- The No solid moving parts nearly reversible heat engine idea leads to many possible designs.
- This design project involves the Ericsson cycle engine where nothing big and solid moves design.
Original Description (revised)[]
A heat powered gas compressor or compressed gas powered heat pump:
This is an open cycle heat engine, which takes in additional working gas and compresses it whenever the storage reservoir is not at its maximum working pressure. Compressed gas can be withdrawn from the high-pressure reservoir as needed, and the engine will replace it, using heat energy extracted from the environmental heat reservoirs. Conversely, the machine can be operated in reverse as a compressed gas powered heat pump which releases some of its working gas at low pressure.
When the heat engine operates between a rather narrow temperature range, most (about 90% for 270K to 300K) of the heat removed from the hot reservoir inevitably arrives in the cold reservoir without doing any work, giving a rather low absolute efficiency. Even so, because it is reversible in the literal sense, it can come close to the best efficiency possible. If you supply excess compressed gas, it can be operated as a heat pump moving heat from the cold reservoir to the hot reservoir. Of course it isn’t perfectly reversible in the sense of conserving entropy, but depending on how many working tanks are provided, how precisely the pressures can be matched, and how slowly the process runs, the engine can store as compressed gas nearly all of the energy removed from the hot reservoir that is not inevitably destined to reach the cold reservoir, or pump nearly the maximum possible heat from cold to hot reservoir for a given amount of compressed gas input.
The thermodynamic cycle has two isobaric steps interleaved with two isothermal steps. A large number of cycles run in parallel, each at a slightly different phase. A perfectly reversible machine would need an infinite number of cycles running in parallel.
Any given volume of working gas moves around the cycle, starting in a cold low pressure tank full of gas.
- The cold isothermal step involves pistons forcing cold hydraulic fluid from a series of cylinders through pipes and valves into the tank while the heat of compression escapes via heat pipe, ending with a cold high pressure tank full of hydraulic fluid and a small bubble of cold high pressure gas. The bubble is allowed to flow up into the cold high pressure gas reservoir, while an equal volume of cold hydraulic fluid flows down out of the reservoir.
- The high pressure isobaric step (a continuous process) involves sending high pressure gas from the cold high pressure reservoir through the counter-current heat exchanger to the hot high pressure reservoir.
- The hot isothermal step starts with a tank full of hot hydraulic fluid with a small bubble of high pressure gas metered in from the reservoir, and involves allowing the hot hydraulic fluid to flow out of the tank through pipes and valves into a series of cylinders, where the fluid forces each piston in turn to move a small distance, ending with a tank full of hot low pressure gas and the hydraulic fluid distributed into a number of different cylinders.
- The low pressure isobaric step (also a continuous process) involves sending low pressure gas from the hot low pressure reservoir through the counter-current heat exchanger to the cold low pressure reservoir.
Counter-current heat exchanger[]
The isobaric steps occur in a counter-current heat exchanger in which hot low pressure gas gives up heat to cold high pressure gas. The work necessary to keep the low pressure gas at constant pressure is supplied by the high pressure gas which must give up work to stay at constant pressure. Insofar as no work and no heat are exchanged with the environment, the isobaric steps taken together are perfectly reversible. A more realistic description of a counter-current heat exchanger is given below.
Isothermal tanks filled with gas and hydraulic fluid[]
The isothermal steps occur in tanks filled partly with working gas and partly with hydraulic fluid, with heat siphon tubes (i.e., gravity feed heat pipes) spread evenly throughout the tanks. The heat siphons in hot isothermal tanks lead downward to a common tank of liquid refrigerant at the hot temperature. The siphons in the cold isothermal tanks contain liquid refrigerant and lead upward to a common condenser at the cold temperature.
All of the hot tanks are kept in an insulated room kept at the hot temperature, and all of the cold tanks are kept in a separate insulated room kept at the cold temperature.
During a single isothermal step, each tank contains a constant amount of working gas, which stays in the tank until the final pressure is reached. A cold tank starts full of cold fluid, which is drained into the cold low pressure reservoir while cold low pressure gas flows up from the reservoir into the tank. Then, cold fluid is forced into the tank from a series of cylinders. Finally a small bubble of high pressure gas is released up into the cold high pressure reservoir as cold fluid flows down, returning to the start of the cycle for a given tank.
A hot tank goes through a similar cycle in reverse: it starts full of hot fluid, and a small bubble of high pressure hot gas is metered into the tank while an equal volume of fluid leaves. Then, hot fluid flows from the tank into a series of cylinders while the hot gas expands and the pistons move. Finally, the tank full of hot low pressure gas is vented up into the hot low pressure reservoir while hot fluid flows downward from the bottom of the reservoir into the tank.
