The laws of physics show that the Carnot cycle is the most efficient thermodynamic cycle that can be achieved. These same laws show that the Stirling cycle and second cycle Ericsson have exactly the same efficiency.
Each of the three cycles involve a succession of four thermodynamic transformations:
If the Carnot engine was never built, the industry uses Stirling and Ericsson engines. I think if Robert Stirling had invented the engine described by Carnot, he would certainly have built so that if Carnot had thought about the Stirling engine, the scientific community would have said “it is impossible to build”.
Here is my explanation: if we consider the Stirling cycle the theoretical point of view we have to analyze each of the four transformations according to the methods of classical thermodynamics which consider that the processes are quasi-static close to equilibrium. We must admit also that the regenerator is perfect and there are no internal dead volumes. We conclude with absolute certainty that the Stirling engine is impossible to build. It would be the same conclusion for the Ericsson engine. The main difference between Sadi Carnot and Robert Stirling was the one built without really understanding how it works and the other understood without knowing how to build it.
If we compare these three engines seriously, we find that the simplest of them is that of Carnot. It does not need regenerator, heat exchanges take place during the isothermal transformations, widely studied for Stirling engines and Ericsson and the working gas can be moved easily without the need for valves or flaps. Strangely the engine simplest and most basic mechanical terms has never been done.
Making an engine to convert heat into mechanical or electrical energy requires a new vision of thermodynamics presented for the first time by Curzon and Ahlborn in a paper published in 1973: "Efficiency of a Carnot Engine at Maximum Power Output" (This same result was independently obtained by Novikov and Chambadal). Since, to differentiate the theoretical Carnot cycle that describes a functional Carnot engine, some call it “the Curzon engine”. In practical terms, the Carnot engine has been more studied than the Stirling engine without ever having been made. These studies reveal the potential of this machine that will find its place in the real economic world.
For all these reasons that we will undertake its industrial production.
Figure 1 shows the original drawing created by Carnot to develop the engine and explain how it works. This drawing was published in 1824 under the title "Reflection on the Motive Power of Fire and on Machines fitted to Develop That Power". Fields marked A and B represent the hot and cold heat sources.
Figure 1
To my knowledge, few engineers were critical of this mechanical assembly and none have proposed alternative architectures. Let's start by doing a serious analysis of what should be a realistic Carnot engine.
Here are the basic functional requirements for the Carnot engine:
1. This is a complete and closed mechanical system containing a working gas,
2. Its volume is variable,
3. Its operation is sequential and continuous.
4. It moves the gas in three separate internal spaces.
a) In contact with the hot heat source.
b) In contact with the cold heat sink.
c) Without any contact with these two sources.
5. The functional architecture allows the gas to operate as best as possible the four thermodynamic processes, described by the theoretical Carnot cycle.
6. A system should recover the mechanical energy generated by the thermodynamic transformations.
This engine shown in Figure 1 is in contradiction with the constraint number 4. The architecture suggested by Carnot must be rejected.
To these basic functional constraints I propose some recommendations, useful for making an efficient and commercially acceptable engine. The list presented here is not exhaustive.
• The heat losses by conduction between the two sources of heat should be minimized.
• The general architecture of the system must remains the same whatever the conditions of entry and performance desired.
• The exchange of heat between the sources and gases occurring in an effective manner to achieve maximum power, as defined by Novikov, Curzon and Ahlborn.
• Good seals are needed to keep the working inside the engine. (no gas leak)
• The maximum internal pressure must be acceptable and should not cause ruptures.
• The engine should be simple.
• Manufacturing costs must be reasonable.
• Maintenance can be performed by regular technicians.
• Etc.
All these constraints and recommendations require forgetting about the quest for a hypothetical ideal machine, without sacrificing the expected performances of a realistic Carnot engine. An advanced mathematical approach is necessary to verify all of our technological choices.
One of the mechanical architecture I suggest (the way of thinking of Robert Stirling)
To begin, we must answer to the six functional constraints already mentioned above
• 1 - A cylinder closed at one end.
• 2 - A piston driven by a kinematic (for example, a sinusoidal motion).
• 3 - A simple mechanical link to move the internal gas from one space to others.
• 4 - To create three spaces you must use two displacers.
• 5 - Displacers hide the heat sources when they are not used.
• 6 - Kinematics has a flywheel to store energy from the adiabatic transformations, or a second set in opposition of CYCLE must be provided, the entire system then extracts energy from the force difference created by two symmetrical sets.
