As the NOx limit in regulation is corrected to $15\%O($dry$),$ your first task is to correct the

correlation between NOx and Flame Temperature shown below to $15\%02.$

Once the

equivalence ratio is determined for a flame temperature, you can assume complete reaction

between methane and air so that you can determine the composition of combustion products. Use

the definition of $[$NOx$]\_15$ to convert $[$NOx$]$ in ppmv to $[$NOx$]\_15.$

$[NOx{]}_{15}(ppmv)=[NOx](ppmv)\frac{20\mathrm{.}95\%-15\%}{20\mathrm{.}95\%-[02{]}_{d}ry}$

where $20\mathrm{.}95\%$ is the oxygen content in standard air and $[02]\_$dry is the oxygen content in $\%$ in dry

combustion exhaust, meaning that the water as a product for combusting methane has been removed

before measuring oxygen content.

Note: For this part of calculations, assume the gas turbine has a pressure ratio of $20,$ and efficiency is

at $90\%$ for both compressor and turbine. Be sure to update both pressure and initial temperature

when you use the adiabatic flame temperature calculator.

a$)$ Make a plot of $[$NOx$]\_15$ vs$.$ Flame Temperature.

b$)$ What's the theoretical flame temperature limit for meeting the emission regulation as set forth

by ECCC?

c$)$ In practical, perfect mixing cannot be achieved either due to limitations in mixing length or due

to combustion dynamics. To make sure that the emission standard can be met, what's the flame

temperature if we choose a more conservative emission target of $[$NOx$]\_15=10$ ppmv$?$

With the flame temperature determined from $1(c)$ and assuming that the flame temperature is the

same as TIT $($turbine inlet temperature$),$ determine design pressure ratios for following scenarios.

Note $2$: an iterative process is needed as a change in PR$/$compressor efficiency results in a different

pair of pressure$/$initial temperature for the combustion process, consequently the adiabatic flame

temperature.

$($a$)$ Best engine efficiency when both compressor and turbine have $90\%$ efficiency? What's engine

efficiency as calculated using non$-$ideal Brayton cycle?

$($b$)$ Largest engine power density when both compressor and turbine have $90\%$ efficiency? What's

engine efficiency as calculated using non$-$ideal Brayton cycle?

$($c$)$ Best engine efficiency when both compressor and turbine have $85\%$ efficiency? What's engine

efficiency as calculated using non$-$ideal Brayton cycle?

$($d$)$ Largest engine power density when both compressor and turbine have $85\%$ efficiency? What's

engine efficiency as calculated using non$-$ideal Brayton cycle?

Now consider the use of cooling air for hot$-$gas path components, including combustor, transition

piece and turbine blades and stators. Assume the max. flame temperature is set by $1($c$)$ and assume

$70\%$ of compressor discharge air is used for combustion and $30\%$ for cooling.

$($a$)$ What's the new TIT temperature?

Here assume compressors and turbines are of $90\%$

efficiency and the same PR as determined in $2($a$).$

$($b$)$ In fact, the lowered TIT as a result of mixing with cooling air in $3($a$)$ results in a lowered PR for

best efficiency. Again, assume $90\%$ efficient compressors and turbines, determine the PR for

best engine efficiency and the corresponding TIT.

this may require a few iterations to get

the proper PR or TIT.

$($c$)$ What's the best engine efficiency under conditions $3($b$)?$ What's efficiency deficiency in

comparison to $2($a$)$ as a result of using $30\%$ compressor discharge air for cooling therefore

lowering the TIT.

$($d$)$ Repeat steps $3($a$)$ to $3($c$)$ by assuming $85\%$ efficient compressors and turbines. Compare best

engine efficiency with cooling to that of $2($c$)$ and report efficiency gap as a result of engine

cooling air.

$4.$ The PR calculations in steps $2-3$ were assuming that the gas turbine is to be run in the simple$-$cycle

mode. Now assume the gas turbine was designed to run in the combined$-$cycle mode with a

bottoming steam turbine. To avoid using expensive super alloys for exhaust duct and stream

turbine, the exhaust gas temperature is limited to $655$C$.$ Practically, the gas turbine exhaust

temperature is expected to be between $450$ C and $650$C$.$ Assuming $90\%$ efficient compressors and

turbines, and assume TIT is the same as that was determined in $3($b$).$ What$$s the PR range of the gas

turbine engine in combined cycle so that the engine exhaust is between $450$C and $650$C $($assuming

engine exhaust is fully expanded to $1$ atm$).$

$5.$ Again, assume $90\%$ efficient compressors and turbine. By setting the gas turbine exhaust

temperature to be $550$C and TIT as determined in $3($b$)$

$($a$)$ Determine PR of the gas turbine engine and compressor discharge temperature

$($b$)$ Assume ignition delay is insensitive to pr