Connecting pairs of isothermal tanks[]
A large network of pipes, valves, and hydraulic pistons connects the isothermal tanks. Pairs of tanks at nearly equal pressure are connected via a pair of cylinders with linked pistons so that hot hydraulic fluid leaving the higher pressure (hot) tank forces cold hydraulic fluid into the lower pressure (cold) tank. After the flow stops, the pairings are readjusted by closing and opening valves.
Since hot gas is supposed to compress cold gas, the hot tank of a pair must be at a higher pressure than the cold tank. Therefore, a newly started hot tank at maximum pressure must be paired to a nearly completed cold tank at nearly maximum pressure. Both of these tanks are nearly full of hydraulic fluid and the high pressure gas occupies only a small volume.
Similarly, a nearly finished hot tank approaching minimum pressure would be paired to a newly started cold tank at minimum pressure. Both of these tanks contain very little hydraulic fluid and a large volume of gas.
Pistons separate hot and cold hydraulic fluid[]
Hot hydraulic fluid is kept separate from cold hydraulic fluid by means of auxiliary pistons and a set of hot and cold fluid reservoirs. As the gas in the hot tank expands and absorbs heat from gaseous refrigerant condensing inside a heat siphon and running down to the hot heat source, the hydraulic fluid flows out and does work on the piston, which transmits the force to the matching cold piston which does work on the cold fluid which does work on the cold gas, which compresses and transfers heat to liquid refrigerant in a heat siphon, which evaporates and bubbles up to the cold heat sink.
The isothermal processes[]
The hot tank starts nearly full of hot hydraulic fluid. This fluid ends up in the hot fluid reservoir. Similarly, the cold tank starts nearly empty. The cold fluid which enters the tank to compress the gas comes from the cold fluid reservoir by way of a cylinder and piston.
A given pair of tanks is first connected via a piston which gives an advantage to the lower pressure cold tank so that the forces are nearly balanced. After the forces balance, the cold tank is still at a lower pressure than the hot tank. Next, the two tanks are connected via another piston which gives less advantage to the cold tank. Eventually, the advantage is given to the hot tank, which ends at lower pressure than the cold tank. Finally, the two tanks are closer in pressure to other tanks: the hot tank moves to the next lower pressure cold tank, and the cold tank moves to the next higher pressure hot tank, starting again with a piston giving advantage to the cold tank. All of this is accomplished using valves and pipes connecting tanks to cylinders.
Isobaric process reservoirs[]
This brings us back to the isobaric process. The isothermal processes ended with a tank of cold hydraulic fluid and high pressure gas, and another tank of hot low pressure gas with a small amount of hot hydraulic fluid. We don’t want to allow any heat to flow from hot hydraulic fluid to cold hydraulic fluid, since this heat would not be doing any work at all. Therefore, we move the cold high pressure gas to the high pressure gas reservoir and return the cold fluid to the cold hydraulic fluid reservoir. Also, we move the hot low pressure gas to the low pressure gas reservoir and return the remaining hot hydraulic fluid to its proper reservoir.
So we have two large reservoirs, one of cold high pressure gas and one of hot low pressure gas. We want to operate two isobaric processes, warming cold high pressure gas, and cooling hot low pressure gas.
Using work done by expanding hot isobaric gas to compress cold isobaric gas[]
In principle, we want the work available from heating the high pressure gas to go toward maintaining the pressure of the low pressure gas as it cools, but it makes little difference if this is achieved by letting the large constant pressure reservoirs absorb and supply the work, and maintain the pressure separately. Some of the high pressure gas is allowed to do work in preparing additional low pressure working gas to replace high pressure gas withdrawn from the system for use elsewhere.
Goal of isobaric process[]
The goal is to cool somewhat more than a tank full of hot low pressure working gas, ending with the gas filling a cold tank at the low working pressure. Simultaneously, a small volume of cold high pressure gas is to be warmed, ending with the gas occupying a small volume of a hot tank filled with hot hydraulic fluid at the high working pressure.
Implementation of isobaric processes[]
The goal is achieved using a continuous process counter-current heat exchanger, in which hot low pressure gas flows slowly through a series of insulated tanks connected by insulated low heat conductivity tubes. Simultaneously, cold high pressure gas flows slowly through coils of high conductivity (e.g. copper) tubing inside the series of insulated tanks, starting with the last (coldest) tank and ending with the first (warmest). The copper coils of neighboring tanks are connected by insulated low heat conductivity tubes.
This results in a large reservoir of cold low pressure gas and another large reservoir of hot high pressure gas. These reservoirs are kept at constant temperature by heat siphons, and at constant pressure by direct connection to the other reservoirs via the heat exchanger.
There is no need to monitor the temperatures of the tanks of the heat exchanger, as they will naturally arrive at the optimum conditions.
Using the output of the isobaric processes[]
When a new pair of tanks is to be added to the isothermal process, a hot tank is filled with hot hydraulic fluid and the proper volume of gas is admitted (calculated based on the working temperatures and pressures). A cold tank is simply filled with cold low pressure gas from the reservoir.
