James Watt's expansion steam engine
A trade secret
Managing the power
When operated at a lower load than it was intended for, a Newcomen steam engine gave off sharp shocks. To address this problem, Newcomen either decreased the volume of water offered for injection into the vessel or alternatively, for the same result, shut the injection cock earlier. Of course, this is a waste of the uncondensed steam that was thrown away.
In essence, Watt had contrived three solutions for this issue. The first two on the following list were difficult to find when looking at Watt & Boulton's steam engines, which was fortunate for them. Before Watt revealed them in his friend Robison's book on steam engines in 1828, Watt and Boulton were silent for nearly 50 years.
- The regulation valve, which admits steam above the piston, opens to a limited extent and remains open for the duration of the stroke.
- Having the regulation valve open from the start of the stroke and closing it entirely once the piston has only partially descended
- a throttle valve to only allow in as much steam as is necessary to produce the required amount of power
Solution two was used particularly in what is now known as the expansive steam engine.
The expansive engine
As early as 1769 Watt mentions to Dr. Small a method by which he could double the steam's effect to the detriment of enlarging a vessel too much. [2]. Too much probably means that the costs for a larger vessel are not justified by the improvement of the efficiency, i.e. the lower consumption of coal. Boulton & Watt were initially charging on the savings achieved with their steam engines compared to the coal consumption of a Newcomen steam engine of comparable water lifting capacity. Their interest was not to sell oversized engines but to optimize the profit stream from license income over the lifetime of a machine or the patent lifetime, respectively.
Watt's business acumen is revealed when he describes a new business strategy. Alterations made by him to the steam engine allow for scalable power output. Boulton & Watt could erect in a mine, that at the moment only needs the power to pump water from 10 fathoms (18m), an oversized steam engine, the power output of which was throttled by allowing steam expansion. The tradeoff was improved efficiency. In case years later the mine is sunk to 50 fathoms (91m) The power could be adapted and the mine would need to burn only 5 times the coal they had to burn when the pumps lifted water from 10 fathoms. So the efficiency could be kept at the same level. If finally, the mine had to be sunk to 100 fathoms (183m) the mine would need to burn 4 times the coal than at 50 fathoms, i.e. now the efficiency dropped to half of the efficiency at 50 fathoms. [3] The advantage of this business model for Boulton & Watt was that they did not have to change the steam engine when more power was needed but had better efficiency in the beginning. So this strategy was based on long time investment.
Watt shut off the steam inlet valve after only a fourth of the cylinder's stroke had been filled with steam at atmospheric pressure. At this moment, the air pressure acting against the piston from the opposite side is in balance with the pressure force of the steam inside the working portion of the cylinder. The piston won't move in either direction without an extra force. In order to pull on the piston work has to be added to the system and Watt did this by adjusting the counterweight accordingly. Later, the flywheel with its inertia will provide this work. The piston is pushed now against atmospheric pressure, increasing the enclosed steam's volume. The same quantity of steam is now dispersed across a larger volume, resulting in a decrease in steam pressure inside the working compartment. The pressure difference between both sides of the piston tries to push the piston back to its original position, when the steam was cut off. The work to overcome this force is generally known as displacement work.
Watt refers to the process as expanding. The same technique was applied later when steam engines were operated at pressures greater than atmospheric pressure. But, because the steam was now expanding under its own pressure, it was producing displacement work rather than consuming work. The expansion from atmospheric pressure to subatmospheric pressure is now referred to as forced expansion [4] or over expansion [5] in order to distinguish it from expansion used in high pressure steam engines.
Boulton obviously did not want that the operators (fire men) of the steam engine would play around with this aspect of the steam engine. He, therefore, describes that this mechanism could be installed inside the vessel/piston [6] so that its existence is hidden.
Watt describes 30 years later that it was used only with cylinders where steam was also admitted on the side of the piston that was usually charged with the atmospheric pressure [7].
