Source: Minutes of the Proceedings of the Institution of Civil Engineers, Vol 12, N° 896, p.571
Date: May 17th, 1853
Title: On the Conversion of Heat into Mechanical Effect - Discussion
Author: Charles William Siemens, Assoc. Inst. C.E.

Mr. C. Manby, Secretary, read some quotations from a letter addressed by M. Regnault to Colonel Sabine, Treas. Royal Society, (dated April 1853), in which he stated, that he was about to publish, immediately, a series of elaborate experimental researches, on various subjects connected with the effects of heat on elastic fluids ; the results of which would solve many questions long in dispute, and by means of which engineers might accurately calculate the effect of a given amount of fuel, in whatever way it was applied.

M. Regnault communicated in anticipation, that he had arrived at the number 0.237, for the specific heat of air, at constant pressure, and at 0.475, for that of steam, under atmospheric elasticity, the specific heat of water being taken in each case as unity.

The role of the regenerator

Mr. Siemens explained, that the diagrams were chiefly intended to illustrate the peculiar functions of the "respirator," or as Mr. Ericsson had termed it, the "regenerator." Very conflicting opinions had been expressed regarding this most essential element in Ericsson's engine. Some thought that, by its agency, the heat used to effect a stroke of the engine could be wholly recovered, except accidental losses, and that, theoretically, it involved the accomplishment of a perpetual motion. Others, on the contrary, contended that the regenerator was only an obstruction to the passage of the air, and of no utility whatever.

He had endeavoured to prove in his Paper, that neither the one extreme view, nor the other was correct ; that, indeed, the respirator might be usefully employed, to recover that portion of heat which presented itself at the exhaust part of the engine, in the form of free, or sensible heat, but that neither the respirator, nor any other possible contrivance, could recover the heat that was lost in the expansion of the air behind the working piston.

He had adopted the new "dynamical theory of heat" for his argument, because that theory enabled him to calculate the absolute quantities of heat, that must inevitably be sacrificed, to produce a given mechanical effect, and to separate the same from the other and much larger quantity, that served only to form the elastic medium behind the working piston, and which might be recovered, by means of a respirator, unless, as he had shown in the Paper, it was all converted into power, by the expansive action being carried to its last (but impracticable) limits.

Ericsson himself seemed to incline to the idea, that he could recover the whole of the heat by means of his "regenerator," for it would be difficult otherwise to account for the extraordinary insufficiency of heating surface he had provided.

Mr. Siemens could speak confidently as to the mechanical efficiency of action of the respirator, having applied a precisely similar contrivance to a steam engine of his design, some years previously.

The regenerator produces no mechanical effect

Mr. Hawksley contended, that in the caloric engine, the so-called "regenerator" was productive of no mechanical effect, as might be shown, by reducing the engine to a primitive form, so as to get rid of all the complexity consequent upon the
employment of valves and flaps, and air under compression.

In this form the engine might be assumed, for the sake of illustration, to consist of an upper and a lower cylinder, bearing the proportions, in regard to area, of 1 to 2 ; the upper cylinder acting as the pump, or receiver, of cooled air, and the lower cylinder as the expansion, or working vessel. It might also be assumed, that the air was expanded and contracted alternately, from 1 volume into 2 volumes, and from 2 volumes into 1 volume, by the operation of the regenerator placed in the connecting pipe of the two cylinders.

In this case it would readily be seen, that even if the regenerator should actually operate in the manner alleged, yet that no mechanical effect would be produced, because the space vacated by the motion of the lower piston would be exactly equal to the amount of expansion consequent upon that displacement. Therefore, if in this single case no mechanical effect was produced, a fortiori no mechanical effect would result from mere complexity of arrangement, involving no change of principle. The machine, in point of fact, involved a mechanical fallacy, closely allied to the fallacy of perpetual motion, and of quite as simple a character.

The motion of the machine created the space to be filled by the air, after its expansion by the restored heat of the regenerator ; whereas it had been most erroneously imagined, that the expansion was the cause, rather than the consequence of the motion. Had the design of the machine been scientifically correct, it would have been the wonder of the age, whereas, by the confusion of cause and effect, (an easy thing to do in a case of this kind), an endeavour had been made, though with great ingenuity, to realize an impossibility.

Nevertheless, in contradiction to most attempts of a similar kind, this machine would work. It had motion - it would raise a measurable weight - and it would produce mechanical results. No part of these results were, however, produced by the regenerator, but, on the contrary, simply by the coal consumed under the cylinder bottom, and by which means it was caused to operate in the manner of the earliest attempts to employ the expansion of air as a mechanical agent.

