$4.$ Eliminating the Throttle in a Diesel Engine $(30$ points$)$

By direct injecting a Diesel engine it is possible to eliminate the throttle completely and simply reduce the mass of Diesel fuel injected. This effectively runs the engine globally lean, but locally rich near the location of the fuel injector. Let's see what type of benefit this produces. Assume the engine is a $3$L V$6$ Diesel engine running at $2000$RPM$.$ The air coming into the throttling valve is at atmospheric pressure, $\backslash (\backslash$mathrm$\{$p$\}=100\backslash$mathrm$\{$kPa$\}\backslash ).$ At these settings, the volume flow rate of air into the engine is $\backslash (0\mathrm{.}5\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash ).$

i$)$ If the intake manifold ahead of the throttling valve has a cross sectional area of $\backslash (\mathrm{.}002\backslash$mathrm$\{$~m$\}^\{2\}\backslash ),$ what is the velocity of air entering the throttling valve?

j$)$ If the density of the air is $\backslash (1\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash )$ and the viscosity is $\backslash (1\backslash$times $10^\{-6\}\backslash$mathrm$\{$~Pa$\}-\backslash$mathrm$\{$s$\}\backslash ),$ what is the Reynolds number of the flow in the pipe just ahead of the throttling valve? Is it turbulent?

k$)$ While cruising on the highway, the throttling valve is mostly closed resulting in a loss coefficient is $\backslash ($ K$\_\{$L$\}=250\backslash ).$ What is the pressure drop across the throttling valve $($in kPa $)?$

$1)$ If the temperature is constant across the throttling valve, what is the density across the throttling valve? What fraction of the maximum power is the engine running at$?$

m $)$ If the exhaust pressure is atmospheric, how much power is lost to pumping costs $($give result both in kW and in pMEP $)?$

n$)$ Now let's remove the throttling valve and direct inject the engine. How much power do you save? If the engine iMEP $=20$atm, what is the percent increase in engine power getting to the wheel? $-$ IC

K

$($b$)$

Throttling valve Straight Pipe