The first engine with steam expansion was built around August 1777. The performance was not very satisfactory, and its movement was jerky and violent [8]. Despite some modifications, it would appear that Watt lost interest in the expansive engine but Boulton still favored this approach [9]. Boulton applied the expansion principle with double engines and wrote in reference to the "Wheel Maid whim engine": "I never saw an engine take so little steam as this in my life & you may be assured that where a fly [wheel] can apply'd so as to go 300 or 400 ft per minute, the expansive principle in practice will come up to theory" [10]. The double acting engine would have levelled the unequal production of forces and ensured a smoother motion of the piston. Eventually, the principle of expansive action was given up in 1784 when a new valve gear was introduced that prohibited the early closing of the steam valve. [11]
Although displacement work has to be added on balance an excess of work is gained during condensation. For the displacement work the pressure difference between the atmospheric pressure and the pressure after expansion counts. When the volume gained through expansion is condensed, the pressure difference is now, disregarding other thermodynamic effects, the difference between atmospheric pressure and the pressure attained after condensation. Here we also see that if the expansion is as big as it reaches the pressure after condensation its effect wears out.
The expansion principle was implemented in an engine at Soho and a few other places around 1776, and at Shadwell Water Works in 1778. Then, in 1782, it was detailed in a patent among a number of new developments in steam engines.
The steam valve is controlled by plug pins in a plug frame. They are set to open the steam valve fully at the start of the down stroke. The steam valve then closes when the piston has descended a predetermined distance, such as a quarter, third, or half of the cylinder's length. If necessary, the timing can be changed by adjusting the plug pins within a minute. The engine's inertia causes the piston to be pushed further downward, which forces the steam to expand.
The accelerating force is constantly changing as a result of the pressure on the piston. As a result, the motion will no longer be uniform. The load resistance, however, might well be greater than the pressure when the piston is close to the bottom. Making the outer arch head portions spiral-shaped rather than circular could help counteract this.
After Watt had erected many atmospheric engines to his plan with success, he afterwards adopted another arrangement of the parts, in which the steam for the supply of the working cylinder does not pass through the steam case but instead enters from the steampipe, through a valve, immediately into the top of the cylinder. Although the steam case has a connection to the boiler, it only receives enough steam to maintain heat and avoid condensation of the steam inside the cylinder. Messrs. Boulton and Watt started then manufacturing the steam casings out of wrought iron plates around 1778. They chose a gap of 1½ inches as the distance between the inner side of the steam case and the outside of the working cylinder.
The adjacent drawing was taken from an engine erected at Hull, in 1779 and was at the time the standard engine for pumping water. In a working cylinder E, a piston J divides the working cylinder E into a top compartment above the piston J and a bottom compartment below the piston J. The top of the cylinder E is closed by a cover, which is screwed to the top flange of the cylinder itself rather than the top flange of the steam case. A pipe a, which appears in the drawing as a circle, delivers the steam from the boiler to a regulating or throttle valve b. Through a top fluid communication c in the top of the working cylinder E, the steam, after having passed the throttle valve b, is allowed to continuously enter the top compartment of the working cylinder E. A steam pipe d descends from the throttle valve B to the bottom of the cylinder arrangement. An equilibrium valve e at the steam pipe's base regulates the flow of steam via a bottom fluid connection f into the bottom compartment of working cylinder E. When the piston J is about to ascend, the equilibrium valve e opens, and when piston J is about to descend, the equilibrium valve e closes. An exhaust valve i functions in the opposite manner. When the equilibrium valve e is closed, the exhaust valve i opens, allowing the steam in the lower compartment of the working cylinder E to escape through an evaporation pipe g to an external condenser.
A cycle begins with a returning stroke. A working gear closes the exhaust valve i and opens the equilibrium valve e. A partial vacuum from the previous cycle is kept in the eduction pipe g and the condenser by the closed exhaust valve i. As a result of the open equilibrium valve e, steam enters the bottom compartment of the cylinder through the steam pipe d and the bottom fluid communication f. Given that the cross section of the piston rod reduces the area of the piston top exposed to steam, the area of the piston bottom is somewhat larger than on the piston top. As a result, there is a differential in pressure between the top compartment and the bottom compartment, which increases a counterweight's pulling force for completing a returning stroke.
The working gear closes the equilibrium valve e when the piston reaches a specific height, such as one-fourth of the way up. This is the beginning of the expansion phase. The steam in the bottom compartment expands until the end of the returning stroke.
The returning stroke is followed by a working stroke. When the working gear opens the exhaust valve i, the steam in the bottom compartment of the working cylinder extends by its own elasticity and the pressure difference, through the exhaust valve i, into the eduction pipe g, and finally into the condenser, where a partial vacuum was preserved from the previous cycle. The steam cools and condenses there after being met by a jet of cold water. Thus the condenser's vacuum is maintained, if not increased, because the condensed steam occupies less space than originally. More and more steam is forced into the condenser by the pressure differential between it and the working cylinder's bottom compartment. As a result, the steam that is in the upper compartment at atmospheric pressure is no longer opposed to a counterforce and pushes down the piston J. The piston continues to descend until it is close to the bottom of the cylinder. The working gear then closes the exhaust valve i and opens the equilibrium valve e thus starting a new cycle with a new returning stroke.
