Stirling Engine

Introduction

The Haselhurst-Stirling engine design is a high pressure (80 atmospheres) high temperature (up to 600 degrees celsius) design. It has a theoretical efficiency of 60% at 600 C and 35% at 350 C. (Solar cells have a maximum efficiency of about 20%, diesel engines about 35%).

To begin I will simply use a fire to heat the hot side (wood has about 4kW/hrs of energy per kg, and a fire easily reaches temperatures of 600 degrees celsius).
The cold side will be cooled to around 100 degrees celsius by running water (I have a lot of ponds and creeks on my property!). If it works then in the long term I would use solar energy to heat it.

Design

I am using two petrol engines with the heads removed. The motors are connected together 90 degrees out of phase by their fly wheel. One motor becomes the cold side pistons, the other the hot side (see diagram below).
The pistons are modified so they have 10cm of cylindrical solid insulation attached to them followed by 15 cm of cylindrical metal foam (so the piston goes from being 10cm long to being 35 cm long). A 30 cm metal pipe is bolted onto the block for each cylinder such that the longer piston sits in this metal pipe. The pistons operate vertically down (motor is upside down), and the bottom of the metal pipe is filled with molten lead on the hot side and water on the cold side. As the pistons move up and down the metal foam is immersed in the liquid to displace the working gas from the hot side to the cold side.

The two petrol motors are 6 cylinder 3.9 litre 120 kW Ford Falcon motors from 1990 (yes, I live in Australia!). They cost me $40 dollars each from the local salvage yard. Each cylinder has a volume of 650cc. The two motors are connected 90 degrees out of phase by their flywheels. By connecting cylinder one of the hot engine to cylinder one of the cold engine, cylinder two of hot engine to cylinder two of cold engine, etc, we are effectively making six 650cc Stirling engines connected together by the motor's crankshaft.

	In this diagram the working gas fills the metal foam on the hot side and half fills the metal foam on the cold side. In the next 90 degrees rotation the hot piston half immerses the metal foam into the molten lead thus the working gas will be transferred to the cold side where the metal foam is lifting out of the water and cooling the working gas (ready for the next stage - contraction of gas on the cold side).
	The Stirling engine is now rotated 180 degrees (half a turn) from the above diagram. The metal foam on the hot side is completely immersed in lead, thus all the working gas is in the cold side. In the next 90 degrees of rotation the hot metal foam will half lift out of molten lead, the cold metal foam will be completely immersed in water, thus all the working gas will be transferred to the hot side ready for expansion.
	The metal pistons are extended 25 cm by adding 10 cm of solid insulation (so no air can enter) and 15 cm of metal foam (90% air).

Power

Theoretically this design (6 by 650cc = 3.9 liters) should produce the following power;
(I have included results for air and helium as the working gas).

See: Stirling Engine Performance Calculator

Cost

The total cost should be about $2,000 Australian including steel and welding.
For a comparison, the WhisperGen Stirling engine costs $20,000 dollars and is 1kW.

Below are some further details (from my provisional patent application).

The Haselhurst-Stirling Engine

Stirling Engines are theoretically the most efficient heat engines available, where the efficiency is 1 - Tmin/Tmax (in degrees kelvin). Thus the engines are more efficient the greater the temperature difference from the hot side to the cold side.

However, in the past it has been difficult to overcome design problems relating to the required rapid flow of heat energy in the hot and cold pistons, sealing the system at high pressure, and building the motor at a cost efficient price.

The Haselhurst-Stirling engine overcomes these problems by using two petrol engines connected 90 degrees out of phase. One motor is on the hot side, the other motor is on the cold side.
The head and sump of both motors are removed so that we have the block, pistons and crankshaft only. The bore for each piston (90mm) is then connected to the same diameter pipe (heating / cooling pipes) that are 30 cm long and bolt onto the block. The heating and cooling pipes are then connected by a 25mm pipe for each respective cylinder which connect the hot and cold pistons via the regenerator (filled with copper wire to act as heat storage).

The 30 cm heating / cooling pipes are half filled with lead on the hot side and water on the cold side. The working gas is pressurized air or helium.

The pistons have been lengthened by adding 10cm of solid insulation (no air can get into this volume) and 15 cm of cylindrical metal foam (90% porous / air)

When the crankshafts are rotated the piston's metal foam is successively immersed and removed from the liquid at the bottom of the heating and cooling pipes causing the working gas to be moved from the hot side to the cold side and back again. In one complete cycle the hot gas expands and does work, then it is transferred to the cold side where it contracts and does work, then it is transferred back to the hot side to complete the cycle.

