Inventario de Recursos del Fundo Pucayacu

This section establishes the pressure ratio, mass flow rate, recuperator efficiency, and other cycle parameters needed to establish an engine design. The cycle model used here is the simple one reviewed in section 3.2.5 (p. 75). The same model was also used to generate Figure 2.4.

Although that figure showed the tradeoff between efficiency and pressure ratio for small engines, it oversimplified matters by assuming constant turbomachinery efficiencies. This is not quite correct. High pressure ratio compressors and turbines are less efficient because the high pressure blades are smaller, and therefore operate with larger tip clearances and blade trailing edge thicknesses relative to the blade chord. Figure 2.4 therefore needs to be revisited using variable turbine and compressor efficiencies in order to provide a sound basis for design.

Figure 4.2 shows the cycle efficiency as a function of pressure ratio for turbine inlet temperatures representing maximum allowable values for metals and ceramics. The assumptions for these calculations are shown in Figure 4.3, and are justified by work described in various parts of this thesis.

Figure 4.2. Efficiency as a function of pressure ratio (red line) and mass flow rate for a 5.26 kW engine (blue line), based on assumptions shown in Figure 4.3.

Figure 4.3. Assumptions for cycle analysis.

The turbomachinery efficiencies shown in Figure 4.3 are merely assumptions, except at the 2.0 pressure ratio, where they are based on CFD results for the compressor and turbine designs described in upcoming sections. The downward trend with increasing pressure ratio is similar to that given by Wilson ([75] p. 116). As further justification, compressor maps are shown below for three small commercial turbochargers. In the present engine design, these would operate in the yellow marked regions; the first two as one of two stages, the third as a single- stage compressor. Efficiencies (70%, 76%, 76%) are isentropic total-to-total. Since volute exit velocities are unknown, corresponding polytropic total-static values cannot be computed, but if this were possible, the results would differ by at most a few percentage points.

Figure 4.4. Compressor maps for Garrett T3, Mitsubishi TD04, Garrett GT14 turbochargers.

Cycle analysis assumptions

Turbine inlet temperature = 1300C ηt*: .654 + .2/PRc (75.4% at PRc=2)

ηc*: .639 + .2/PRc (73.9% at PRc=2)

PRt = 1 + (PRc - 1) ⋅ (1 - P0)

P0**= 17.8%

εhx = 84%

ηburner = 95% including heat losses

ηturbine-shaft-to-propeller = 90%

* Polytropic total-to-static overall efficiency from first stage inlet to last stage outlet ** Net effect of burner and recuperator stagnation pressure losses, combined per equations and (3.19)

Minor notes on the other assumptions are as follows. The heat exchanger effectiveness and pressure losses are representative of values found in tests and simulations on a prototype ceramic heat exchanger, described in upcoming sections. The burner efficiency of 95% assumes that unburned fuel and combustor heat losses total 5% of the net heat input to the combustor, which will be justified later in this chapter. The 90% turbine-shaft-to-propeller efficiency is commensurate with a series electric propulsion system that are both 95% efficient (aggressive but feasible), or a 90% efficient gearbox (very conservative).

Based on these assumptions, Figure 4.2 shows that a small engine could achieve the target 22% efficiency at pressure ratios from 2.0 to 4.0. It also suggests that the mass flow rate of air to make the power goal diminishes only 20% from 2.0 to its minimum at 3.6, and then beginning to increase again. This may be a surprising result to those with experience designing very large engines, who would intuitively expect a massive increase in specific work (power divided by mass flow) as pressure ratio is pushed upwards from 2:1 to well beyond 4:1. It is the very low turbomachinery efficiencies at small scales that cause specific power trend to be so different in this case.

In the early stages of this project, it was thought that the ideal pressure ratio would be between 2.8 and 3.6, the optima for cycle efficiency and specific work, respectively. However, over time, the engine evolved toward lower pressure ratios, settling at 1.84 for the 3kW engine and at 2.0 for the 5.26 kW engine. Higher pressure ratios caused many difficulties, especially with turbomachinery efficiencies (which came out even worse than the Figure 4.3 trends assumed, perhaps due to the author’s inexperience) and with bearing lives. To reach pressure ratios of 2.8 or more, a high shaft speed is required, to keep the turbomachinery operating near optimum specific speed. High shaft speeds require small bearings, which have small load capacities. The target 1000 hour life set forth in chapter 1 is nearly impossible to achieve with 6mm ID bearings rotating at 200,000 rpm, for example. Such small bearings are so easy to damage during installation, that the probability of reaching the life goal would be slim - even if the axial shaft loads at higher pressure ratios were not a limiting factor (which they are).

At a pressure ratio of 2.0, the chart suggests a mass flow rate of about 56 grams per second. This slightly-higher-than-optimum mass flow rate makes the heat exchanger design more difficult in one sense, as the device must get larger in order to meet the effectiveness goal (which is already aggressive). On the other hand, lower pressures put less stress on the walls of the heat exchanger, offsetting this disadvantage, so the trade seems acceptable.

In sum, this section has described a simple cycle model based on representative turbomachinery efficiencies in this size range, explained why a pressure ratio of 2.0 was chosen for the new engine, and estimated the mass flow rate to be .056 kg/s.