Thymus vulgaris L., Sp Pl.: 591 (1753)

Engines that burn fuel to release heat, and convert that heat to mechanical energy, are “heat engines”. The theoretical maximum efficiency of any heat engine operating with maximum and minimum cycle temperatures of TH and TC, respectively, is the “Carnot efficiency” and is

determined using equation (2.2).

(2.2)

Advanced metals, thermal barrier coatings, and internally cooled blades enable modern engines to run at very high peak cycle temperatures. As of May 2011, the Mitsubishi Heavy Industries J- series M501J combined cycle powerplant had the world’s highest efficiency (60%), and the world’s highest turbine inlet temperature (1600C) [73, 74]. With such a high peak temperature, if the Carnot efficiency were the main limitation, it could theoretically approach 85% efficiency according to Figure 2.1. In crude, simple, miniature turbine engines for model aircraft, peak cycle temperatures are around 900C, theoretically enabling a Carnot efficiency near 75%, yet as noted already, model turbines range from 5-8% efficiency.

Figure 2.1. Carnot efficiency as a function of hot reservoir temperature

Clearly there are other efficiency-robbing processes at work that are far more important than the Carnot limit, especially in small engines. These are as follows. First, in ideal cycles there is no entropy generation, while in real engines, this is unavoidable. Second, even ignoring irreversibilities, most real engine cycles barely even resemble their ideal cycle counterparts, for practical reasons. The next section elaborates.

2.3.2 Ideal vs. real thermodynamic power cycles

Figure 2.2 compares real gas turbine cycles with the ideal Carnot and Ericsson cycles, both of which could achieve the theoretical Carnot efficiency if they could be realized in practice. In part (a), a simple Brayton-cycle gas turbine engine is compared with the ideal Carnot cycle at the same peak temperature. The comparison is appropriate because both cycles use adiabatic compression and expansion processes to move between the cool and hot parts of the cycle. In part (b) of the figure, an intercooled, reheated, recuperated multistage gas turbine is compared with the ideal Ericsson cycle.

Figure 2.2. T-s diagrams (conceptual/qualitative only) of real vs. ideal engine cycles.

Examining the left (green) side, process 1-2i represents the first step of a Carnot cycle: isentropic compression from, say, 300K to 1200K. This would require a compressor pressure ratio of ~190:1. Process 1-2r represents a more practical process: adiabatic but entropy- generating compression to a lower peak temperature. Process 2r-3 represents combustion at constant pressure, heating the working fluid (air) to 1200K, while the ideal process 2i-3 requires the gas to be heated while expanding, remaining at 1200K throughout the process – again, a difficult thing to accomplish in practice. Process 3-4i is ideal isentropic expansion over a 190:1 pressure ratio (impractical) while process 3-4r is nonisentropic expansion through a turbine over a ~5:1 pressure ratio (practical). Process 4i-1 is ideal isothermal compression at 300K (impractical) while process 4r-1 is involves dumping hot exhaust into the atmosphere and replacing it with fresh, cool air at 300K (practical, but wasteful).

Clearly the real Brayton cycle is a poor approximation of the ideal Carnot cycle - a mere sliver of the large rectangle that it “should” be. Most of the cycle takes place at temperatures far from the cold and hot temperatures, leaving large unfilled areas in the corners of the Carnot rectangle. However, it is equally clear that simple Brayton cycles are far more readily implemented than

(a) Simple cycle real gas turbine engine cycle (green/blue) vs. ideal Carnot cycle (black)

Carnot cycles. This alone explains why simple Brayton cycle engines are by far the predominant type of gas turbine engine in the market today.

In part (b) of the figure, an intercooled, reheated, recuperated multistage gas turbine is compared with the ideal Ericsson cycle. The intercooled compressor and reheated turbine approximate the isothermal compression and expansion processes 1-2i and 3-4i in the ideal Ericsson cycle. To traverse between the cool and hot portions of the cycle, a constant-pressure

recuperation process is used, replacing the adiabatic compression process in the

Carnot/Brayton cycles discussed previously. This process uses a heat exchanger to transfer most of the otherwise-wasted heat in the exhaust gases at state 4r to the compressed air at state 2r. The exhaust gases thus cool to state “y” before leaving the engine, warming the compressed air to state “x” just prior to the combustor entrance. Combustion occurs from state “x” to state 3, when the gases expand through part of the turbine. Combustion and expansion occur again in several stages until state 4r is reached. The more reheat/expansion stages, the more closely this resembles the isothermal expansion process 3-4i of the Ericsson cycle.