This finally gives us the following simple architecture to which we add a kinematic assembly (which I do not reveal any here):
FIGURE 2
FIGURE 3
Using Figure 3, which represents the PV diagram of the Carnot cycle, we will try to understand the functional aspect of the proposed architecture. The engine is in position A (P1, V1). Both displacers (D1 and D2) occupy a large part of the cylinder volume and completely hide the cold source. The gas is in contact with the hot source. The isothermal expansion process can begin from this point.
1 - Thermodynamics isothermal expansion process AB.
The movement of the piston causes an increase in volume. The displacers follow stroke of the piston. The gas remains in contact with the heat source and is maintained at temperature T1.
2 - Fast configuration transition
The displacer D1 moves to hide the hot source. The displacer D2 continues to follow the piston motion and hide the cold source. The gas is no longer in contact with any heat sources. The point of the cycle at this time is B.
3 - Thermodynamics adiabatic expansion process B-C
The piston continues to move and expand the working gas. The gas temperature is lowered until it reaches the temperature of the cold source at point C of the cycle.
4 - Fast configuration transition
The D2 displacer frees heat sink by moving closer to D1, all the gas is then in contact with the cold source. The volume occupied by the displacer D2 is equal to the displaced gas volume. The piston reverses the direction of its movement. We are at the point C at the time.
5 - Isothermal compression C-D
The movement of the piston reduces the volume of gas to the value V4. The gas is held in contact with the heat sink and its temperature remains constant up to the point D of the cycle.
6 - Fast configuration transition
The D2 displacer moves toward the piston and mask the cold source, the hot source is hidden by D1 who does not change position.
7 - Adiabatic compression D-A
The volume is reduced until it reaches the value V1. The gas is not in contact with any heat sources, hidden by D1 and D2, its temperature increases by compression effect until reaching the value of the hot source. We are nearly at the point A at this time
8 - Fast configuration transition
The displacer D1 unmasks the hot source by moving closer to D2. Gas is in contact with the hot source. The piston stroke is reversed and the cycle can begin again.
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See the complete cycle below:
The mechanical architecture presented here properly reproduces the Carnot cycle by a sequence of eight steps. This is a statement of principle for its implementation. I know, the two displacers proportions are not perfectly accurate. Feel free to do it if you wish !
Implementing the recommendations:
• The displacers D1 and D2 are made of lightweight materials with high thermal resistance.
• The adiabatic zone of the cylinder is not swept by the piston’s movement, so we can thermally insulate the cylinder in this area. (Inside and outside the cylinder)
• A balance between the aerodynamic losses resulting from the gas movement and dead spaces must be found. This source of irreversibility is to be fight.
• The method, often used with Stirling engines, which consists of heating one end of the motor is a source of significant losses. Heat must be provided to the working gas and not to the cylinder. This is the most important of my recommendations. There are many solutions that enhance the heat transfer from heat sources to the gas. I will not reveal any here.
Benefits of this architecture:
It is Simple, effective and inexpensive. It is Valid for engine or heat pump. Mathematically we have all the levers to optimize its operation. We can adjust the ratio of time between isothermal and adiabatic during phases of compression and expansion. We can also optimize the exchange surfaces by adjusting the overall geometry of the system. Finally, we can adjust the amplitude of movement of the piston according to the temperatures T1 and T2. Therefore, we can act on the power and performance for all operating conditions.
Disadvantages:
To keep this architecture as simple as possible, we must know in advance the conditions of engine operation. This engine will be very sensitive to temperature changes of the two heat sources. It is of course possible to adjust the time allocated to adiabatic changes dynamically, but it will result in additional complexity that will affect the price. This engine is ideal for operation up to 610 K (336.85 ° C) with a cold source at 303 K (30 ° C). For these temperatures the ratio of adiabatic is: 5.750554 (adiabatic ratio). Industrially this engine is designed for applications that need to transform thermal energy at low temperatures.
In conclusion:
We know that the Carnot engine is the best thermodynamic machine it is possible to achieve. Unlike dogmatic assertions expressed by those who have not think about its mechanical architecture so simple and obvious.
The Carnot engine is classified as an external combustion engine, as all heat transfers to and from the working fluid take place through the engine wall. This engine is noted for its high efficiency compared to steam or internal combustion engines, quiet operation, and the ease with which it can use almost any heat source.
