Engine operating point

The single spool engine (Figure 1.17) is the simplest gas turbine that can be used for driving a load. In this configuration both the engine compressor and the load are driven by the turbine. Since the engine cannot operate if the load speed is zero, the output torque at zero output speed, also referred to as stall torque, is zero. Also, very little torque is available at low output speed. For this reason, this architecture is almost solely employed for power generation where the shaft must rotate at synchronous speed irrespective of power level.

For vehicle propulsion, the free power turbine engine (Figure 1.18) is preferred.

Here the load is driven by a free power turbine separate from that driving the engine compressor. The compressor and turbine combination that provides the hot, high pressure gas that enters the free power turbine is generally referred to as gas generator.

Unlike the single spool engine the stall torque is around 2 times that at full power and 100% speed. At part load, the compressor efficiency remains higher than for a single

Fig. 1.17 Single spool shaft power engine [138] – shown with cold end drive

spool turboshaft since the gas generator speed is not tied to that of the load. For a given power or gas generator speed the power turbine speed may vary over a wide range, depending on the absorption characteristics of the driven load. Figure 1.19a illustrates the variation of Specific Fuel Consumption⁶ (SFC) versus the shaft output power and power turbine speed. Note that this efficiency map has been built by using referred parameters [138] which allows us to use it independently of flight conditions. There also exist free power turbine engines with multi spool gas generators [55] resulting in different compressor designs. However, the variation of SFC is basically similar to that for a single spool free power turbine engine.

Fig. 1.18 Free power turbine engine [138] – shown with hot end drive

6ratio of fuel flow to shaft ouput power

0

(a) Effect of power turbine speed on turboshaft SFC [138]

50

(b) SFC variation for cube law opera-tion

Fig. 1.19 Typical performance charts of a free power turbine engine

The turboshaft efficiency of the TP1 aircraft can be analysed with Figure 1.19a.

For a given turboshaft output power, there is an optimum free power turbine speed which minimises the SFC. As shown, a cube law operation for the output shaft speed coincides roughly with this ideal running line of best SFC. The evolution of SFC with output power along the cube law is plotted on Figure 1.19b. In order to get the best efficiency of the gas turbine, the output speed must be kept close to the ideal running line. The propeller speed being tied to that of the output shaft of the gas turbine, the optimum propeller operating points from Table 1.4 studied in Section 1.3.1 have been reported in Figure 1.19a accordingly. Despite the generic nature of these performance maps, thus approximating the performance characteristics of the TP1 aircraft engines, running the turboprop engine according to the optimum operating points of the propeller alone yields to gas turbine operating points approaching its ideal operating line, thus pointing out the good overall performance of the turbine engine and variable-pitch propeller combination but also the difficulty to drastically improve it.

Along the ideal running line, the gas turbine efficiency increases with the output power and reaches its maximum value at the design power (Figure 1.19). From there, the engine should be operated at the design power in cruise to benefit from the lowest SFC. However, the gas turbine size can be driven by take-off or climb capability requirements. For example, as the TP1 aircraft engines are sized by the time-to-climb constraint, the cruise power is approximately 14% less than the design power at the selected cruise level resulting in part load operation of the engines. This power gap is noticeable between the climb segment and the cruise of Figure 1.3. Climbing to a higher cruise altitude will reduce this gap and help operating the engine closer to its highest efficiency point. This highlights once again the importance of considering the trajectory during the aircraft design optimisation. An alternative would be to downsize the gas turbine for the selected cruise altitude and provide power boost to meet the limiting design requirements through an additional power generation system.

Of course the effect of the additional weight of this secondary power generation is to be taken into account when evaluating overall cruise performance. Nonetheless, a quick first calculation can be made assuming a constant aircraft weight and combining the data of Figures 1.19 and 1.21. As presented more into details in Section 1.3.3, the gas turbine efficiency decreases when selecting a smaller gas turbine. By being 14%

oversized for the cruise segment, the TP1 engine is 1% less efficient than at the design power according to Figure 1.19. A 14% smaller engine (2,150 take-off horsepower versus 2,500 take-off horsepower for the TP1 aircraft) has a 2.8% worst efficiency than

the TP1 engine at design power based on the PWC data regression of Figure 1.21.

Considering the 1% penalty for the TP1 engine due the part load operation in cruise, the efficiency penalty for the downsized gas turbine at the selected cruise conditions falls to 1.7% versus the TP1 engine. Of course this result is based on approximated data and assumes that both maximum take-off and maximum climb ratings can be scaled in the same way. However it shows that the interest of engine downsizing for the TP1 aircraft is not straight forward in term of engine efficiency, not to mention that weight penalties have not been considered. More detail engine models will help concluding about the interest of engine downsizing in this thesis.

If the gas turbine efficiency is good during high power demand phases, the picture changes when it comes to idle operations. While the gas turbine power in idle is between 5% to 10% of the available power under same conditions, its efficiency can be 4 times poorer. Let us come back to the taxi case introduced in Section 1.3.1. For a 60% output speed (value linked to propeller rpm in taxi through fixed reduction gearbox), increasing the output power from 5% – the power required for two propeller taxi – to 10% – the power required for single propeller taxi – reduces the specific fuel consumption by a factor of 2, which confirms that the single engine taxi is preferred to reduce fuel burn.

This leads us to consider two options to decrease the energy consumption in low efficiency phases of a gas turbine: modify the number of prime movers and/or add secondary energy sources.