Hot gas engine technology []

Basic operating principle of Stirling engines

The Heat2Power Technology is a substantial further development of the Stirling engines referred to here as "classic". First, the thermodynamics underlying all Stirling engines and the operating principle of classic engines are described.

A Stirling engine is a periodically operating heat engine that converts thermal energy into mechanical energy ("Heat-To-Power"). The operating principle of the Stirling engine is based on the alternating heating and cooling of an enclosed quantity of gas. The working gas is heated in a continuously heated chamber (cylinder), causing it to expand.

The expansion of the gas drives the engine. In another chamber (cylinder), the gas is then cooled and compressed. It oscillates back and forth between these two chambers. Stirling engines are usually designed as piston engines, but other designs also exist.

The engine can produce work because the work required for compression at a cold temperature is less than the work released during expansion at a hot temperature.

Heat is supplied to the enclosed gas from the outside, so the engine can be operated with any external heat source. Since the gas is not exchanged, a particularly suitable gas such as helium or hydrogen can be used.

Conventional Stirling engines ("classic engine") store the heat contained in the working gas in a regenerator as it travels from the hot to the cold chamber to improve efficiency. The regenerator releases the heat when the gas flows back from the cold to the hot chamber.

"However, general knowledge and understanding of Stirling engines is still so limited that even among experts there is a great deal of disagreement, not only regarding their basic applications or desirable design features, but also regarding the appropriate analytical approach for their design and optimization."
(T. Finkelstein, Foreword to Allan J.Organ: "Thermodynamics and Gas Dynamics of the Stirling cycle Machine")

Types of Stirling engines

There are various types of Stirling engines ("Alfa," "Beta," and "Gamma") of the classic design, distinguished by the arrangement of the working and displacer pistons. The New Stirling Engine Technology we are discussing here is an Alfa-type engine, based on the principle developed by Alexander Kirk Rider, hence also called the "Rider Engine." The other designs will not be discussed here.

In general, a classic Alfa-type Stirling engine consists of a hot working cylinder with a heater at the cylinder head, a cold compression cylinder with a cooler at the cylinder head, a regenerator, and a crankshaft.

The pistons are housed in separate cylinders and drive the common crankshaft. The approximately 90° offset of the cooled cylinder ensures that the gas can expand or compress through one piston while the other piston moves only slightly near top or bottom dead center. Since both cylinders are connected by a pipe and a regenerator, the work cycle (expansion and compression) propagates to the top of the other piston in the following cycle.

Alfa-Stirling Motor — Example of a modern Alfa Stirling engine of classic design

The cycle of an Alfa Stirling engine

The Stirling process consists of four steps. The following illustrations show these cycles in an Alfa-type machine.

Isothermal expansion in the Alfa-Stirling engine — 1: Isothermal expansion

Isochoric cooling in the Alfa Stirling engine — 2: Isochoric cooling

Isothermal compression in the Alfa Stirling engine — 3: Isothermal compression

Isochoric heating in the Alfa Stirling engine — 4: Isochoric heating

Thermodynamic process

Isochoric cooling of the Stirling process — 2-3: Isochoric cooling

isothermal compression of the Stirling process — 3-4: isothermal compression

Isochoric heating of the Stirling process — 4-1: Isochoric heating

The thermodynamic cycles in detail

➀ ➁

Isothermal Expansion in a Hot Cylinder

T = const. during the expansion of the gas.
The heat Q supplied to maintain the temperature corresponds to the work W done.

➁ ➂

Isochoric Cooling in the Regenerator

At constant volume, the temperature and pressure of the gas decrease. The heat removed is stored in the regenerator and returned to the gas in step ➃ ➀

➂ ➃

Isothermal compression in a cold cylinder

T = const. during gas compression.
The work W done by changing the volume corresponds to the amount of heat Q to be dissipated.

➃ ➀

Isochoric Heating in the Regenerator

The heat extracted during step ➁ ➂ is returned to the gas. At constant volume, the temperature and pressure of the gas increase.

What is the best working gas for a Stirling engine system?

Modern "classic" Stirling engines mostly use helium as the working gas. Air, hydrogen, or nitrogen would also be conceivable.

