, respectively. It is only essential for this invention that the compression as a whole leads from a starting point 4| to an end point 43 which has both a substantially higher temperature and a substantially smaller entropy, and that the expansion as a whole leads from a starting point 44 to an end point 46 which has both a substantially lower temperature and a substantially larger entropy.

With substantially larger entropy we do not mean an increase in entropy due to internal losses, but an increase corresponding to an increase in useful expansion work; and with substantially smaller entropy at the end point of compression we mean a decrease in entropy corresponding to a saving in mechanical compression work. In other words, a straight line connecting, for example in Fig. 4, the starting point 4| and the end point 43 of the compression, shall have a substantial inclination both against the horizontal and the vertical, forming a very roughly approximated perpendicular to the isobars 43--44 and 464l. This distinguishes the new cycle from those known in the art, which aim at ideal compression lines either throughout horizontal (isothermal) or throughout vertical (isentropic), deviating therefrom only to the extent due to the imperfection of the practical means of execution.

It is within the scope of this invention to realize, compression in a way as may be represented by curves of various forms between the points 4! and 43 thus characterized. The same holds good for curves representing the expansion between points. 44 and 46. While the cycle. with the fundammital isothermic-isentropic angle (3l-32- 33, and. 34-35-36 in Fig; 3), gives the highest theoretical efliciency, deviations therefrom may be resorted to for practical considerations. For example the isothermic. part of the compression and/or expansion may be approximated by intercooling and/or re-heating in a definite number of individual points between stages of compression or expansion, respectively; 'Ilhe intercooling and/or re-heating may lead back to the starting temperature or to a different temperature. Fig. 5 shows such a cycle with intercooling and reheating in two individual points each. The corresponding schematic Hexagon cycle is indicated in dotted. lines. In its form of execution by intercooling and reheating in individual points, the Hexagon cycle falls partly within the scope of our co-pending applications Serial No. 399,242 of June 21, 1941, and Serial No. 401,702 filed July 10, 1941, the latter now abandoned.

It hasalready been realized that too late reheating may adversely affect the efliciency and it has been proposed to restrict reheating to the first part of the expansion. It has, however, never before been recognized that such. consideration is only a part of a basic general, law which applies equally to. the compression as well as to.

the expansion, and that the combined application of corresponding new rules to cooled compression and heated expansion leads to a new superior cycle as described hereinbefore.

Fig. 6 shows by way of a non-limiting example a combustion turbine power system of the continuous combustion type operating on the cycle described.

Ambient air is taken in at 60 into multistage compressor means 6|, compressed, and cooled during compression in coolers 62a, 62b, 62c, and 62d. The cooling takes place only during the first part of the compression, the second part being uncooled.

Thus the compressed air leaves the compressor means at 62 at a substantially increased temperature, is further preheated in recuperator means 63, and finally heated to the metallurgically admissible temperature by internal combustion of fuel in heater 64. Thereafter it is expanded in multistage turbine means 65, and reheated during expansion in reheaters 66a, 68b, and 66c. The heating takes place only during the first part of the expansion, the second part being unheated. Thus the working fluid leaves the expansion means at 61 at a substantially reduced temperature, and is further cooled by regenerative heat exchange in recuperator 63 before being exhausted to the atmosphere at 68.

The turbine means drive the compressor means,

and the excess power serves to drive an electric generator 69.

The means described are basically the same as for an Ericsson cycle; the difference consists in the arrangement of both the coolers and heaters exclusively in the first part of the compression and expansion, respectively, the second part of both processes being near-isentropic. The present invention further comprises rules for the proper selection of the relative position of the starting point and end point of compression and expansion respectively. For the theoretical Hexagon cycle with exact isothermic-isentropic compression and expansion, and fo cycles closely approximating this fundamental form, applicants have found that highest efliciency is reached if the temperature rise during compression is per cent of the absolute temperature at the start of compression, and the temperature drop during expansion is per cent of the absolute temperature at the start of the expansion, where e is the thermal overall eiiiciency of the practical cycle, and It is the efficiency of the waste heat regeneration.

These formulae determine, as it were, the spot between the Brayton and the Ericsson cycle where efficiency is highest, sloping down towards either side. But since the point thus determined is the apex of a continuous efficiency curve of parabolic character, a margin in the temperatures derived from the formulae up to six to eight per cent of the absolute temperatures involved does not yet materially reduce the efficiency.

For cycles with a compression represented in a T-S diagram by a more irregular curve, or broken line, it has been found that the favorable effect of the new cycle is achieved if the compression end temperature is by the value derived from the above formula, or at least by forty degrees centigrade, higher than the highest temperature in the first half of the compression range, that is at any pressure under /2.(p1+p2). In Fig. 5, for example, the point 53 shall be more than 40 degrees oentigrade higher in temperature than the point 52'; This rule leads to a compression with a predominantly isotherrnic first part, and a predominantly isentropic second part, irrespective of the special character of the curve in the T-S diagram representing the practical performance of the compressing and cooling means.