Hence he urged, that the caloric-engine possessed no advantages over the air-engine, invented more than twenty years ago by Mr. Parkinson, and afterwards patented by Messrs. Crossley and Parkinson, (the original working model of which engine was exhibited and set in action.)

On the contrary, no inconsiderable amount of resistance was occasioned by the friction of the air, in its passage through the meshes of the regenerator, for which a large deduction must be made, from the theoretical effect of the machine, when considered as an ordinary air expansion engine, and in so far, this ponderous machine was inferior to others of a more simple type.

The regenerator uses heat otherwise wasted

Mr. Pole stated, that the indicator diagram referred to by Mr. Siemens was obtained in the course of a series of experiments on the Cornish engine at the East London Water-works, Old Ford, undertaken by Professor Moseley and himself, at the instance of the British Association, in 1843 and 1844.
As the engine in question had been more carefully examined, and its dimensions and capabilities were more accurately known, than perhaps any other of the kind, he conceived great reliance might be placed on the results.

The diagram of the steam's action in the cylinder showed, undeniably, that the pressure in expanding, became greater than Marriotte's law would give, and still greater than according to the law assumed to obtain by De Pambour. A large number of experiments tried on other engines, and under different circumstances, had always given the same result. Although, as he had shown in the work alluded to, several causes existed to influence the variation of pressure, the subject was well worthy of further investigation.

He had also made some calculations upon the same engine, with reference to the economical effects of the heat, and came to nearly similar conclusions with Mr. Siemens. He found, that if an engine of that kind, expanding 3.5 times, were absolutely perfect, each unit of heat given out by the combustion of the fuel, ought to develop about 134 units of work ; but the amount actually produced, in the shape of water raised, was only about 80 units, or 60 per cent. less than the theoretical result.

He had endeavoured to discover at what parts of the engine this loss occurred, and had found it might be distributed about as follows:

  1. Imperfect combustion, and other causes of waste of heat in the boiler: 12.5
  2. Heat expended in raising the temperature of the feed water to boiling-point: 12.5
  3. Friction, imperfect vacuum, air-pump, &c., or power wasted in working the engine: 15

Total of 1 +2 +3 : 40

  1. Useful effect realized: 60

Total calorific power of the fuel: 40 +60 = 100

With regard to the general question of the utility of the so-called "regenerator" of the hot-air engine, he conceived it would be found that, as in many other disputed cases, the truth lay between the extremes. He considered that those who asserted, on the one hand, that this appendage was altogether fallacious and useless, were equally wrong with those who insisted, on the contrary, that it was capable of reproducing the power, without any consumption of heat. This might be shown by a consideration of what took place when air was expanded by heat.

The quantity of caloric necessary to produce this effect consisted of two distinct parts, each of which performed an entirely separate office in the process. One portion was employed in communicating sensible heat to the mass, i.e., in raising its temperature a certain number of degrees, while the other portion was expended in supplying the latent heat demanded by the expansion of bulk of the air ; it being understood, according to the usual theory (although differently expressed by the more modern dynamical hypothesis), that a certain quantity of heat became latent in an elastic fluid, whenever its volume was increased.

The ratio of these two amounts of heat was known ; for (assuming the pressure to remain constant), if the whole quantity expended was represented by 14, the portion used in communicating sensible heat would be about equal to 10, and that absorbed in latent heat equal to 4.

Now it might easily be conceived that, by the subsequent application of some apparatus on the principle of the regenerator, the sensible portion of the heat might be abstracted from the heated air ; but the other portion, the 4/14, of latent heat, could only be restored on one condition, namely, by compressing the air again to its former bulk, which would require an absorption of power, precisely the same in amount as had been developed during its expansion ; so that, if the whole heat was restored, no power was gained, or if the power was retained, a portion of the heat must be lost.

But it was also evident, that if no saving apparatus like the regenerator were applied, not only the latent, but also the sensible heat, a much larger quantity, must be thrown away ; and, therefore, in restoring a good part of this to be used again in the next supply of air, the contrivance' was undoubtedly beneficial, and might of itself turn the scale of the success, or failure of the machine.

Without it, 14 parts of heat must be used for every charge of air; with it, theoretically, only 4 were required. Such, he conceived, was the simplest view of the office of the regenerator, although in practice its action was often complicated by other considerations, and was, therefore, more difficult to trace.

The air temperature coming out of the regenerator

In the Paper so ably rendered by Mr. Manby, - Secretary, - objections bad been brought against the alleged advantage of the regenerator, which Mr. Pole could not agree with.

The first was, that the escaping air must expand, and so lose temperature. Now, it was not at all necessary to the action of the engine, that the air should leave the cylinder at a density greater than that of the atmosphere, and unless it did, the loss from this cause could not occur.