Here are some of its main characteritics and advantages:
High Efficiency Most steel engines have a thermodynamic limit of 37% (little bit higher for diesel engines). Even when aided with turbochargers and stock efficiency aids, most engines retain an average efficiency of about 20%. Our design allows the output to reach XX% and in theory it could reach a maximum of XX%. Practical efficiency depends of temperature level and differences but it’s still higher than actual technologies. Waste heat is easily harvested (compared to waste heat from an internal combustion engine) making Carnot engines useful for dual-output heat and power systems
Multi-Source Engine
Carnot engines can run directly on any available heat source, not just one produced by combustion, so they can run on heat from solar, geothermal, biological, nuclear sources or waste heat from industrial processes.
Low Temperature work
Unlike other technologies, the Carnot engine is very suitable for low temperature applications such as concentrated solar power (CSP), geothermal energy and more generally any low temperature fluids or gases coming from any heat sources (exhaust gases, power station, data centers, etc.). It can use flows from 80 to 650 C. See the Technological Comparison Chart.
Better reliability and easier maintenance The engine mechanisms are in some ways simpler than other reciprocating engine types. No valves are needed, and the burner system can be relatively simple. Because of the absence of matter exchange with its environment and the absence of inner chemical reactions, this engine suffers less deterioration than an inner combustion engine.
Reversible Driven by another engine, it becomes a heat pump capable of cooling or heating, dependent on requirements. It is extremely flexible. It can be used as CHP (combined heat and power) in the winter and as coolers in summer.
Safe, discret and oxygen-free A Carnot engine uses a single-phase working fluid which maintains an internal pressure close to the design pressure, and thus for a properly designed system the risk of explosion is low. In comparison, a steam engine uses a two-phase gas/liquid working fluid, so a faulty release valve can cause an explosion. The limitation of vibrations caused by explosion’s absence makes this engine quieter than reciprocal engines. Moreover the Carnot engine can be built to run quietly and without an air supply, for air-independent operation (ie: submarines, spatial applications).
Modularity and flexibility
Possibility to use the same engine for different applications with only minor modifications. Moreover, the Carnot architecture allows to develop a wide range of power based on the same design. It means the possiblity of scaling up or down the engine power without the need of costly and time consuming design studies.
Since the beginning of our work, we have always kept in mind the final objective of this project: produce a competitive engine that will be sold
To achieve this goal, our engine must comply with the following criteria:
- Bring a useful technological breakthrough - Be efficient - Avoid unnecessary complexity - Be reliable
Accordingly, the conception of our engine is driven by a pragmatic approach in our technological choices. I the meantime, we are focusing on the market
1. A market orientated approach:a useful and efficient innovation
During the 60s, France and Great Britain teamed up to develop a revolutionary supersonic airplane that was able to cruise at twice the speed of sound, more than two times faster than conventional airliners. This airplane named Concorde was an amazing aircraft packed with the latest technologies. It reaches its specifications, it was a technological success, and it was fast and effective. Passengers could now cross the Atlantic in only 3 hours. The Concorde was useful but was it efficient? Not at all. This airplane was amazingly noisy, complex to maintain and its operating costs were excessively high, especially in term of fuel consumption. Meanwhile, Boeing showed up with his new Jumbo-Jet, the 747, a disgraceful fat plane that could carry up to 500 passengers on long range trips. The 747 wasn’t especially revolutionary in term of technology, it rather was an evolution of existing technologies. Less than 20 Concorde have been produced while Boeing still proposes its 747 today after having sold over a thousand units worldwide.
This is a perfect example of how a technological wonder can be a commercial disaster. The technology has to bring useful innovation that must be efficient, cost effective and match with the market needs. We keep that in mind since the early stage of our engine conception. We have identified potential applications and market demand. We also know that the success of our project lies on strict specifications definition. We do not have the ambition to change the world nor create the new technological revolution. We know the strengths and limits of this Carnot engine, we have identified promising applications while uncertain markets and uses have been deliberately rejected.
2. A pragmatic technological approach: keep it simple, make it reliable
Another key to success is to build an affordable and reliable engine by avoiding, as much as possible, any unnecessary complexity. A user centered approach commands to offer a cost-effective technology that will be easy to use, integrate to existing systems, and cheap to maintain. The Carnot engine will be built based on existing mechanical components commonly used in automobile and compressor industry. It doesn’t include any hazardous substances or highly pressurized gases. Our engine is meant to be built, used and serviced according to usual industry standards.
Adrian Bejan: “The method of thermodynamic optimization of finite-size systems and finite-time processes” Entropy Generation Minimization, CRC Press, Boca Raton, Fla, USA, 1996.