The basic advantage is to allow all of the heat release in the cycle to occur at a high temperature, near the limit of the materials/cooling/coatings technology for the particular engine in question. In accordance with Carnot’s observation, this leads to higher cycle efficiencies.

In sum, the cycle pictured in part (b) is a closer relative of the ideal Ericsson cycle than the Brayton is to the Carnot in part (a), so the former should be more efficient. This sets the stage for discussing technological trends over time that have led to higher efficiencies, and how they could be applied to very small engines. The right sides of the figures above will serve to illustrate certain key points.

2.3.3 Large aircraft engine efficiency-improvement trends

Over time, advances in turbine engine technology have led to higher cycle efficiencies. In large, simple-cycle engines – which are by far the dominant portion of the worldwide gas turbine market – this has generally been accomplished by increasing the overall pressure ratio, the turbine inlet temperature, and the compressor and turbine efficiencies [66, 75-78].

The effects of these trends are shown on the right (blue) side of Figure 2.2 (a). Higher pressure ratios lead to a higher post-compression temperature at 2r and lower post-expansion temperature at 4r, enlarging the quadrilateral and making it fit the rectangle somewhat better, though still not very well. Higher turbine inlet temperatures increase the Carnot efficiency of both the real and the ideal cycle, so even if the “fit” does not get better, the maximum efficiency

does increase. Higher turbomachinery efficiencies increase the slope of segments 1-2r and 3-4r, bringing them closer to the straight vertical walls of the Carnot cycle rectangle.

Terrestrial applications like stationary power generation and ship propulsion have different design constraints. Here, power-to-weight and power-to-volume ratios matter less than cycle efficiency, so the cycles illustrated in (b) are more appropriate design choices. Here, higher pressure ratios increase the width of the trapezoid, while higher temperatures increase its height. The real cycle approximates the ideal cycle reasonably well for both wide and narrow trapezoids, and heat is added at high temperatures in both cases. Therefore, the cycle can be reasonably efficient, regardless of the cycle pressure ratio. Engineers starting the design process with a blank slate will have wide latitude to select the engine pressure ratio that balances fuel efficiency, engine life, and capital cost to most effectively meet the desires of the market. Moderate pressure ratios accomplish this. For example, the Solar Turbines Mercury 50 4.6MW recuperated gas turbine operates at a pressure ratio of 9.9:1 [79], and the Textron- Lycoming AGT1500 that powers the M1 Abrams tank runs at 13.8:1 [75].

McDonald et al. have provided a comprehensive review of the relatively few recuperated aircraft engines that have been developed throughout history, along with recommendations for new research directions [78, 80, 81]. In Part I they note that recuperated engines were

“…not deemed attractive enough to deploy in an era of low-fuel cost, and based on the limited magnitude of the increased range, when considering the combined weight of the heavier engine and reduced fuel inventory (i.e. effect of the parasitic heat exchanger weight). Repeatedly, over the years the nemesis of the more complex thermodynamic cycle was identified as the lack of high-temperature heat exchanger technology readiness, notably their excessive weight and size, and more importantly their questionable integrity and reliability when operating in a severe thermally cyclic environment.”

In Part III they point out that

There are many areas not covered in this paper that need to be addressed, the salient ones including the following. The parasitic weight of the heat exchangers, and the extent to which fuel inventory can be reduced to offset this by the virtue of lower SFC needs detailed evaluation. From the flight test of a helicopter powered by a recuperated turboshaft engine many years ago, a reduction in engine noise was observed due to the “muffling” effect of the recuperator. Noise attenuation for the various heat exchanged engines discussed in this paper needs to be addressed. Also the effect that the thermal capacitance of the recuperator and IC have on engine power change and throttle response is important in the design of the control system. A topic that the authors have not seen addressed in the open literature is the increased vulnerability of heat exchanged engines to foreign material ingestion (e.g. birds, dust, ice, etc.). Such debris could end on the matrix faces of the IC and recuperator. While future aeroengines will have clean combustion, the possibility of fouling of the recuperator would have to be investigated.

Finally, Figure 2.3, taken from [82], provides a comprehensive survey of large aircraft engines; the most efficient one, the AL-34, is also the recuperated engine. This shows how dramatically a recuperator can improve fuel efficiency.

Figure 2.3. Turboshaft aircraft engines, plotted by power and SFC [82]. The AL-34 (circled in red) is the only recuperated engine on the chart, and is also the most efficient.