Secondly, M. Cazalat imagined, that the resistance offered to the air, in passing through the meshes of the regenerator must absorb a great deal of power ; but this was merely a question of arrangement and area of passages, and experience had shown that the loss from this cause, under proper management, was scarcely appreciable, M. Cazalat's third objection was derived from his calculations of the temperature of the regenerator, after the passage through it of the hot and cold air respectively.

Assuming the air to leave the cylinder at 521.5° (the atmosphere being at 32°) he found that the temperature of the regenerator would be about 277°, and concluded, therefore, that at every stroke 245° of heat would be wasted in the atmosphere, and must be supplied again by the fuel to the entering air.

Now, Mr. Pole contended, that this was not a fair way of considering the action of the regenerator, inasmuch as M. Cazalat assumed the air to be mixed with the copper uniformly, in one mass, without taking into consideration the gradation between the hot and cold ends, an arrangement upon which the peculiar beneficial effect of the apparatus entirely depended ; the temperature of the outgoing or entering air being determined, in fact, not by the mean temperature of the whole "Regenerator," but by that of the last plate it went through, which was very different.

The different effect of a similar mass of metal, according as it was disposed in different ways, might easily be shown. Taking the weight of air to be equal to 75 lbs., and the weight of copper to be equal to 1,680 lbs., for convenience of calculation, then, according to M. Cazalat's supposition, if the copper was supposed to be collected in one mass, and the air intimately to be mixed with it, during its passage through the air would escape into the atmosphere with an excess of 245°, and enter the cylinder with an equal deficiency.

To ascertain the temperature of a mixture of any two substances; let W and w be their respective weights, C and c their specific heats, and T and t their temperatures before mixing. Their temperature of mixture = (WCT + wct) / (WC + wc)

Now, if the same quantity of copper were divided into eight parts, and arranged in eight separate plates, the result would be much more favourable, the loss in each stroke being reduced from 245° to less than 100° ; and by dividing it still further, a still greater economy would result. This consideration should not be lost sight of, in the discussion of the merits of the regenerator, as experience had shown it to be of great importance in practice.

It must be allowed, that the general action of caloric, in producing power, was still involved in much obscurity. The heat was often considered in reference to its quantity only, but it was certain also, that its intensity performed a very important
part; and, it had even been surmised, that power might be obtained by the reduction of intensity alone, without any change of quantity. An investigation of the subject often produced anomalous cases, very difficult to account for, on the ordinary suppositions.

For this reason he thought that any additions to the knowledge of this subject were much to be desired, and he considered that Engineers should look forward with interest to the important communications which M. Regnault, probably the first living authority on such matters, had promised shortly to give to the world.

The regenerator usefulness

Mr. W. G. Armstrong concurred in the arguments that had been advanced, both by Mr. Siemens and by Mr. Pole. He could not but think that the regenerator did fulfil an important function in the engine. If with an ordinary cylinder and piston, a charge of heated air were introduced beneath the piston, and then allowed to expand, until it reached an equilibrium with the external medium, the whole available heat would be utilized, and the maximum mechanical effect would be realized in a single operation.

Now the same result would virtually be obtained, by stopping the piston at any point short of the ultimate limit, and transferring to a renewed charge of air the heat remaining unutilized in the first charge. Thus the quantity of heat required to make up the full temperature of the second charge would be diminished, to the extent of that which was saved from the first charge. This transference of unutilized heat was performed by the regenerator, and the advantage of its application must be admitted to the extent that it accomplished that object.

Mr. E. Woods observed, that if the mechanical equivalent of heat was 730 foot-pounds, as it appeared to be, on the average of the experiments by Messrs. Holtzman, Joule, Rankine, and Thompson, alluded to in Mr. Siemens' Paper, then there was still great margin for improvements.

Mr. C. May said, that in an engine with a steam-jacket, the steam being confined in a vessel of greater heat than itself, and being maintained at that temperature by the pressure of steam communicating with the valve, might probably account for the expansive curve showing a greater pressure than the ordinary rule gave.

Mr. E. A. Cowper stated, that in an indicator diagram taken from an engine with no steam-jacket, the expansion curve was a little above the ordinary rule, at the end of the stroke. This, he considered, indicated that the latent and sensible heat of steam together amounted to a greater quantity in high-pressure steam, than in low-pressure steam. Steam, or gases, in expanding, and so giving out power, lost heat. Part of the sensible heat became latent in the production of power, and this heat could only be recovered, by expending the power already produced, in again condensing the steam back to its original bulk, when the latent heat again became sensible. As, however, the general object was to produce power, this plan could not, of course, be entertained.

Therefore, the heat which was sensible, and became latent by the expansion in producing power, was, in fact, the necessary theoretical expenditure of heat required to produce power ; and no engine could be made to work by simply supplying the loss of heat by radiation.

