Blade Geometry Module

The hub to tip ratio (HTR) used to define the geometry of the blade was deduced from [Hong et al. 2005], and applies to the first stages of the high pressure turbine blades. Other parameters such as hub, tip and mean radius, as well as the blade height and cross sectional area for root-mid blade section, were derived using equations 5.14 to 5.19 and the outcome are presented in section D (Table 5.1). These parameters as well as those obtained from the lifing module were used for hot end gas path sizing.

Tip diameter, rT = (5.14)

Hub diameter, rH = rT * HTR (5.15)

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Blade Height, mid-root blade section, hMR = rM – rH (5.17)

Distance from CG (rotation axis for root-mid sec), dCGMR = rH + 0.5 hMR (5.18) Cross section area for root-mid blade, ASECMR = 0.5 [rM

2 + rH

2

] (5.19)

Since, the first stage of the rotor blade for GE 9E class engines uses directionally solidified (DS) GTD111, a nickel alloy material that can withstand high firing temperatures, stresses and varying operating conditions [Schilke, 2004]; the blade density was calculated using equation 5.20 with material composition in Table 4.1 (Appendix IV). This equation is said to be insensitive to Cobalt (Co) and Chromium (Cr) and has been validated by comparing measured densities of the sample casting to the calculated densities, [Biondo et al. 2010].

Density of Turbine Blade Material (GTD 111):

[0.307667639+ (% Mo * 0.000452137) + (% W * 0.001737591) - (% Al * 0.004497133) - (% Ti * 0.001240936) + (% Ta * 0.002133375)] * 27679.9047 (5.20) Where: 27679.9047 is a conversion factor from lb/in3 to kg/m3, % Mo is the percentage by Weight of Molybdenum, % W is the percentage by Weight of Tungsten, % Al is the percentage by Weight of Aluminum, % Ti is the percentage by Weight of Titanium, % Ta is the percentage by Weight of Tantalum.

The blade life was deduced using equations 5.21-5.26. Here, a reference blade life was set at 26280 hours for the baseline study, while further analyses were deduced in relation to the reference point. Assumptions include emissivity factor of 0.5, design point rotational speed of 11250 rpm, carefully selected to develop a reference point for the engine blade. Typically, the GTD111 DS blade material is coupled with advanced cooling technologies and protective coatings for effective cooling and to extend the blade creep life and tensile strength while increasing its capacity to endure substantial level of stress. Since, the emissivity factor of 0.5 was assumed; further analyses were carried out to assess the sensitivity of the study to increasing or decreasing emissivity factor.

Using emissivity factor and rotational speed, the metal blade temperature was estimated with equation 5.21 while the estimation of the centrifugal force acting on the blade at the mid-root section was achieved with equation 5.23.

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ω= (5.22)

Centrifugal force (root-mid blade), CFmr = (5.23)

σ= (5.24)

= (5.25)

The Larson Miller Parameter (LMP) was extrapolated from figure 5.2 using the value of centrifugal stress obtained from equation 5.23-24.

Figure 5.2: Larson–Miller parameter diagram for GTD-111 and other superalloys [Sajjadi et al. 2002] The total blade life was then calculated from the time to failure (tf) with application of a

safety factor (Sf) of 1.21, a value selected to achieve a design reference point for analysis (equation 5.26).

(5.26)

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For further fuel analysis and to allow a comparison among the different fuels and to the baseline, creep factor, which is a ratio of the nominal blade life to the reference state (design or a reference point), was obtained using equation 5.27.

Creep Factor, CF = (5.27)

This creep factor was used to estimate a maintenance schedule using equation 20. Maintenance Schedule = Plant Life (PL)/(AOH*Creep Factor) (20)

Thus, the baseline study has a creep factor of 1. This means the nominal creep life is equal to the creep life at the reference or design point (ISO condition) and applies to a single operating point. Outside the reference design condition, the creep factor reduces below 1, due to the operation and exposure of the engine to thermal stress and mechanical load. Hence, at condition other than the reference point, creep factor would be less or above 1. A creep factor above 1 indicate that the engine is operated optimally such that there is increase in component life as compared to the reference point while a creep factor below 1 mean that the engine is operated under conditions that would minimize the life of the engine components, as in this case, the HPT blades. This information is important to determine the hours and remaining life of component parts and to determine the possible maintenance cost that could be incurred. In typical plants, this is also used develop a maintenance plan for reduced operation and maintenance costs.

6.1.1.1. Maintenance Cost

The maintenance cost is estimated from the remaining blade life, an output of the lifing model and using equations 5.28-5.35.

Maintenance (M) Cost/annum= M Cost variable/annum + M Cost fixed/annum (5.28) M Cost fixed/annum = MFF * Installed capacity (5.29) M Cost variable/annum = (Unplanned M Cost + Planned M Cost) per annum (5.30) Planned M Cost = (MFV * Installed capacity * AOH * NPMS)/PL (5.31) Unplanned M Cost = (MFV * Installed capacity * AOH * NUMS)/PL (5.32) Where:

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MFV - variable maintenance factor ($/kWh/schedule) AOH - annual operating hours (hours)

NUMS, number of unplanned maintenance schedule per annum = MS - NPMS NPMS, number of planned maintenance schedule per annum

PL - project/engine life (years)

MS = (PL/ (LCREF* CF)) ` (5.33)

When:

CF = 1, NUMS = 0, because MS = NPMS (5.34)

CF < OR > 1, NUMS = MS – NPMS (5.35)

The fixed M cost should account for planned maintenance services over the life time of the engine while the variable M cost should account for unplanned maintenance services resulting from operation and over the life time of the engine. Both fixed and variable M cost factors are adopted from [Nigerian Electricity Regulatory Commissio (NERC), 2012]. Further analyses were carried out to assess the sensitivity of the study to increasing or decreasing M cost factor. In other words,

M cost ($) = Fixed + (Unplanned variable cost + Planned variable cost) (5.36)