**
Latent Power Turbines**

**
A more detailed technical discussion**

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**

**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.

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

[Final Report
for Innovate UK (Technology Strategy Board) Project 131512.]

**2 Formulae linking
electrical power input and output**

U

**
(i)**
Under ideal conditions where there is no drag, the net power output from the
system **
Power**_{output}
is related to the power input to the fan **
Power**_{into
fan} by

**
Power**_{output
}= (**n ^{2}-1**)
x (

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

**
Power**_{output
}= (**n ^{2}-1**)
x (

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.

**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:

**4.1 The internal black box **

**
Figure 4.**
T**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 **

**
mechanical engine** that performs the following functions:

**first law**, the air temperature must fall as
its kinetic energy increases.

**
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**

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

**
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
re

**
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.
**
D****H**
is the net heat extr

_{ }

**Finding out more**

1 Details of the many ways in which LP Turbines could change our society

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

2
Courtney, W. A. and West, R,
Latent Power Turbines Ltd, *Technical report for Innovate UK (TSB) Project. Number 131512-23, *
(April 2015).* *
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