Calculating Temperature of Fuel-Air Mixture

[dboozer]

Homework Statement

In many spark-ignition engines, liquid fuel is added to the inlet air upstream of the inlet manifold above the throttle. The inlet manifold is heated to ensure that under steady-state conditions the fuel is vaporized before the mixture enters the cylinder.

At normal wide-open throttle operating conditions, in a four-stroke cycle 1.6 L (Vd) displacement four-cylinder engine, at 2500 rpm (N), the temperature of the air entering the carburetor is 40C. The heat of vaporization of the fuel in 350 kJ/kg and the rate of heat transfer to the intake mixture is 1.4 kW. Estimate the temperature of the inlet mixture as it passes through the inlet valve, assuming that the fuel is fully vaporized. The volumetric efficiency is 0.85. The air density is 1.06 kg/m^3 and cp for air is 1 kJ/kgK. You may neglect the effects of the heat capacity of the liquid and vapor fuel.

Homework Equations

Volumetric Efficiency: Ratio of the mass of air inducted into the cylinders to the mass of ambient air
$\eta_v =\frac{m_a}{\rho_a V_d}=\frac{2 \dot{m_a}}{\rho_a V_d N}$

Rate of Heat Transfer
$\dot{Q} = \dot{m} c \Delta T$

The Attempt at a Solution

Not 100% sure where to start.

Calculating the mass of air inducted into the cylinders is straightforward... I'm just not sure how to tie it all together.

 

[dboozer]

The mass of air inducted into the cylinders is

0.85(1.06 kg/m^3)(1.6 L)(1 m^3/1000 L)(1000 g/kg) = 1.44 g

 

[dboozer]

Since

$\dot{Q}_{air}=c_p \dot{m}_a \Delta T=c_p m_a \Delta T (\frac{N}{2})$,

You can calculate the change in temperature of the air to be

$\Delta T = 46.62 C$

and thus the final temperature of the air is 86.62 C.

The problem says you can neglect the effects of the heat capacity of the liquid and vapor fuel, but how do I take the temperature of the fuel into account for the temperature of the mix?

 

[dboozer]

No one has any input or ideas? Surely there's someone who can help me!

 

[dboozer]

A friend helped me out earlier...

The fuel-air mixture is traveling through the inlet manifold toward the engine. The inlet manifold is heated so as to vaporize the fuel.

Assuming an equivalence ratio of 0.8 and a stoichiometric A/F of 14.4, one can calculate the mass of the fuel mixed with the air. Know the specific heat of vaporization of the fuel allows us to determine how much energy was absorbed by the fuel to vaporize. The rest of the energy was absorbed by the air.

The 86.62 C calculated before is the maximum value of the air during this process and assumes no fuel in the mix.