This is an animated diagram of the standard Alpha Stirling Engine cycle.

Advantages of the Haselhurst-Stirling Engine

1. By using existing technology of petrol engines we are able to build cheap efficient Stirling engines with high quality engineering and high power output.

2. By using two 6 cylinder petrol / diesel engines connected 90 degrees out of phase we are effectively building 6 stirling engines, each with a volume of 650cc, connected by the motor's crankshaft.

3. By removing the head and extending the pistons with the 30cm heating cooling pipes (with similar ID) we get the further advantages of;

3.1 Increasing heat transfer (much greater surface area).

3.2 We move the heat source away from the block / piston thus extending the working life of the motor.

4. By using one way ball valves to direct the flow of the working gas into liquid (so it bubbles through molten lead / copper on the hot side, water / copper on the cold side) we can further significantly improve the surface area and heat transfer to the working gas.

5.Because this is an external combustion engine it can use any heat source, including the sun, thus producing a carbon / pollution free energy supply.
(Though this is true of all Stirling engines, it is important to state!)

Physics Calculations: Stirling Engine Heat Flow

Ultimately the success of a Stirling engine depends on getting heat in and out of the working gas quickly!

Below are my calculations (please correct any errors!).

They are based on a 3.9 liter, 10kW air machine (20 kW if He is used), temperature = 350 degrees Celsius at 40 Atmospheres Pressure.

Note: Conductivity Foam (solid ligaments) = Conductivity of solid × relative density × .33. Thus for Aluminum
where thermal conductivity = 143 W/mc, then thermal conductivity of 10% foam should be: 143/30, about 5 W/mc
Kinematic viscosity (M^2 / s) = Dynamic Viscosity / density

How much heat do we need?

H (joules) = mass by C by Specific Heat

For our Stirling engine, combining all six cylinders we have:

3.9 liters by 40 atmospheres = 156 liters, where density of Nitrogen = 1.25g/litre
So nitrogen has a mass of 195 grams.

Assume motor turns at 5 rps (300RPM)

Thus we need to heat 5 * 195 = 975 grams of nitrogen to be raised 250 degrees C each second.

Power in Joules/second = 975 grams times 250c times 1.04 = 250,000 Joules/s = 250kW

** This number seems high to me given we are working on a 10 to 20 kW machine assuming around 35% efficiency! I assume machine outputs are realistically based on the fact that you never heat or cool your gas completely.

Heat Conduction

So we need to get 250kW of heat energy H into the gas each second, where;

H = kA (T2 - T1)/L (joules/second) and k = thermal conductivity (J/smC = W/mC)

Below we will look at the three main areas of heat flow.
1. Through the 100mm diameter carbon pipe by 10mm wall thickness.
2. From the molten lead into the metal foam.
3. From the metal foam into the working gas (air / nitrogen or Helium).

1. Through the 100mm diameter carbon pipe by 10mm wall thickness.

Our total surface area is 6 times the surface area of each 100mm diameter heating pipe at 25 cm length. Thus total Surface Area = 5,000 cm^2 for the 6 heating pipes.

Heat flow through 1cm carbon steel = 50 by 0.5m^2 by 250c / 0.01m = 625kW

Which equates to 125W/cm^2.

From the above it seems that we can get 2.5 times more heat energy in to the heating cylinder though the 10mm carbon steel wall than is required.

So now we need to consider the heat flow into and out of the metal foam;

2. The heat flow from the molten lead into the metal foam

(When the metal foam piston is immersed in the liquid metal - the working gas is in the metal foam on the cold side).

We have approximately 1 litre of lead and 1 litre of metal foam in each of our 6 heating pipes (15 cm by 10 cm diameter), so there is ample lead to heat the metal foam. If we assume that each cc of metal foam has a surface area of 10cm^2 then 6,000 cc of metal foam = 60,000 cm^2 surface area. Finally, I will assume an average thickness of 0.1 cm for the metal foam, thus

H = 5 by 6 m^2 by 250 C by 1000 = 7,500 kJ (ten times more than we need, and this is consistent with the high surface area and heat flow characteristics of metal foam.)

3. The heat flow from the metal foam to the working gas

(When the piston / metal foam is lifted from the molten lead - the working gas is being moved back into the metal foam in the hot cylinder).