An analysis of the above formulae shows that both the Brayton and the Ericsson cycles are special border cases of the general Hexagon cycle for following reasons: If the assumed pressure range is so small that the corresponding temperature rise for isentropic compression equals the value derived from the first formula, the Hexagon cycle loses its isothermal parts and deteriorates into a Brayton cycle. If, at the other hand, the efliciency of waste heat regeneration is assumed as one hundred per cent, (:1), the Hexagon cycle loses its isentropic parts and deteriorates into an Ericsson cycle.

Though these considerations have predominantly theoretical importance, they are deemed necessary for the ready comprehension of the essence and bearing of the new Hexagon cycle. In practical applications such border cases will never occur: It takes a prescribed total pressure ratio of under 1:3 to make the Brayton cycle the best and such limitation will hardly ever be met in practice; and hundred per cent efiiciency of waste heat regeneration is an unattainable theoretical assumption, as is hundred per cent internal efliciency for a turbine.

It is further necessary for the complete comprehension of the bearing of the new Hexagon cycle to realize that also'the Carnot cycle appears as one border case of the universal solution represented in the above equations. If we assume no waste heat regeneration, (lc=0), but ideal compression and expansion without losses, and a pressure range sufiiciently wide to permit approach to the ideal Carnot efiiciency the introduction of these values for k and 6 results in a temperature rise during compression equal T2T1, and an identical value for the temperature drop during expansion. Thus the equations directly prescribe the entire temperature range between the lowest temperature T1 and the highest temperature T2 to be bridged by isentropic compression and expansion, thereby representing the ideal Carnot cycle as another special solution of the general relations herein disclosed. The Carnot cycle thus emerges from the above equations as the best cycle for its conditions, that is, for ideal compression and expansion without internal losses. But for actual compression and expansion means with internal efliciences small than one hundred per cent, the equations furnish values for the temperature differences during compression and expansion much smaller than the entire temperature range, thereby designating a six-cornered Hexagon cycle as the best possible cycle for the assumed conditions. In other words, if the huge pressure ranges necessary for the realization of the Carnot cycle were available, as they might conceivably be in future, but practical compressors and turbines are to be reckoned with, the practical Hexagon cycle is superior to any practical Carnot cycle for identical conditions.

The difference is very considerable: For a calculated example in which the internal losses bring the Carnot cycle down from 69 per cent ideal efiiciency to thirty per cent practical efficiency, the corresponding Hexagon cycle still retains fifty per cent practical eficiency under identical assumptions.

From the foregoing description it will be evident that the invention may be embodied in many specific forms and arrangements of apparatus, and that certain features of the invention may be employed to the exclusion of others. Accordingly, it is to be understood that the invention includes all forms of apparatus that may fall within the scope of the appended claims.

What we claim is:

1. In the method of producing power in heat engines through cyclic changes of a gaseous Working fluid, the sequence of compression from a starting point of given pressure and temperature to a compression end point of substantially smaller entropy and a temperature more than forty degrees centigrade higher than the temperature at any point within the first half of the compression range, heating to a still higher temperature at substantially constant pressure, expansion therefrom to a point of substantially larger entropy, substantially lower temperature, and a pressure substantially equal to that of the compression starting point.

2. In the method of producing power in heat engines through cyclic changes of a gaseous working fluid, the sequence of near-isothermic cooled compression, uncooled compression, nearisobaric heating, near-isothermic heated expansion, unheated expansion to a pressure near the starting pressure of compression, the uncooled compression covering a pressure range at least forty per cent of the total difference between the highest and the lowest pressure in the system.

3.. In the method of producing power in heat engines through cyclic changes of a gaseous working fluid, the sequence of near-isothermic compression approximated by intercooling in a plurality of individual points between stages of compression, uncooled compression, near-isobaric heating, near isothermic expansion approximated by reheating in a plurality of individual points between stages of expansion, and unheated expansion to a pressure near the starting pressure of compression, the uncooled compression covering a pressure range of at least forty per cent of the total difference between the highest and the lowest pressure in the system.

4. In the method of producing power in heat engines through cyclic changes of a gaseous Working fluid, the sequence of near-isothermic cooled compression, uncooled compression, nearisobaric heating, near-isothermic heated expansion, unheated expansion to a pressure near the starting pressure of compression, the end temperature of said uncooled compression bein more than forty degrees centigrade higher than the highest temperature during that part of the compression where the pressure is lower than the arithmetical mean of the lowest and the highest pressure in the system.

5. In the method of producing power in heat engines through cyclic changes of a gaseous working fluid, the sequence of near-isothermic compression approximated by intercooling in a definite number of individual points between stages of compression, uncooled compression to a compression end temperature more than forty degrees centigrade higher than the temperature at any point within the first half of the compression range, near-isobaric heating, near-isothermic expansion approximated by reheatin in a definite number of individual points between stages of expansion, unheated expansion to a pressure near the starting pressure of compress1on.'

JOHANN KREITNER. FREDERICK NETTEL.

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