Latent Power Turbines

A more detailed technical discussion

Contents

1  Brief summary of current results

2  Formulae linking electrical power input and output

3  LP Turbines and the Carnot equation

4  Treating an LP Turbine as a pair of nested black boxes

5  An enthalpy-pressure chart for LP Turbines

1    Brief summary of current results

This is a photograph of the closed loop system we are using for our research.

Figure 1. Our original plan was to use metal piping for the complete loop. But to save on costs, some sections were made from blue plastic mains water pipes.

Here is a descriptive summary of our results:

Figure 2. The changes in temperature and pressure around the loop were in line with our predictions.

In order to check that our experimental results were not a fluke, we repeated the experiments over a number of days using different fan speeds.

We also built an environmental chamber around the converging-diverging zone and used an electrical heating system to alter the 'laboratory' air temperature. The results were always in line with our expectations.
[Final Report for Innovate UK (Technology Strategy Board) Project 131512.]

However, we did not have sufficient funds to commission the design and construction of a bespoke turbine. Instead, we had to improvise, using a cannibalised set of air conditioning unit fan blades. These had entirely the wrong shape, producing a lot of turbulence and preventing a net output of power.

The quantitative results are currently being written up for journal publication.

2    Formulae linking electrical power input and output

Using a correctly designed rotor for our next round of research, these are the formulae that will apply:

(i) Under ideal conditions where there is no drag, the net power output from the system Poweroutput is related to the power input to the fan Powerinto fan by

Poweroutput = (n2-1) x (Powerinto fan

Where n is the constriction ratio. For example, for our test rig, the air speed increases by a factor of 3 as it passes through the constriction. So n = 3.
The square term appears because the kinetic energy of the moving air depends on the square of its speed.

(ii) Allowing for drag and other power losses, this equation becomes

Poweroutput = (n2-1) x (Powerinto fan - DW)

Where DW is the energy consumed/second overcoming drag and other losses.

[Proof of these equations is reserved for publication in a journal paper.]

3    LP Turbines and the Carnot equation

Latent Power Turbines have two novel design features that give them surprising properties.

(i) They incorporate a thermal feedback loop.

(ii) They can run 'cold' at a lower temperature than the laboratory air.

Figure 3 below explains how the internal heat engine can have a very low Carnot efficiency, while still allowing the LP Turbine as a closed loop engine to have a high thermal efficiency.

Figure 3. Thermal feedback explains the apparent paradox between low heat engine and high LP Turbine efficiencies.

4    Treating an LP Turbine as a pair of nested black boxes

The black box approach provides another way of understanding how a Latent Power Turbine can appear to be 100% thermally efficient, without violating the laws of thermodynamics.

Before examining the 'black boxes' we need to write a few notes about the first and second laws of thermodynamics.

The first law Essentially this tells us that energy cannot be created or destroyed. It can only change from one form to another.

The second law Textbooks and thermodynamics experts can write the second law in a number of different ways. But all of them encapsulate the following truths about nature:

(i) An engine that converts heat into another form of energy can never be 100% efficient. Some heat must always be rejected into a cold reservoir at a lower temperature than it entered the heat engine .

(ii) Heat can only flow from a warmer body to a colder body.

4.1 The internal black box

This is a heat engine.

Figure 4. The internal black box is a heat engine that must be consistent with the second law of thermodynamics. That is, it must posse a hot reservoir and a cold reservoir with some of the heat being rejected into the cold reservoir.

4.2 The external black box

This represents a closed loop mechanical engine that performs the following functions:

(i) It speeds up the working fluid (room temperature air) by passing it through a converging section of the conduit. In order to be consistent with the first law, the air temperature must fall as its kinetic energy increases.

(ii) It recycles the rejected heat.

(iii) It takes advantage of the second law because anywhere round the loop where the working fluid is cooler than room temperature, it can draw in heat from the warmer room.

Figure 5. The external black box is a heat recycling system. It can only recycle the heat and add extra 'top-up heat' because a converging-diverging system is used to ensure that the hot reservoir is always at a lower temperature than the surrounding laboratory air.

Key points to note:

(i) This representation is only valid because the hot reservoir is below laboratory temperature, with the cold reservoir being at an even lower temperature.

(ii) A superficial interpretation suggests that this is a system the violates the laws of thermodynamics by reducing entropy. This interpretation is not valid because the external black box is only one part of a larger system that must include the final destination as very low grade heat that the work output is destined to reach.

5    An enthalpy-pressure chart for LP Turbines

A thermodynamic chart that faithfully describes a working LP Turbine would be rather cumbersome and impossible to verify by experiment because in the vicinity of the heat engine, several thermodynamic processes overlap.

To simplify the analysis we will notionally lag the converging-diverging section so that heat from the environment is forced to enter the system in the following parallel sided section of the duct.

Figure 6. All parts drawn in blue are lagged so that heat only enters the loop after the engine has done external work.

Lagging the parts offers no practical benefits but is convenient for separating out the heat flow processes in a manner that can be experimentally verified.

Figure 7. Enthalpy – Pressure chart with heat flow processes separated out.

For ease of explanation, we have assumed that the temperature at B will be ambient. It is possible that this temperature will need to be slightly below ambient for the temperature gradient across the bare metal walls to draw in replacement heat. This simplification does not affect the shape of the chart.

A            At A the fan does work on the air so the air warms to above ambient temperature. Prior to A, the air inside the conduit is assumed to be at ambient temperature.

B            The air starts to cool as soon as it enters the throttling throat. B is the point at which the temperature has fallen back to ambient.

C            This is the point immediately after the air has transited the turbine. The air has cooled thanks to throttling and also because the turbine has done work, powering the generator. There has also been some heating due to friction as the conduit tapers and as the air passes through the narrow gaps between the turbine blades.

C’           Is the lowest point on the enthalpy-pressure chart that would have been reached if there had been no heating and corresponding pressure increase due to friction. ( Enthalpy-Pressure chart only.)

D            At the end of the lagged throttling constriction the air temperature is below ambient because the air has done net work driving the turbine.

E            Heat flows in through the conduit walls so that (in this ideal analysis) the air temperature has been restored to ambient. DH is the net heat extracted from the environment during the cycle.

Finding out more

References
These are our original research reports for Innovate UK (Technology Strategy Board) who part funded the Latent Power Turbine research