Revised design[]
Considerable simplification is possible if a system of hydraulics is used to convert all of the different pressures to a common intermediate pressure.
Consider a hydraulic jack. A small force applied to the handle forces a small diameter piston to move a large distance, displacing a small volume of fluid. This fluid flows from the small cylinder into the large diameter main cylinder, where it forces the large diameter piston to move a small distance. The force appearing at the main piston is much larger than the force applied to the handle.
When the handle is released, a check valve permits fluid to refill the small cylinder from a reservoir. To lower the jack, a valve is opened allowing fluid to flow out of the main cylinder back into the reservoir.
The same mechanism can be used to convert pressures. Low pressure fluid acting on a large diameter piston produces force equal to the pressure times the piston area. This force is transmitted via a rigid linkage to a small diameter piston. A large flow into the large cylinder directly results in a small flow out of the small cylinder. If this flow is opposed, low pressure applied to the large cylinder results in high pressure appearing in the small cylinder.
To apply this to the isothermal processes, a large number of double-ended pistons are provided, all connected to a common pressure reservoir. By double-ended piston, we mean a pair of cylinders of different diameters with pistons rigidly linked as described in the previous paragraph.
Each tank is connected to a rotary valve. The rotor of the valve connects the center port to exactly one output port, leaving the other output ports closed. Suppose there are N output ports. A single pipe with T joints connects the i-th output port of all hot tanks to a single double-ended piston. Thus we need N double ended pistons in the hot room, and N double ended pistons in the cold room. The common end of each of the pistons connects to a manifold which contains intermediate temperature hydraulic fluid and runs between the hot and cold room.
The i-th manifold is supposed to contain hot (or cold) fluid of a specified pressure. This can be controlled by a simple mechanical system: each manifold is also connected to a large fluid reservoir which is maintained at a constant pressure by any convenient means, e.g., the reservoir is a tall cylinder covered by a properly weighted piston so that the pressure in the manifold is dominated by the weight of the piston.
Given this system of rotary valves and manifolds, it is no longer necessary to speak of pairs of tanks. Instead, each hot tank moves through its cycle independently of the cold tanks.
Second revised design[]
In the cold (hot) room, we have N compression (expansion) tanks and N-2 constant pressure fluid reservoirs and attached double ended pistons, together with one low pressure fluid and gas reservoir and one high pressure fluid and gas reservoir. A rotary valve with 2N ports is arranged so that each tank is connected to exactly one piston and reservoir in sequence as the valve is rotated. There is one pipe from each tank to the rotary valve, and one pipe from the valve to each reservoir. The low and high pressure reservoirs (which are not attached to cylinders) probably require a more complicated arrangement.
In the cold room, tanks start full of low pressure gas and end full of fluid. This dictates that the cold low pressure reservoir must be below the tanks so that whenever a tank is connected to the low pressure reservoir, fluid will drain out of the tank down through the valve into the reservoir, and gas will flow from the reservoir through the valve into the tank. Similarly, the cold high pressure reservoir must be above the tanks, so that the small high pressure gas bubble in the tank will flow up through the valve into the reservoir while a compensating amount of fluid will flow into the tank.
In the hot room, the positions are reversed: the hot low pressure reservoir is above the tanks, and the hot high pressure reservoir is below them. Also, only a measured amount of high pressure gas can be permitted to enter the hot expansion tank. If too much high pressure gas were to enter the tank, gas would flow into the fluid reservoirs which are supposed to contain only fluid.
The heat engine is operated by slowly turning the rotary valve. Each tank will stay at the pressure dictated by the constant pressure fluid reservoir.
It is not immediately obvious how work can be continually absorbed by tanks in the cold room and continually emitted by tanks in the hot room, without some mechanism for restoring the piston positions. Work done by the hot tanks appears as motion of the pistons pushing intermediate fluid from the hot room into the cold room, where it does work on the cold double ended pistons, pushing cold fluid into the cold tanks. Clearly, these pistons will soon reach the end of their range of motion and operation must stop.
There must be a path for intermediate hydraulic fluid to move back from the cold room to the hot room. This is done in a simple manner: the rotary valves in both rooms have to operate in step. After fluid flow has stopped (or essentially stopped), the two rotary valves move to an intermediate position, so that all tanks are closed off but all constant pressure reservoirs remain connected to their matching cylinder. Then there is no applied pressure on the pistons from any tanks. Instead, a restoring force appears which forces intermediate fluid to flow from the cold room into the hot room. All of the cold pistons move so that the intermediate fluid piston has moved to the top of the cylinder and forced all of the intermediate fluid out of the cylinder, and the attached cold fluid piston has moved to the bottom of the cylinder, which is full of cold fluid which has flowed out of the attached cold constant pressure reservoirs. Similarly, all of the hot pistons move so the intermediate fluid piston is at the bottom of the cylinder, the attached hot fluid piston is at the top, and the hot fluid has flowed into the hot constant pressure reservoirs.