Phoenix Turbine Builders Club

Turbine Efficiencies

March 2007

Last month we looked at traditional turbine designs and the basic Momentum equation that explains how turbines work. This month we will look at the mathematics of horsepower and efficiency, and the superiority of the disc turbine.

We'll start out with the equation:

The kinetic energy, or work, of any system is equal to the mass, times the square of velocity, divided by 2. At first this may suggest that efficiency increases more rapidly by increasing the velocity until real empirical data proves that to increase the velocity by a factor of 2 requires 8 times the input energy. 

In other words, in the case of an airplane, a large diameter propeller is always more efficient than a small diameter prop due to the larger prop moving much greater volumes of air. Also, to increase an airplane's speed by a factor of 2 requires 8 times the horsepower.

This explains in part why conventional turbines are so inefficient. They use about 2/3 of their available horsepower compressing air. About 50% of the compressed air is for combustion, the other for cooling.

It takes an enormous amount of power to compress large volumes of air up to around 450 psi. This high pressure air is needed for creating a high velocity air flow.

In order to increase turbine efficiencies, we have to increase the mass flow while gaining high velocity through a different mechanism of physics. In our case, we will use the phenomenon of detonation. Using low air velocities and chamber pressures, we use the normally destructive pre-ignition combustion cycle to generate extremely high pressures and velocities.

Normal engine "knock" cycles may produce cylinder pressures around 1200 psi, while pre-ignition cycles result in 10,000-20,000 psi peak cylinder pressures, destroying an engine in seconds.

So these extremely efficient pre-ignition combustion cycles that would blow apart any piston or conventional turbine engine are exactly what we are looking for in our engine.

That leads us to the next discussion: Why are conventional turbines destroyed by pre-ignition events while the disc turbine not only survives, but thrives on it? 

Aside from the fact that conventional turbine sidewall construct could not handle the pressures or fatigue cycles, the blades themselves will not handle the stresses. Imparting heat and cyclic high energy pulses on a cantilevered blade (suspended on only one end) exerts an extremely high fatigue stress point where the blade meets the rotor. -- In a relatively short amount of time, the constant bending moment will separate the blade from the rotor. 

The second factor is heat. Heat is conducted from the blade only on the rotor end.

The disc turbine is a totally different mechanism. With the geometric element (blade, vane, etc.) placed perpendicular to and between the discs, it is supported on both ends, greatly increasing its strength, rigidity, and resistance to fatigue/stress moments.

Also, being placed between discs aids in conducting heat from both ends of the blade, increasing the heat transfer rate by a factor of two or more.

So our approach to improving turbine efficiencies is to use pulse detonation events to create high to hypervelocity gas streams, greatly reducing the need for expensive, multistage mechanical compressors.

By changing the hot rotor section from an axial bladed design to an inflow disc type blade or vane system, our turbine will sustain much higher heat and energy oscillations, allowing us to further reduce the weight of the engine.

Next month we will continue with compressor types, their efficiencies, and how we might begin to design our gas turbine.