Can better efficiencies be achieved with helium or hydrogen? Existing knowledge on this is based on the non-generalizable experience of engines used for common low power outputs. Hydrogen offers the most favorable properties from a thermodynamic perspective. However, since hydrogen always poses an explosion hazard, makes steel brittle, and diffuses through many materials, it is unsuitable here. The question, therefore, is: air or helium as the working gas?

	Density	Specific Heat capacity c_p	Specific Heat capacity c_v
Air (dry)	1,29 kg/m³	1,005 kJ/(kg·K)	0,72 kJ/(kg·K)
Helium	0,179 kg/m³	5,193 kJ/(kg·K)	3,22 kJ/(kg·K)

Air is about 7 times heavier (denser) than helium, but has only about 5 times the specific heat capacity. This means that a machine with a given volumetric throughput cannot transfer more heat with helium than with air.

The specific heat capacity c_v of polyatomic gases like air increases with rising temperature, and the isentropic exponent κ (the ratio c_p/c_v) decreases as a result. At standard pressure, the value of κ for helium is consistently 1.67. For air, however, the value of κ = 1.4 at 0°C decreases progressively with increasing temperature, approaching κ = 1.3 in the temperature range relevant for Stirling engines, around 800°C.

If the hot cylinder does not undergo the ideal case of isothermal expansion (p·Vⁿ = const., with n=1) but instead approaches the adiabatic case (n=κ), different pressure conditions result.

Comparison of adiabatic and isothermal processes

Isothermal process (n=1): The process occurs at a constant temperature. Heat transfer is necessary to maintain the constant temperature.
Adiabatic process (n=κ): No heat transfer takes place – the system is thermally insulated. Energy change occurs exclusively through work, not heat.

These circumstances partially negate the advantages of helium over air.

Advantages of Helium:

Very good thermodynamic properties
Smaller regenerator required
Less friction/flow losses

Disadvantages of helium:

High costs
High effort required for sealing
An automatic refilling device is needed

Calculations have shown that the advantage of helium over air in terms of the required regenerator size (counterflow tube bundle heat exchanger) is particularly relevant at low power levels:

Required regenerator heat exchange area depending on gas flow rate — Required heat exchange area of the regenerator
depending on gas flow rate
(based on: T_max=800°C, T_min=150°C, p_max=75 bar, p_min=3 bar)

If you want to optimize the equipment, you should definitely consider using air as the working gas and a larger regenerator. In return, you can do without the additional equipment for helium handling. The advantage of helium over air diminishes with increasing power output. This applies particularly to the targeted power range of the Heat2Power Technology.

Notes on design and thermodynamics

The pV diagram of the Stirling cycle actually shows not four, but six process steps. The lowest pressure occurs after the condenser (before entering the compression cylinder). The highest pressure does not occur at the outlet of the compression cylinder, but after passing through the heater.

pV diagram of the Stirling process with heat recovery from the regenerator — Stirling process with heat recovery from the regenerator

These steps are illustrated in the pV diagram above. The heat dissipation in the regenerator ➁ ➂ corresponds to the heat input in the regenerator ➃ ➀ towards the working cylinder. The greater the heat exchange in the regenerator, the smaller the remaining amounts of heat to be supplied/discharged in the heater/cooler. This directly reveals the potential for increasing power and efficiency:
Increasing the amount of heat transferred in the regenerator either reduces the required size of the cooler or increases the temperature difference (and thus the efficiency) between the hot and cold sides (downward shift of the curve ➂ ➃).

The plant's performance depends entirely on the correct design of the regenerator!
The regenerator is the key element for the plant's efficiency.

Weaknesses of classic Stirling engines

Despite their theoretical potential, classic Stirling engines never became widely adopted. The main reasons for this are the following technical weaknesses:

Isothermal energy as an unrealistic ideal process: Expansion and compression at a constant temperature are practically unattainable. The necessary immediate heat removal or addition leads to high losses and reduces efficiency. Adiabatic processes would be physically more sensible, but were not consistently implemented in classical concepts.
Regenerator problem: Classical regenerators cause dead volume, flow losses, and incomplete heat recovery. Instead of increasing efficiency, there is often a drastic decrease in the compression ratio. Textbook formulas are not applicable here – practice shows counterproductive effects.
Erroneous assumptions in the pV diagram: Many diagrams ignore additional pressure stages (e.g., minimum after the cooler, maximum after the heater). Pressure and volume ratios are not directly proportional, but depend on the isentropic exponent. As a result, real-world processes deviate significantly from the theoretical curves.
Mechanical and thermal losses: Friction, gap losses, and heat conduction between hot and cold areas are often underestimated. Heating the cylinder walls during expansion is ineffective – the gas only remains at the wall for milliseconds, and no significant heat exchange takes place. Additional heat input in the expansion cylinder does not increase performance, but only increases losses.
Design limitations: Deviations from the 90° cylinder arrangement reduce additional forces, but worsen the already low effective compression ratio. The amount of gas that actually performs work does not correspond to the amount heated or cooled – a further loss of efficiency.

Conclusion: These weaknesses explain why the classic design never achieved a breakthrough. They also demonstrate why a new technology is needed – an engine that consistently utilizes thermodynamic principles adiabatically, minimizes losses, and finally translates the theoretical advantages into practice.

"In the middle of difficulties lie the opportunities" (A. Einstein)

This is how to build the perfect Stirling engine

The aforementioned weaknesses give rise to clear requirements for a new design:

An ideal Stirling engine is not a collection of romantic textbook assumptions, but a system consistently optimized for real heat and flow processes. The following guidelines address thermodynamics, flow, mechanics, and loss minimization.

Clearly separate process management: Separate changes of state (heating, cooling, expansion, compression, gas transfer) clearly in time and space. Avoid overlaps so that pressure and temperature profiles remain controllable.
Adiabatics preferred: Expansion and compression should be performed adiabatically whenever possible, rather than being "forced" isothermally. This increases the effective pressure ratio and reduces unnecessary heat exchange during the operating cycles.
Utilizing high temperature differences—without wall heating illusions: Relevant heat must reach the working gas, not just the cylinder walls. Short contact times mean: focus on effective heat input in the right volume, not on surface wall temperatures.
Appropriate regenerator size: Avoid dead volume, pressure loss and incomplete heat recovery. A regenerator must not noticeably worsen the compression ratio—otherwise the losses outweigh the benefits.
Aligning the pV diagram with reality: Take additional pressure minima/maximums into account (downstream of cooler, downstream of heater). Consider the relationship between pressure and volume using the isentropic exponent, not simplify linearly.
Guiding the flow with minimal loss: Short, generous conductor cross-sections, gentle deflections, low pulsation. Goal: Minimal pressure loss and no heat transfer between hot and cold parts.
Maximize compression ratio—effectively, not nominally.: Strictly minimize sealing points, gap dimensions and backflow. The effective compression ratio determines the useful work per cycle and power density.
Reduce mechanical friction: Precise guidance, low lateral forces, as few sealing points as possible. Where possible, choose kinematic concepts that minimize side loads and reduce lubrication requirements..
Consistent implementation of thermal separation: Thermally decouple hot and cold areas, avoid thermal bridges, prioritize insulation. Capture radiant heat and return it for usable use, instead of losing it..

Conclusion: The "perfect" Stirling engine is not based on idealizations, but on real-world time and energy distributions. Clear process control, adiabatic operating cycles, an effective compression ratio, and radical loss minimization are the key components.

Perspectives for Stirling technology

These principles demonstrate that the classic design is insufficient – and why a new generation of engines is needed.

The previously designed and manufactured engines of the classic design deliver only low power outputs, have low efficiency, and therefore a limited range of applications. They share with the modern Heat2Power engine only the basic principle of converting heat into mechanical work.

The analysis of the thermodynamic weaknesses clearly shows:
To fully exploit the potential of the Stirling process, new concepts are needed. Only through consistently adiabatic process control, minimized losses, and optimized mechanics can the theoretical efficiency be translated into practice.

This opens up a perspective beyond the classical design:
Stirling technology can become a high-performance system for stationary power generation, ship propulsion, and the utilization of previously unused waste heat. It will then no longer compete with small niche engines, but with gas engines, microturbines, and large diesel engines.

Conclusion: The future of Stirling technology does not lie in the classic design,but in a new generation of engines that consistently utilize thermodynamic principles and significantly push the efficiency limits.

The following pages explain the [] Heat2Power-Engine in detail.

Contact + License Inquiry

Dipl. Ing. Thomas Seidenschnur
info@heat2power.com