$1.$ Turbocharger Engine Matching Problem

In this problem, we are going to try to match a turbocharger to a six cylinder $3\mathrm{.}2$ L gasoline engine. The engine makes $\backslash (100\backslash$mathrm$\{$~kW$\}(\backslash$sim $130\backslash$mathrm$\{$HP$\})\backslash )$ of power at $5000$RPM naturally aspirated. We want to add a turbocharger to bump the power up by $\backslash (100\backslash \%\backslash )$ at this RPM to $200$ kW $(260$ HP $).$ The engine has an $\backslash (8$: $1\backslash )$ compression ratio, runs with a volumetric efficiency of $\backslash (85\backslash \%\backslash )$ and $\backslash (10\backslash \%\backslash )$ lean $(\backslash (10\backslash \%\backslash )$ excess air based on Stoichiometry$).$ You can assume losses of $200$ kPa in MEP from friction and accessories. An intercooler is placed downstream of the compressor so that the air entering the engine is cooled to $\backslash (100^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ I have chosen a Garrett brand turbocharger that is supposed to be compatible for horsepowers between $250$ HP and $350$ HP $,$ but they have a whole class of similar turbochargers with different characteristics. The compressor and tubine maps are shown below. We will use an online package for problem $2$ to do a full design. Here we are going to determine if this system does indeed fit the engine and, if we design it for the maximum RPM$,$ what type of boost and power increase can we expect at $3000$RPM$.$ OK$,$ let's start the process.

To get a $\backslash (100\backslash \%\backslash )$ increase in power, we need a $\backslash (100\backslash \%\backslash )$ increase in density. What boost in the intake pressure does that correspond to$?$ This problem isn't so easy because we have to incorporate the intercooler and the compressor efficiency into the calculation.

a$)$ First, find the mass flow rate of air needed to get the $\backslash (100\backslash \%\backslash )$ boost at $4500$ RPM$.$

b$)$ Now, let's approximate the efficiency of the compressor. Note that the pressure boost is always larger than the density boost so read up the curve and pick an efficiency for a pressure boost of somewhere between $2\mathrm{.}0$ and $2\mathrm{.}5($this is a guess which we will refine in a minute$).$ From the efficiency, calculate the increase in temperature and density of the air across the compressor assuming it starts at atmospheric temperature and pressure.

c$)$ If the flow through the intercooler occurs at constant pressure, what is the density at the outlet of the intercooler? What is the heat transfer rate out of the air?

d$)$ How close were your guess of the boost? Did you get the right density? If not, refine your guess on the boost and recalculate until you are close on the density. Now read off the efficiency and RPM of the compressor needed to obtain the needed boost. How much power is required to run the compressor?

e$)$ Now that we know what is going into the engine, run the Otto cycle calculation either by hand or using the ICE$\_$cycle.m Matlab code and determine the temperature and pressure of the gas exhausting out through the turbine. The problem here is that the exhaust temperature and pressure change with time during the exhaust process, so let's use an average value for each to calculate the turbine performance. Find the RPM and mass flow rate on the turbine map and determine the corresponding pressure ratio and turbine efficiency. Can the turbine handle this exhaust flow rate or with the waste gate need to be opened? What is the final temperature and pressure of the exhaust gas exiting the tailpipe?

f$)$ Now let's take this same turbocharger and see how effective it is at lower RPM$.$ What boost in HP does the turbocharger produce at full throttle at $3000$RPM$?$ How about at $1500$RPM$?$

Compressor Map for turbocharger selected. Note: $\backslash (11\backslash$mathrm$\{$~b$\}/\backslash$mathrm$\{$min$\}=0\mathrm{.}00756\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Also note solid lines are in RPM not $\backslash (\backslash$mathrm$\{$N$\}/\backslash$mathrm$\{$T$\}^\{\backslash$wedge$\}0\mathrm{.}5\backslash )$ and the contour lines are of compressor efficiency. Finally, the air flow is not normalized in this map it is in $\backslash (1\backslash$mathrm$\{$~b$\}/\backslash$mathrm$\{$min$\}\backslash ).$ Turbine Flow Map $-$ Note this data has been corrected$/$normalized as we did in class with the temperature and pressure entering the tubing $($state $3$ in this diagram$).$ The contour lines are of turbine fractional efficiency $($not percentage$).$