He must contend, however, that the sensible heat that was left in the steam, or air, after it had been expanded, could be stored up in plates of metal, or wire gauze, to a considerable extent, and that these plates, so heated, might be used to heat fresh steam, or air, that was about to be used for obtaining power.

Mr. D. K. Clark remarked, that in his experiments on locomotives, he had found that with cylinders in the smoke-box, the curve of expansion was very little above that given by Marriotte's law ; but that when the cylinders were exposed, it differed materially. He thought that in the diagram alluded to by Mr. Pole, the steam-jacket had influenced the form of the curve.

Mr. Siemens agreed with Mr. Hawksley's proposition, that an engine of his proportions could not give out any power. The valve between the two cylinders in Ericsson's engine was as necessary as it was between the boiler and cylinder of an ordinary steam-engine, and could not be replaced by the regenerator, which had a very different office to fulfil.

Ericsson's engine might indeed be compared to a steam-engine, in which the boiler was represented by the air-chamber between the two cylinders, and the feed-pump by Ericsson's pumping cylinder. Ericsson had the disadvantage of sacrificing two-thirds of his power to move the pump, but had the advantage of expending no latent heat to form his elastic medium. But it must be borne in mind, that Ericsson had to add to his air a larger amount of sensible heat, of which only a small proportion was really expended in expansion, and the remainder would go to waste, unless it was recovered by the regenerator.

Nevertheless, the drawbacks to Ericsson's engine, on account of the great resistance of the pump, the small working pressure, the insufficiency of heating surface, and the working of a piston in a heated cylinder, were so great, that he thought no beneficial results could be expected from it.

James Stirling about his own hot air engine

Mr. James Stirling, through the Secretary, after alluding to the specification of his brother's, the Rev. Dr. Stirling's, original patent for an air-engine, in 1816, quoted by Mr. Leslie, said that the engine then described was nearly similar to that mentioned in the Paper read to the Institution in June 1845 ; the only difference was that it had but one air-vessel, with a piston working in the open end of it, and the interior airtight vessel, or plunger, was worked by a rod, passing through a stuffing-box, in the centre of the piston.

In small engines, where the surfaces of the passages between the air-vessel and the plunger bear a large proportion to the volume of air to be acted upon, these surfaces themselves form a considerable portion of the regenerating process ; but the specification described this passage as "partially filled with studs, or with wires wound round the plunger, for the purpose of heating and cooling the air more completely, and with less waste ;" and a passage filled with wire gauze was actually tried in one of Dr. Stirling's earliest experimental engines.

He constructed an engine of this description, in 1818, for pumping the water from a quarry in Ayrshire, which work it performed very well, until, from the carelessness of the engineman, the bottom of the air-vessel was overheated, and being made of boiler plate, of a flat conical form, it was crushed down by the pressure of the heated air, and rendered useless.

This engine did not work to the power expected, and it was feared, at the time, that the air-vessels, for engines of large power, would require to be of enormous size. The undertaking was, therefore, for the moment abandoned.

In 1824, it occurred to him, that the difficulties attending the large working parts might be got over, and the dimensions of the engine greatly reduced, by working with air of a higher density, produced by mechanical compression. This involved the necessity of a closed cylinder, or double-acting engine, with two air-vessels, in order that there might be no means of escape for the compressed air, except by the piston and plunger rods.

Having made some experiments with a working model constructed on this principle, these improvements were patented in the beginning of 1827, conjointly by Dr. Stirling and himself. In 1828, an engine on this principle, with a cylinder 26 inches in diameter and 3 feet stroke and about 20 horse-power, was constructed at Messrs. C Girdwood & Co.'s, Glasgow.

It was then found, that the small part of the heat which the "Regenerator" failed to extract from the air, in its passage to the cold end of the air-vessels, accumulated to such an extent, that the requisite difference of temperature, between the two ends of the air vessels, could not be kept up, and that the power consequently fell off considerably.

This engine was again abandoned ; and it was only after overcoming this last difficulty, by the refrigerating apparatus, described in his Paper in 1845, and after testing its efficacy for several months, on a small engine, with a
cylinder 3 5/8 inches in diameter, and 12 inches stroke, which worked to two-horse power, that the present patent was taken out.

A full account of the engines constructed under this patent, was given in the Paper before mentioned. From some difficulties experienced in the management of the furnaces, and in heating the air-vessels equally, the use of the engine there described, was discontinued about a year after the date of the Paper, after it had worked efficiently for more than three years.

Still the subject was not abandoned ; and he hoped, ere long, to bring it again under the notice of the Institution, with this, he might almost say, its only imperfection, entirely removed.