Analysis of atmospheric engine with forced expansion
The expansion ratio r is defined as the total cylinder volume, when the volume enclosed by the piston is at its maximum divided by the volume enclosed by the piston when the steam is cut off.
For a demonstration of the calculation of the increase of efficiency of an atmospheric steam engine with forced expansion I chose an expansion ratio of 1:2, i.e. the steam inlet valve is closed when the piston is halfway up, or in other words, when the volume of the cylinder is filled with one part of steam and the steam is expanded to twice this volume.
PV diagram number 2 indicates the moment when the inlet valve is closed and no more steam is admitted into the cylinder. Between numbers 2 and 2* the piston is still moved upwards by the inertia of the flywheel. The flywheel is adding work to the system (and thereby is slowed down a bit). Assuming that volume and pressure of the steam are changing so quickly, that there is no time to exchange heat with the cylinder walls this process is considerd to be an adiabatic process. The diagram shows the curves for an adiabatic process (green dashed line) and an isothermal process (dashed red line).
Reaching the end of the stroke (number 3*), or a little bit before to smoothen the inversion of the stroke, the communication to the condenser is enabled and the underpressure that remained in the external condenser starts the condensation process. As long as the energy gained from condensation is higher than the sum of the energy the flywheel had to "lend" to force expansion the atmospheric steam engine and the energy that is delivered to a consumer, the steam engine will start a new cycle.
The Heat and Work involved at each step are explained in [5] and are summarised in the following table:
The work in steps W3'3 and W34 can be summarized as W3'4 = W3'3 + W34 = (p1-p4)(v4-v3'). The total work Wtotal becomes then:
and the efficiency η becomes:
Pressure p1 is the atmospheric pressure and pressure p4 is the pressure inside the working cylinder after condensation and is known as a function of the temperature of the condensed water. Volume v3' is the internal volume of the working cylinder and we assume it to be the volume that holds 1kg of steam of 100°C = 1.672 m3. With an expansion ratio r = 2 the volume at stage 2 becomes v2 = ½⋅1.672 m3 = 0.836m3. The internal energy at stage 2 for 1kg of steam is 2506 kJ. For ½kg of steam it becomes 1253 kJ. The tricky part is now to calculate u2'.
As we can see from the PV diagram at state 2' the point is not on the saturated steam curve, but in the water-steam region, somewhat in between the saturated water curve and the saturated steam curve. The value for U2' is therfore in between the value uvapour and uliquid as a function of the so called steam quality χ. The steam quality is defined as the proportion of saturated steam (vapour) in a saturated condensate (liquid)/steam (vapour) mixture. The range of x is between 0 (100% liquid (condensate) and 1 (100% steam, no liquid (condensate).
Internal energy, u, enthalpy h and entropy s are tabled in steam tables with a value when their proportion is completely liquid (χ=0)and when their proportion is completely vapour (χ= 1). For any mixture with a steam quality χ the liquid proportion is consequently 1-χ. The liquid portions and vapour portions of internal energy, u, enthalpy h, and entropy s add up linearly. For example the internal energy uχ of a mixture of χ portion steam and 1-χ portions of water can be calculated as:
Similar the entropy sχ of a mixture of steam can be calculated as
But how do we get the steam quality χ for 2' ?
For example in the steam table for temperature we look for the value of the specific volume v2 at 100°C. This is at atmospheric pressure 1.6718. As by an expansion rate r=2 we allowed the specific volume to double we now look in the same column for the closest values for v2' = 3.3436. These are 3.5372 for T = 79°C and
As we have assumed that the process from 2 to 2' is an adiabatic process the entropy s is constant, i.e. s2 = s2'. At process state 2 the value for a 100% vapour. At state 2' the same value is for a mixture of condensate and vapour. But there is no steam table that shows the entropy for any steam quality other than χ = 1. However, with a spread sheet we can create new columns that show the values for
The diagram below shows the efficiency rate> for various expansion ratios and temperatures at the termination of the condensation process. If we utilize steam at atmospheric pressure, the optimum efficiency is obtained for the highest temperature difference between steam and condensation temperature.The steam must be nearly cooled to the freezing point of water in order to operate at its optimum theoretical efficiency. There was no option for such a low temperature. The water that was pumped out of a mine was, undoubtedly, approximately 8°C. A tradeoff made to increase the working cycle frequence, i.e. the number of strokes per minute, for example, was to allow a cycle to restart before the condensation process was completed. This resulted in a higher temperature to which the steam was cooled inside the working cylinder. There are reports that mention that the temperature of the condensed water in Newcomen machines was as high as 70°C. Watt operated with condensation temperatures between 30°c and 40°C.
