How to make a Carnot engine?
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.
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.
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):
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.
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.
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.
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.