Latent Power Turbines

 The proof of concept experiments

We have decided to release the design for our planned experiments, in the hope that it will be replicated and validated by an independent research group at the earliest possible opportunity.

 Latent Power Turbine theory makes two predictions:

1. When saturated steam passes through a constriction or nozzle, the pressure and temperature drops are minimal compared with the flow of an unsaturated vapour or gas.

2. When saturated steam passes through a turbine unit the pressure and temperature drops across the turbine are minimal compared with the flow of an unsaturated vapour or gas.

Testing the first prediction
When saturated steam passes through a constriction or nozzle, the pressure and temperature drops are minimal compared with the flow of an unsaturated vapour or gas.

Figure 1. In separate experiments, warm gas then saturated vapour will be passed through a constriction.
If the initial temperatures and flow rates are similar, the theory predicts that the temperature and pressure drops inside the constricted zone will be reduced when the gas is replaced by saturated vapour.

Pointes to note: (i) The system will need to be well lagged, (ii) Bernoulli's equation should make predictions in fairly good agreement with the measured gas flow data (iii) Bernoulli's equation breaks down when a saturated vapour flows through the constriction. (See note below.)

Testing the second prediction
When saturated steam passes through a turbine unit the pressure and temperature drops across the turbine are minimal compared with the flow of an unsaturated vapour or gas.

Figure 2. In separate experiments, warm gas then saturated vapour will be passed through a turbine.
If the initial temperatures and flow rates are similar, the theory predicts that for similar power outputs, the exit port temperature and pressure drops will be reduced when the gas is replaced by saturated vapour.

A note on Bernoulli’s equation

Gases are compressible; nevertheless, changes in pressure can be estimated with a fair degree of accuracy using Bernoulli’s equation. This states that for an incompressible, non-viscous fluid undergoing steady flow,
the pressure (p)
plus the kinetic energy per unit volume (1/2x density, r x velocity, v squared)
plus the potential energy per unit volume (density ,r x acceleration due to
       gravity, g x height h)

is constant at all points on a streamline.

Thus,

p + 1/2rv² + rgh = A constant

 An extended form of Bernoulli’s equation that caters for viscous drag effects has been used by engineers for at least fifty years [1], but the question of phase changes due to condensation or evaporation does not appear to have been addressed.

Modifying Bernoulli’s equation to cater for saturated vapours
If the gas is replaced with a saturated vapour then the standard form of Bernoulli’s equation breaks down.
Any tendency to cool on passing through the nozzle taper will result in the production of small condensation droplets and the release of latent heat. Consequently, the temperature and pressure drops will be minimal, even though the saturated vapour has acquired kinetic energy.
On passing through the flared section, the latent heat processes are reversed, with heat being absorbed as the water droplets evaporate. The rate of mass flow remains constant through all sections of the conduit perpendicular to the streamlines. In the case of a saturated vapour, the rate of volume flow drops as a consequence of condensation in the nozzle, then increases as a consequence of evaporation in the flared section. This argument assumes that  the condensation droplets continue to move forward as an aerosol and do not come to rest as pools of liquid inside the conduit.

In order to produce an equation that is useful for all types of vapour an additional term dQ_l /dV needs to be added to the basic equation.
The term dQ_L /dV represents the latent heat lost/gained per unit volume.

Thus the generalised form of Bernoulli’s equation is

p + 1/2rv² + rgh - dQ_L /dV = A constant

When condensation occurs and latent heat is liberated, the minus sign is retained in front of the latent heat term. A positive sign is used if evaporation occurs and latent heat is absorbed.

Reference
[1] Segletes, S. B. and Walters, W. P., “A note on the application of the
     extended Bernoulli equation” International Journal of Impact Engineering,
      Volume 27, Issue 5, May 2002, Pages 561-576

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