The graphic shows that, in theory, adopting a high expansion ratio can result in high efficiency rates.At some point, the efficiency decreases and falls even below zero, i.e. the machine consumes more power than it produces and thus will stop to work. This model does not account for mechanical losses, which probably make expansions greater than a factor of 10 unfeasible. Watt did not employ an expansion ratio larger than 4, as was said above.
We also have to keep in mind that the for the same power a atmospheric steam engines cylinder volume is proportional to the expansion ratio. An atmospheric steam engine with an expansion ratio of 10 must have a ten time larger cylinder. This increases the building costs probably over-proportional as the cylinder walls have to be designed thicker for a wider cylinder diameter to withstand the atmospheric pressure.
Watt measured the pressure inside the working cylinder at various positions of the piston. Dr Robinson developed a calculation method that was using hyperbolic logarithm.
In the next diagram I compared the data published by James Watt with the maximum efficiency of an atmospheric steam engine. The diagram shows the maximum efficiency of an atmospheric steam engine plotted over the expansion ratio. The starting point is set to the value 1, which represents the maximum thermal efficiency of 6.4% in case of no expansion. As Watt's steam engines were running at about 50% of the maximum efficiency I set the starting point of Watt's steam engine at 0.5. From the relation between the two graphs we can see, that for small expansion ratios the gain is much less than 50% for the theoretical maximum for a given expansion ratio. Only for an expansion ratio of 1:8 the Watt steam engine is catching up with the relative performance of almost 40% of the theoretical maximum. However, at this expansion ratio the Watt engines were not running smoothly and Watt used for atmospheric steam engines never more than an expansion ratio of 1:4.
The expansion, however, produced a less favorable pressure profile for the descending piston. One possible solution to counteract this effect is to design the connecting machinery in such a manner that the chain at the large lever's outer end will consistently apply the same amount of force to raise the pump rods. Typically, the chains that joined the piston rods to the arch head of the beam ran around the circumference of a circle. To produce a constant force when lifting the water, the piston's force on the lever and pump rods can be adjusted by forming these segments into suitable spiral parts. [20] This compensation was the subject of Mr. Watt's third patent, issued on March 12, 1802, for certain improvements upon steam-engines and certain new pieces of mechanism to be added thereto.
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[1] Robison, page 126
[2] Boulton Papers, Watt to Dr. Small 28 May 1769 cited in H.W. Dickenson & R. Jenkins, James Watt and the Steam Engine, republished edition 1981, page 120.
[3] Boulton & Watt Colln.: Letter Books. Watt to Meason, 24 April 1777; cited in H.W. Dickenson & R. Jenkins, James Watt and the Steam Engine, republished edition 1981, page 120.
[4] Gerald Müller, Faculty of Engineering and the Environment, University of Southampton, Highfield, The atmospheric steam engine as converter for low and medium temperature thermal energy. Available at ScienceDirect
[5] Vítor Augusto Andreghetto Bortolin, Bernardo Luiz Harry Diniz Lemos, Rodrigo de Lima Amaral, Cesar Monzu Freire, Julio Romano Meneghini, Thermodynamical model of an atmospheric steam engine, Journal of the Brazilian Society of Mechanical Sciences and Engineering (2021), https://doi.org/10.1007/s40430-021-03209-9
doi.org/10.1007/s40430-021-03209-9/>
[6] Boulton & Watt Colln.: Letter Books. Boulton to Watt, 16 May 1777; cited in H.W. Dickenson & R. Jenkins, James Watt and the Steam Engine, republished edition 1981, page 120.
[7]
[8] H.W. Dickenson & R. Jenkins, James Watt and the Steam Engine, republished edition 1981, page 122.
[9] Ibid.
[10] Ibid, page 126.
[11] Ibid.
[20] John Farey, page 340.