Again we will use the same surface area and assume a gas length of 3 times the average of the metal foam structure thus 3 mm.

H = 0.024 by 6 m^2 by 250 C by 333 = 12,000J = 12 kJ each second = 12kW.

So from the above we see that the limiting heat flow is from the metal foam to the working gas (as expected, heat flow through gas is low).

However;

1. Helium has 7 times the thermal conductivity of air / Nitrogen which would increase the heat transfer to 84kW which is about right for our proposed 20kW machine running with Helium as its working gas at 40 Atm and 350 degrees (thus about 35% efficiency).

2. The liquid lead will form spherical droplets on the metal foam surface that will further increase heat flow from the metal foam to the working gas.

From the above it seems that the required heat flow for our 10 kW (air) or 20 kW (He) Stirling engine is theoretically possible.

But have I made any errors or forgotten to include things!?

The true test - I now need to build it! The machine is simple to build - I hope to update this page in the next week with actual results from a physically real machine.

Geoff Haselhurst (23rd March, 2009)

PS - I have not included on this page how the machine will be pressurized. I have three options;

1. Enclose the 2 motors in 2 carbon seamless steel pipes each 40cm diameter by 80cm long. I have explained this with my other Stirling engine design.

2. Use the car air conditioner's compressor to collect air from sump (as it leaks past pistons) and pump it back into the machine at 40 Atmospheres. This may require using 6 gas valves and injecting the air back in during the expansion phase (you could use a low voltage modification of the ignition system to drive this.)

3. Work with Diesel engines (which handle twice the compression, thus are better) and use the fuel injectors to inject compressed air into the machine.

NOTES: For my reference.

Using copper high tensile wire (from aerial power cables).

Wire is 7 strands by .1cm diameter.

Thus area = 3.14 by .05 ^2 = 0.008 cm^2 per strand.

If I assume 30% copper wire (70% air) then I need 1.17 litres of copper = 1,170 cc of copper.

Thus 0.008 cm^2by L = 1,170 cc, so L = 146250 cm of one strand, so 20893 cm of 7 strand copper wire.

Assume each 7 strand copper wire is 20 cm long, so I need 1,044 cm of wire, thus 174 wires for each cylinder.

Surface area of wire is .314cm by length. Thus total surface area 45,922 cm^2.

So surface area of copper wire in each cylinder = 7650 cm^2 (this gives a SA / V ratio of 11.7 - similar to 5PPI Copper foam).

Thus heat transfer is (assume gas distance L is 2mm, so 1/L = 500 m);

H = 0.024 by 4.5 m^2 by 250 C by 500 = 13,500J = 13.5 kJ each second = 13.5kW.

Seems OK!!

How much Lead and Copper do we need?

At 40 Atmospheres pressure, 250C Temperature (350C hot, 100C cold)
and 5 Rev/second (300RPM).

Total of 1,000 grams of nitrogen / second. Energy = 975 grams times 250c times 1.04
= 250,000 Joules/s = 250kW

How many grams of Lead? 1.04/.13 times 975g = 8 times 975g = 7,800 grams
thus volume = 7,800/11.3 = 690cc, thus 115cc for each cylinder.

How many grams of Copper? 1.04/.376 times 975g = 2.76 times 975g = 2,700 grams
thus volume = 2,700/8.8 = 306cc, thus 50cc for each cylinder.

In each 20 cm of 100mm (1.2litres) heating / cooling cylinder we have;

50% Lead, thus 600cc = nearly 6 times required amount. Thus lead would only drop 50 degrees C for air to rise 300 degrees C.

50% copper, thus 600cc = nearly 12 times required amount. (Need about 200 wires per cylinder!)
Thus copper would only drop 25 degrees to air, but would also lose heat to Lead. And as heat flow through copper is 5 times faster most heat would come from copper.

How much Copper do we need in Regenerator?

Assume 25mm ID pipe, A=5cm^2. Length on hot side is 20cm, thus volume = 100cc.

If 50% full of copper then 50cc of copper (equal to required), 50cc of air (2.5cm^2).

IF we use 100mm pipe then A = 60cm^2.

If we use 50mm pipe then A = 20cm^2.
So 5cm = 100cc at 80% copper, air 20cc (4cm^2).
Or 10cm = 200cc at 80% copper (160cc = 3 times heat energy) and 40cc air (6% cylinder volume)

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